Using SPSS version 14 Joel Elliott, Jennifer Burnaford, Stacey Weiss


 Stephanie Lane
 1 years ago
 Views:
Transcription
1 Using SPSS version 14 Joel Elliott, Jennifer Burnaford, Stacey Weiss SPSS is a program that is very easy to learn and is also very powerful. This manual is designed to introduce you to the program however, it is not supposed to cover every single aspect of SPSS. There will be situations in which you need to use the SPSS Help Menu or Tutorial to learn how to perform tasks which are not detailed in here. You should turn to those resources any time you have questions. The following document provides some examples of common statistical tests used in Ecology. To decide which test to use, consult your class notes, your Statistical Roadmap or the Statistics Coach (under Help menu in SPSS). Data entry p. 2 Descriptive statistics p. 4 Examining assumptions of parametric statistics Test for normality p. 5 Test for homogeneity of variances p. 6 Transformations p. 7 Comparative Statistics 1: Comparing means among groups Comparing two groups using parametric statistics Twosample ttest p. 8 Paired Ttest p. 10 Comparing two groups using nonparametric statistics Mann Whitney U test p. 11 Comparing three or more groups using parametric statistics Oneway ANOVA and posthoc tests p. 13 Comparing three or more groups using nonparametric statistics KruskalWallis test p. 15 For studies with two independent variables Twoway ANOVA p. 17 ANCOVA p. 20 Comparative Statistics 2: Comparing frequencies of events Chi Square Goodness of Fit p. 23 Chi Square Test of Independence p. 24 Comparative Statistics 3: Relationships among continuous variables Correlation (no causation implied) p. 26 Regression (causation implied) p. 27 Graphing your data Simple bar graph p. 30 Clustered bar graph p. 31 Box plot p. 32 Scatter plot p. 32 Printing from SPSS p. 33
2 Start SPSS and when the first box appears for What would you like to do? click the button for Type in data. A spreadsheet will appear. The setup here is similar to Excel, but at the bottom of the window you will notice two tabs. One is Data View. The other is Variable View. To enter your data, you will need to switch back and forth between these pages by clicking on the tabs.!" # $ % % Suppose you are part of a biodiversity survey group working in the Galapagos Islands and you are studying marine iguanas. After visiting a couple of islands you think that there may be higher densities of iguanas on island A than on island B. To examine this hypothesis, you decide to quantify the population densities of the iguanas on each island. You take 20 transects (100 m 2 ) on each island (A and B), counting the number of iguanas in each transect. Your data are shown below. A B First define the variables to be used. Go to Variable View of the SPSS Data Editor window as shown below. The first column (Name) is where you name your variables. For example, you might name one Location (you have 2 locations in your data set, Island A and Island B). You might name the other one Density (this is your response variable, number of iguanas). Other important columns are the Type, Label, Values, and Measure. o For now, we will keep Type as Numeric but look to see what your options are. At some point in the future, you may need to use one of these options. o The Label column is very helpful. Here, you can expand the description of your variable name. In the Name column you are restricted by the number & type of characters you can use. In the Label column, there are no such restrictions. Type in labels for your iguana data. o In the Values column, you can assign numbers to represent the different locations (so Island A will be 1 and Island B will 2 ). To do this, you need to assign Values to your categorical explanatory variable. Click on the cell in the Values column, and click on the that shows up. A dialog box will appear as below. Type in 1 in the value cell and A in the value label cell, and then hit Add. Type in 2 in the value cell and B in the value label cell. Hit Add again. Then Hit OK.
3 o In the Measure column, you can tell the computer what type of variables these are. In this example, island is a categorical variable. So in the Location row, go to the measure column (the far right) and click on the cell. There are 3 choices for variable types. You want to pick Nominal. Iguana density is a continuous variable... since scale (meaning continuous) is the default condition, you don t need to change anything. Now switch to the Data View. You will see that your columns are now titled Location and Density. To make the value labels appear in the spreadsheet pull down the View menu and choose Value Labels. The labels will appear as you start to enter data. You can now enter your data in the columns. Each row is a single observation. Since you have chosen View Value Labels and entered your Location value labels in the Variable View window, when you type 1 in the Location column, the letter A will appear. After you ve entered all the values for Island A, enter the ones from Island B below them. The top of your data table will eventually look like this: &
4 $ ( %!) * ( + ", " $  Once you have the data entered, you want to summarize the trends in the data. There a variety of statistical measures for summarizing your data, and you want to explore your data by making tables and graphs. To help you do this you can use the Statistics Coach found under the Help menu in SPSS, or you can go directly to the Analyze menu and choose the appropriate tests. To get a quick view of what your data look like: Pull down the Analyze menu and choose Descriptive statistics, then Frequencies. A new window will appear. Put the Density variable in the box, then choose the statistics that you want to use to explore your data by the clicking on the Statistics and Charts buttons at the bottom of the box (e.g., mean, median, mode, standard deviation, skewness, kurtosis). This will produce summary statistics for the whole data set. Your results will show up in a new window. SPSS can also produce statistics and plots for each of the islands separately. To do this, you need to split the file. Pull down the Data menu and choose Split File. Click on Organize output by groups and then select the Island [Location] variable as shown below. Click OK. Now, if you repeat the Analyze Descriptive statistics Frequencies steps and hit Okay again, your output will now be similar to the following for each Island. Statistics(a) Statistics(b) Density N Valid 20 Missing 0 Mean Median Mode Std. Deviation Variance Skewness Std. Error of Skewness.512 Kurtosis Std. Error of Kurtosis.992 Range 6.00 Minimum Maximum a Island = A Density N Valid 20 Missing 0 Mean Median Mode 15.00(a) Std. Deviation Variance Skewness.475 Std. Error of Skewness.512 Kurtosis Std. Error of Kurtosis.992 Range Minimum 9.00 Maximum a Multiple modes exist. The smallest value is shown b Island = B '
5 Histogram Histogram Island: A Island: B Frequency 4 3 Frequency Density Mean = Std. Dev. = N = Density Mean = Std. Dev. = N = 20 From these summary statistics you can see that the mean density of iguanas on Island A is smaller than that on Island B. Also, the variation patterns of the data are different on the two islands as shown by the frequency distributions of the data and their different dispersion parameters. In each histogram, the normal curve indicates the expected frequency curve for a normal distribution with the same mean and standard deviation as your data. The range of data values for Island A is lower with a lower variance and kurtosis. Also, the distribution of Island A is skewed to the left whereas the data for Island B is skewed to the right. You could explore your data more by making box plots, stemleaf plots, and error bar charts. Use the functions under the Analyze and Graphs menus to do this. After getting an impression of what your data look like you can now move on to determine whether there is a significant difference between the mean densities of iguanas on the two islands. To do this we have to use comparative statistics. NOTE: Once you are done looking at your data for the two islands separately, you need to unsplit the data. Go to Data Split File and select Analyze all cases, do not create groups. #  $ $ As you know, parametric tests have two main assumptions: 1) approximately normally distributed data, and 2) homogeneous variances among groups. Let s examine each of these assumptions. Before you conduct any parametric tests you need to check that the data values come from an approximately normal distribution. To do this, you can compare the frequency distribution of your data values with those of a normalized version of these values (See Descriptive Statistics section above). If the data are approximately normal, then the distributions should be similar. From your initial descriptive data analysis you know that the distributions of data for Island A and B did not appear to fit an expected normal distribution perfectly. However, to objectively determine whether the distribution varies significantly from a normal distribution you have to conduct a normality test. This test will provide you with a statistic that determines whether your data are.
6 significantly different from normal. The null hypothesis is that the distribution on your data is NOT different from a normal distribution. For the marine iguana example, you want to know if the data from Island A population are normally distributed and if the data from Island B are normally distributed. Thus, your data must be split. (Data Split File Organize output by groups split by Location) Don t forget to unsplit when you are done! To conduct a statistical test for normality on your split data, go to Analyze Nonparametric Tests 1 Sample KS. In the window that appears, put the response variable (in this case, Density) variable into the box on the right. Click Normal in the Test Distribution check box below. Then click OK. A output shows a KomolgorovSmirnov (KS) table for the data from each island. Your pvalue is the last line of the table: Asymp. Sig. (2tailed). If p>0.05 (i.e., there a greater than 5% chance that your null hypothesis is true), you should conclude that the distribution of your data is not significantly different from a normal distribution. If p<0.05 (i.e., there is a less than 5% chance that your null hypothesis is true), you should conclude that the distribution of your data is significantly different from normal. Note: always look at the pvalue. Don t trust the test distribution is normal note below sometimes that lies. If your data are not normal, you should inspect them for outliers which can have a strong effect on this test. Remove the extreme outliers and try again. If this does not work, then you must either transform your data so that they are normally distributed, or use a nonparametric test. Both of these options are discussed later. OneSample KolmogorovSmirnov Test(c) Density N 20 Normal Mean Parameters(a,b) Std. Deviation Most Extreme Absolute.218 Differences Positive.132 Negative KolmogorovSmirnov Z.975 Asymp. Sig. (2tailed).298 a Test distribution is Normal. b Calculated from data. c Island = A OneSample KolmogorovSmirnov Test(c) Density N 20 Normal Mean Parameters(a,b) Std. Deviation Most Extreme Absolute.166 Differences Positive.166 Negative KolmogorovSmirnov Z.740 Asymp. Sig. (2tailed).644 a Test distribution is Normal. b Calculated from data. c Island = B For the iguana example, you should find that the data for both populations are not significantly different from normal (p > 0.05). With a sample size of only N=20 the data would have to be skewed much more or have some large outliers to vary significantly from normal. If your data are not normally distributed, you should try to transform the data to meet this important assumption. (See below.)  ( Another assumption of parametric tests is that the variances of each of the groups that you are comparing have relatively similar variances. Most of the comparative tests in SPSS will do this test /
7 for you as part of the analysis. For example, when you run a ttest, the output will include columns labeled Levene s test for Equality of Variances. The pvalue is labeled Sig. and will tell you whether or not your data meet the assumption of parametric statistics. If the variances are not homogeneous, then you must either transform your data (e.g., using a log transformation) to see if you can equalize the variances, or you can use a nonparametric comparison test that does not require this assumption.  " " " "  $ 1 If your data do not meet one or both of the above assumptions of parametric statistics, you may be able to transform the data so that they do. You can use a variety of transformations to try and make the variances of the different groups equal or normalize the data. If the transformed data meet the assumptions of parametric statistics, you may proceed by running the appropriate test on the transformed data. If, after a number of attempts, the transformed data do not meet the assumptions of parametric statistics, you must run a nonparametric test. If the variances were not homogeneous, look at how the variances change with the mean. The usual case is that larger means have larger variances. If this is the case, a transformation such as common log, natural log or square root often makes the variances homogeneous. Whenever your data are percents (e.g., % cover) they will generally not be normally distributed. To make percent data normal, you should do an arcsinesquare root transformation of the percent data (percents/100). To transform your data: Go to Transform Compute. You will get the Compute Variable window. In the Target Variable box, you want to name your new transformed variable (for example, Log_Density ). There are 3 ways you can transform your data. 1) using the calculator, 2) choosing functions from lists on the right, or 3) typing the transformation in the Numeric Expression box. For this example: In the Function Group box on the right, highlight Arithmetic by clicking on it once. Various functions will show up in the Functions and Special Variables box below. Choose the LG10 function. Double click on it. In the Numeric Expression box, it will now say LG10[?]. Doubleclick on the name of the variable you want to transform (e.g., Density) in the box on the lower left to make Density replace the?. Click Ok. SPSS will create a new column in your data sheet that has logvalues of the iguana densities. NOTE: you might want to do a transformation such as LN (x + 1). Follow the directions as above but choose LN instead of LG10 from the Functions and Special Variables box. Move your variable in the parentheses to replace the?. Then type in +1 after your variable so it reads, for example, LN[Density+1]. NOTE: for the arcsinesquare root transformation, the composite function to be put into the Numeric Expression box would look like: arcsin(sqrt(percent data/100)). 0
8 After your transform your data, redo the tests of normality and homogeneity of variances to see if the transformed data now meet the assumptions of parametric statistics. Again, if your data now meet the assumptions of the parametric test, conduct a parametric statistical test using the transformed data. If the transformed data still do not meet the assumption, you can do a nonparametric test instead, such as a MannWhitney U test on the original data. This test is described later in this handout. $ ( % % $ $ $ + $ $ % + $ 3 $ " + $ This test compares the means from two groups, such as the density data for the two different iguana populations. To run a twosample ttest on the data: First, be sure that your data are unsplit. (Data Split File Analyze all cases, do not create groups.) Then, go to Analyze Compare Means Independent Samples Ttest. Put the Density variable in the Test Variable(s) box and the Location variable in the Grouping Variable box as shown below. Now, click on the Define Groups button and put in the names of the groups in each box as shown below. The click Continue and OK. 2
9 The output consists of two tables Group Statistics Density Island N Mean Std. Deviation Std. Error Mean A B Density Equal variances assumed Equal variances not assumed Levene's Test for Equality of Variances F Sig. Independent Samples Test t df Sig. (2tailed) ttest for Equality of Means Mean Difference 95% Confidence Interval of the Std. Error Difference Difference Lower Upper The first table shows the means and variances of the two groups. The second table shows the results of the Levene s Test for Equality of Variances, the tvalue of the ttest, the degrees of freedom of the test, and the pvalue which is labeled Sig. (2tailed). Before you look at the results of the ttest, you need to make sure your data fit the assumption of homogeneity of variances. Look at the columns labeled Levene s test for Equality of Variances. The pvalue is labeled Sig.. In this example the data fail the Levene s Test for Equality of Variances, so the data will have to be transformed in order to see if we can get it to meet this assumption of the ttest. If you logtransformed the data and reran the test, you d get the following output. Group Statistics Island N Mean Std. Deviation Std. Error Mean Log_Density A B Independent Samples Test Log_Density Equal variances assumed Equal variances not assumed Levene's Test for Equality of Variances F Sig. t df Sig. (2tailed) ttest for Equality of Means Mean Difference 95% Confidence Interval of the Std. Error Difference Difference Lower Upper Now the variances of the two groups are not significantly different from each other (p =0.112) and you can focus on the results of the ttest. For the ttest, p=0.015 (which is <0.05) so you can conclude that the two means are significantly different from each other. Thus, this statistical test provides strong support for your original hypothesis that the iguana densities varied significantly between Island A and Island B. 4
10 WHAT TO REPORT: Following a statement that describes the patterns in the data, you should parenthetically report the tvalue, df, and p. For example: Iguanas are significantly more dense on Island B than on Island A (t=2.5, df=38, p<0.05). " You should analyze your data with a paired ttest only if you paired your samples during data collection. This analysis tests to see if the mean difference between samples in a pair is = 0. The null hypothesis is that the difference is not different from zero. For example, you may have done a study in which you investigated the effect of light intensity on the growth of the plant Plantus speciesus. You took cuttings from source plants and for each source plant, you grew 1 cutting in a high light environment and 1 cutting in a lowlight environment. The other conditions were kept constant between the groups. You measured growth by counting the number of new leaves grown over the course of your experiment. Your data look like this: Plant Low Light High Light Enter your data in 2 columns named Low and High. Each row in the spreadsheet should have a pair of data. In Variable View, leave the Measure column on Scale. Leave Values as None. Go to Analyze Compare Means Paired Samples Ttest. Highlight both of your variables and hit the arrow to put them in the PairedVariables box. They will show up as LowHigh. Hit OK. The following output should be produced. The output consists of 3 tables Paired Samples Statistics Pair 1 Low Light High Light Std. Error Mean N Std. Deviation Mean Paired Samples Correlations Pair 1 Low Light & High Light N Correlation Sig Pair 1 Low Light  High Light Paired Samples Test Paired Differences 95% Confidence Interval of the Std. Error Difference Mean Std. Deviation Mean Lower Upper t df Sig. (2tailed)
11 The first table shows the summary statistics for the 2 groups. The second table shows information that you can ignore. The third table, the Paired Samples Test table, is the one you want. It shows the mean difference between samples in a pair, the variation of the differences around the mean, your tvalue, your df, and your pvalue (labeled as Sig (2tailed)). In this case, the Pvalue reads 0.000, which means that it is very low it is smaller than the program will show in the default 3 decimal places. You can express this in your results section as p< WHAT TO REPORT: Following a statement that describes the patterns in the data, you should parenthetically report the tvalue, df, and p. For example: Plants in the high light treatment added significantly more leaves than their counterpart plants in the low light treatment (t=6.3, df=9, p<0.001). $ + $ $ $ %67 The ttest is a parametric test, meaning that it assumes that the sample mean is a valid measure of center. While the mean is valid when the distance between all scale values is equal, it's a problem when your test variable is ordinal because in ordinal scales the distances between the values are arbitrary. Furthermore, because the variance is calculated using squared deviations from the mean, it too is invalid if those distances are arbitrary. Finally, even if the mean is a valid measure of center, the distribution of the test variable may be so nonnormal that it makes you suspicious of any test that assumes normality. If any of these circumstances is true for your analysis, you should consider using the nonparametric procedures designed to test for the significance of the difference between two groups. They are called nonparametric because they make no assumptions about the parameters of a distribution, nor do they assume that any particular distribution is being used. A MannWhitney U test doesn t require normality or homogeneous variances, but it is slightly less powerful than the ttest (which means the MannWhitney U test is less likely to show a significant difference between your two groups). So, if you have approximately normal data, then you should use a ttest. To run a MannWhitney U test: Go to Analyze Nonparametric tests 2 Independent samples and a dialog box will appear. Put the variables in the appropriate boxes, define your groups, and confirm that the Mann Whitney U test type is checked. Then click OK.
12 The output consists of two tables. The first table shows the parameters used in the calculation of the test. The second table shows the statistical significance of the test. The value of the U statistic is given in the 1 st row ( MannWhitney U ). The pvalue is labeled as Asymp. Sig. (2 tailed). Ranks Density Island N Mean Rank Sum of Ranks A B Total 40 Test Statistics(b) Density MannWhitney U Wilcoxon W Z Asymp. Sig. ( tailed) Exact Sig. [2*(1.003(a) tailed Sig.)] a Not corrected for ties. b Grouping Variable: Island In the table above (for the marine iguana data), the pvalue = 0.003, which means that the densities of iguanas on the two islands are significantly different from each other (p < 0.05). So, again this statistical test provides strong support for your original hypothesis that the iguana densities are significantly different between the islands. WHAT TO REPORT: Following a statement that describes the patterns in the data, you should parenthetically report the Uvalue, df, and p. For example: Iguanas are significantly more dense on Island B than on Island A (U=91.5, df=39, p<0.01). $  $ $ $ % % + +! 8!"  Let s now consider parametric statistics that compare three or more groups of data. To continue the example using iguana population density data, let s add data from a series of 16 transects from a third island, Island C. Enter these data into your spreadsheet at the bottom of the column Density. Density (100 m 2 ) Island C: To enter the Location for Island C, you must first edit the Value labels by going to Variable View: add a third Value (3) and Value label (C). Then, back on Data View, type a 3 into the last cell of the Location column, and copy the C and paste it into the rest of the cells below. The appropriate parametric statistical test for continuous data with one independent variable and more than two groups is the Oneway analysis of variance (ANOVA). It tests whether there is a
13 significant difference among the means of the groups, but does not tell you which means are different from each other. In order to find out which means are significantly different from each other, you have to conduct posthoc paired comparisons. They are called posthoc, because you conduct the tests after you have completed an ANOVA and it shows where significant differences lie among the groups. One of the Posthoc tests is the Fisher PLSD (Protected Least Sig. Difference) test, which gives you a test of all pairwise combinations. To run the ANOVA test: Go to Analyze Compare Means Oneway ANOVA. In the dialog box put the Density variable in the Dependent List box and the Location variable in the Factor box. Click on the Post Hoc button and then click on the LSD check box and then click Continue. Click on the Options button and check 2 boxes: Descriptive and Homogeneity of variance test. Then click Continue and then OK. The output will include four tables Descriptive statistics, results of the Levene test, the results of the ANOVA, and the results of the posthoc tests. The first table gives you some basic descriptive statistics for the three islands. Descriptives Density A B C Total 95% Confidence Interval for Mean N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum The second table gives you the results of the Levene Test (which examines the assumption of homogeneity of variances). You must assess the results of this test before looking at the results of your ANOVA. Density Test of Homogeneity of Variances Levene Statistic df1 df2 Sig & &
14 In this case, your variances are not homogeneous (p<0.05), the data do not meet one of the assumptions of the test. Thus, and you cannot proceed to using the results of the ANOVA comparisons of means. You have two main choices of what to do. You can either transform your data to attempt to make the variances homogeneous or you may run a test that does not require homogeneity of variances (a nonparametric test like Welch s Test for three or more groups). First, try transforming the data for each population (try a log transformation), and then run the test again. The following tables are for the log transformed data. Log_Density A B C Total Descriptives 95% Confidence Interval for Mean N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum Test of Homogeneity of Variances Log_Density Levene Statistic df1 df2 Sig Now your variances are homogeneous (p>0.05), and you can continue with the assessment of the ANOVA. The third table gives you the results of the ANOVA test, which examined whether there were any significant differences in mean density among the three island populations of marine iguanas. ANOVA Log_Density Between Groups Within Groups Total Sum of Squares df Mean Square F Sig Look at the pvalue in the ANOVA table ( Sig. ). If this pvalue is > 0.05, then there are no significant differences among any of the means. If the pvalue is < 0.05, then at least one mean is significantly different from the others. In this example, p = 0.01 in the ANOVA table, and thus p < 0.05, so the mean densities are significantly different. Now that you know the means are different, you want to find out which pairs of means are different from each other. e.g., is the density on Island A greater than B? Is it greater than C? How do B & C compare with each other? The Post Hoc tests, Fisher LSD (Least Sig. Difference), allow you to examine all pairwise comparisons of means. The results are listed in the fourth table. Which groups are and are not significantly different from each other? Look at the Sig. column for each comparison. B is different from both A and C, but A and C are not different from each other. ' '
15 Multiple Comparisons Dependent Variable: Log_Density LSD (I) Island A B C (J) Island B C A C A B Mean Difference 95% Confidence Interval (IJ) Std. Error Sig. Lower Bound Upper Bound * * * * *. The mean difference is significant at the.05 level. WHAT TO REPORT: Following a statement that describes the general patterns in the data, you should parenthetically report the Fvalue, df, and p from the ANOVA. Following statements that describe the differences between specific groups, you should report the pvalue from the posthoc test only. (NOTE: there is no Fvalue or df associated with the posthoc tests only a pvalue!) For example: Iguana density varies significantly across the three islands (F=5.0, df=2,53, p=0.01). Iguana populations on Island B are significantly more dense than on Island A (p<0.01) and on Island C (p=0.01), but populations on Islands A and C have similar densities (p>0.90). $  $ $ $ % 9 * Like a MannWhitney U test was a nonparametric version of a ttest, a KruskalWallis test is the nonparametric version of an ANOVA. The test is used when you want to compare three or more groups of data, and those data do not fit the assumptions of parametric statistics even after attempting standard transformations. Remind yourself of the assumptions of parametric statistics and the downside of using nonparametric statistics by reviewing the information on Page 11. To run the KruskalWallis test: Go to Analyze Nonparametric Tests K Independent Samples. Note: Remember for the MannWhitney U test, you went to Nonparametric tests 2 Independent Samples. Now you have more than 2 groups, so you go to K Independent Samples instead, where K is just standing in for any number or more than 2. Put your variables in the appropriate boxes, define your groups, and be sure KruskalWallis box is clicked on in the Test Type box. Click OK...
16 The output consists of two tables. The first table shows the parameters used in the calculation of the test. The second table shows you the statistical results of the test. As you will see, the test statistic that gets calculated is a chisquare value and it is reported in the first row of the second table. The pvalue is labeled as Asymp. Sig. (2tailed). Ranks density Location A B C Total N Mean Rank Test Statistics(a,b) density ChiSquare df 2 Asymp. Sig..004 a Kruskal Wallis Test b Grouping Variable: Location In the table above, the pvalue = 0.004, which means that the densities on the three islands are significantly different from each other (p < 0.01). So, this test also supports the hypothesis that iguana densities differ among islands. We do not yet know which islands are different from which other ones. Unlike an ANOVA, a KruskalWallis test does not have an easy way to do posthoc analyses. So, if you have a significant effect for the overall KruskalWallis, you can follow that up with a series of twogroup comparisons using MannWhitney U tests. In this case, we would follow up the KruskalWallis with three MannWhitney U tests: Island A vs. Island B, Island B vs. Island C, and Island C vs. Island A. WHAT TO REPORT: Following a statement that describes that general patterns in the data, you should parenthetically report the chisquare value, df, and p. For example: Iguana density varied significantly across the three islands ( 2 =11.3, df=2, p=0.004). : " " $ " (, % + + +! 8!3! 8! In many studies, researchers are interested in examining the effect of >1 independent variable (i.e., factors ) on a given dependent variable. For example, say you want to know whether the bill size of finches is different between males and females of two different species. In this example, you / /
17 have two factors (Species and Sex) and both are categorical. They can be examined simultaneously in a Twoway ANOVA, a parametric statistical test. The twoway ANOVA will also tell you whether the two factors have joint effects on the dependent variable (bill size), or whether they act independently of each other (i.e., does bill size depend on sex in one species but not in the other species?). What if we wanted to know, for a single species, how sex and body size affect bill size? We still have two factors, but now one of the factors is categorical (Sex) and one is continuous (Body Size). In this case, we need to use an ANCOVA an analysis of covariance. Both tests require that the data are normally distributed and all of the groups have homogeneous variances. So you need to check these assumptions first. If you want to compare means from two (or more) grouping variables simultaneously, as ANOVA and ANCOVA do, there is no satisfactory nonparametric alternative. So you may need to transform your data. +! 8! Enter the data as shown to the right: The two factors (Species and Sex) are put in two separate columns. The dependent variable (Bill length) is entered in a third column. Before you run a twoway ANOVA, you might want to first run a ttest on bill size just between species, then a ttest on bill size just between sexes. Note the results. Do you think these results accurately represent the data? This exercise will show you how useful a twoway ANOVA can be in telling you more about the patterns in your data. Now run a twoway ANOVA on the same data. The procedure is much the same as for a Oneway ANOVA with one added step to include the second variable to the analysis. Go to Analyze General Linear Model Univariate. A dialog box appears as below. Your dependent variable goes in the Dependent Variable box. Your explanatory variables are Fixed Factors Now click Options. A new window will appear. Click on the check boxes for Descriptive 0 0
18 Statistics and Homogeneity tests, then click Continue. Click OK. The output will consist of three tables which show descriptive statistics, the results of the Levene s test and the results of the 2way ANOVA. From the descriptive statistics, it appears that the means may be different between the sexes and also different between species. Dependent Variable: Bill size Sex Female Male Total Species Species A Species B Total Species A Species B Total Species A Species B Total Descriptive Statistics Mean Std. Deviation N From this second table, you know that your data meet the assumption of homogeneity of variance. So, you are all clear to interpret the results of your 2way ANOVA. Levene's Test of Equality of Error Variances a Dependent Variable: Bill size F df1 df2 Sig Tests the null hypothesis that the error variance of the dependent variable is equal across groups. a. Design: Intercept+Sex+Species+Sex * Species 2 2
19 The ANOVA table shows the statistical significance of the differences among the means for each of the independent variables (i.e., factors or main effects. Here, they are Sex and Species) and the interaction between the two factors (i.e., Sex * Species). Let s walk through how to interpret this information Dependent Variable: Bill size Source Corrected Model Intercept Sex Species Sex * Species Error Total Corrected Total Tests of BetweenSubjects Effects Type III Sum of Squares df Mean Square F Sig a a. R Squared =.870 (Adjusted R Squared =.845) Always look at the interaction term FIRST. The pvalue of the interaction term tells you the probability that the two factors act independently of each other and that different combinations of the variables have different effects. In this billsize example, the interaction term shows a significant sex*species interaction (p < 0.001). This means that the effect of sex on bill size differs between the two species. Simply looking at sex or species on their own won t tell you anything. To get a better idea of what the interaction term means, make a Bar Chart with error bars. See the graphing section of the manual for instructions on how to do this. If you look at the data, the interaction should become apparent. In Species A, bills are larger in males than in females, but in Species B, bills are larger in females than in males. So simply looking at sex doesn t tell us anything (as you saw when you did the ttest) and neither sex has a consistently larger bill when considered across both species. The main effects terms in a 2way ANOVA basically ignore the interaction term and give similar results to the ttests you may have performed earlier. So, the pvalue associated with each independent variable (i.e., factor or main effect) tells you the probability that the means of the different groups of that variable are the same. So, if p < 0.05, the groups of that variable are significantly different from each other. In this case, it tests whether males and females are different from each other disregarding the fact that we have males and females from two different species in our data set. And it tests whether the two species are different from each other disregarding the fact that we have males and females from each species in our data set. 4 4
20 The twoway ANOVA found that species was significant if you ignore the interaction. This suggests that species A has larger bills overall, mainly because of the large size of the males of Species A, but does not always have larger bills because bill size also depends gender. WHAT TO REPORT: If there is a significant interaction term, the significance of the main effects cannot be fully accepted because of differences in the trends among different combinations of the variables. Thus, you only need to tell your reader about the interaction term of the ANOVA table. Describe the pattern and parenthetically report the appropriate Fvalue, df, and p). For example: The way that sex affected bill size was different for the two different species (F=95.6, df=1,16, p<0.001). (Often, a result like this would be followed up with two separate ttests.) If the interaction term is not significant, then the statistical results for the main effects can be fully recognized. In this case, you need to tell your reader about the interaction term and about each main effect term of the ANOVA table. Following a statement that describes the general patterns for each of these terms, you should parenthetically report the appropriate Fvalue, df, and p. For example: Growth rates of the both invasive and native grass species were significantly higher at low population densities than at high population densities (F=107.1, df=1,36, p<0.001). However, the invasive grass grew significantly faster than the native grass at both populations densities (F=89.7, df=1,36, p<0.001). There is no interaction between grass species and population densities on growth rate (F=1.2, df=1,36, p>0.20).! 8! Remember, ANCOVA is used when you have 2 or more independent variables that are a mixture of categorical and continuous variables. Our example here is a study investigating the effect of gender (categorical) and body size (continuous) on bill size in a species of bird. Your data must be normally distributed and have homogeneous variances to use this parametric statistical test. Enter the data as shown to the right: The two factors (Species and Body Size) are put in two separate columns. The dependent variable (Bill size) is entered in a third column. To run the ANCOVA: Go to Analyze General Linear Model Univariate as you did for the twoway ANOVA. Put your dependent variable in the Dependent Variable box. Put your categorical explanatory variable in the Fixed Factor(s) box. Put your continuous explanatory variable in the Covariate(s) box. Click on Options. A new window will appear. Click on the check boxes for Descriptive Statistics and Homogeneity tests, then click Continue. Click on Model. A new window will appear. At the top middle of the popup window, specify the model as Custom instead of Full factorial. Highlight one of the factors shown on the left side of the popup window 5
21 (under Factors & Covariates ) and click the arrow button. That variable should now show up on the right side (under Model ). Do the same with the second factor. Now, highlight the two factors on the right simultaneously and click the arrow, making sure the option is set to interaction. In the end, your Model popup window should look something like the image below: Click Continue and then click OK. The output will consist of four tables which show the categorical ( betweensubjects ) variable groupings, some descriptive statistics, the results of the Levene s test and the results of the ANCOVA. From the first and second table, it appears that males and females have similarly sized bills. BetweenSubjects Factors sex Value Label N 1.00 male female 8 Descriptive Statistics Dependent Variable: bill_size sex Mean Std. Deviation N male female Total From the third table, you know that the data meet the assumption of homogeneity of variance. So, you are clear to interpret the results of the ANCOVA (assuming your data are normal ). Levene's Test of Equality of Error Variances(a) Dependent Variable: bill_size F df1 df2 Sig Tests the null hypothesis that the error variance of the dependent variable is equal across groups. a Design: Intercept+sex+body_size+sex * body_size The ANCOVA results are shown in an ANOVA table which is interpreted similar to the table from the twoway ANOVA. You can see the statistical results regarding the two independent
22 variables (factors) and the interaction between the two factors (i.e., Sex * Body_size) are shown on three separate rows of the table below. Dependent Variable: bill_size Tests of BetweenSubjects Effects Source Type III Sum of Squares df Mean Square F Sig. Corrected Model (a) Intercept sex body_size sex * body_size Error Total Corrected Total a R Squared =.862 (Adjusted R Squared =.827) As with the 2way ANOVA, you must interpret the interaction term FIRST. In this example, the interaction term shows up on the ANOVA table as a row labeled sex*body_size and it tells you whether or not the way that body size affects bill size is the same for males as it is for females. The null hypothesis is that body size does affect bill size the same for each of the two sexes. In other words, the null hypothesis is that the two factors (body size and sex) do not interact in the way they affect bill size. Here, you can see that the interaction term is not significant (p=0.649). Therefore, you can go on to interpret the two factors independently. You can see that there is no effect of Sex on bill size (p=0.525). And, you can see that there is an effect of Body Size on bill size (p<0.001). Let s see how this looks graphically. Make a scatterplot with the dependent variable (Bill Size) on the yaxis and the continuous independent variable (Body Size) on the xaxis. To make the Male and Female data show up as different shaped symbols on your graph, move the categorical independent variable (Sex) into the box labeled Style as shown below: sex male female bill_size body_size
23 From the figure you can see 1) that the way that body size affects bill size is the same for males as it is for females (i.e., there is no interaction between the two factors), that males and females do not differ in their mean bill size (there is clear overlap in the distributions of male and female bill sizes), and 3) that body size and bill size are related to each other (as body size increase, bill size also increases). WHAT TO REPORT: If there is a significant interaction term, the significance of the main effects cannot be fully accepted because of differences in the trends among different combinations of the variables. Thus, you only need to tell your reader about the interaction term from the ANOVA table. Describe the pattern and parenthetically report the appropriate Fvalue, df, and p). For example: The way that prey size affected energy intake rate was different for large and small fish (F=95.6, df=1,16, p<0.001). (Typically, a result like this would be followed up with two separate regressions (see pg. 27 below) one for large fish and one for small fish.) If the interaction term is not significant, then the statistical results for the main effects can be fully recognized. In this case, you need to tell your reader about the interaction term and about each main effect term of the ANOVA table. Following a statement that describes the general patterns for each of these terms, you should parenthetically report the appropriate Fvalue, df, and p. For example: Males and females have similar mean bill sizes (F=0.4, df=1,12, p>050), and for both sexes, bill size increases as body size increases (F=68.3, df=1,12, p<0.001). There is no interaction between gender and body size on bill size (F=0.2, df=1,12, p>0.60). $ ( % $ ) (  )! ; " : This test allows you to compare observed to expected values within a single group of test subjects. For example: Are guppies more likely to be found in predator or nonpredator areas? You are interested in whether predators influence guppy behavior. So you put guppies in a tank that is divided into a predatorfree refuge and an area with predators. The guppies can move between the two sides, but the predators can not. You count how many guppies were in the predator area and in the refuge after 5 minutes. Here are your data: number of guppies in predator area in refuge 4 16 Your null hypothesis for this test is that guppies are evenly distributed between the 2 areas. To perform the ChiSquare Goodness of fit test: &
24 Open a new data file in SPSS In Variable View, name the first variable Location. In the Measure column, choose Ordinal. Assign 2 values: one for Predator Area and one for Refuge. Then create a second variable called Guppies. In the Measure column, choose Scale. In Data View, enter the observed number of guppies in the 2 areas. Go to Data Weight Cases. In the window that pops up, click on Weight Cases by and select Guppies. Hit OK. Go to Analyze Nonparametric Tests Chisquare. Your test variable is Location. Under Expected Values click on Values. Enter the expected value for the refuge area first, hit add then enter the expected value for the predator area and hit add. Hit OK. In the Location Table, check the values to make sure the test did what you thought it was going to do. Are the observed and expected numbers for the 2 categories correct? Your ChiSquare value, df, and pvalue are displayed in the Test Statistics Table. NOTE: Once you are done with this analysis, you will likely want to stop weighting cases. Go to Data Weight Cases and select Do not weight cases. WHAT TO REPORT: You want to report the 2 value, df, and p, parenthetically, following a statement that describes the patterns in the data.  )! ; <" $ " If you have 2 different test subject groups, you can compare their responses to the independent variable. For example, you could ask the question: Do female guppies have the same response to predators as male guppies? The chisquare test of independence allows you to determine whether the response of your 2 groups (in this case, female & male guppies) is the same or is different. You are interested in whether male and female guppies have different responses to predators. So you test 10 male and 10 female guppies in tanks that are divided into a predatorfree refuge and an area with predators. Guppies can move between the areas predators can not. You count how many guppies were in the predator area and in the refuge after 5 minutes. Here are the data: number of guppies in predator area in refuge male guppies 1 9 female guppies 3 7 Your null hypothesis is that guppy gender does not affect response to predators or in other words, that there will be no difference in the response of male and female guppies to predators. Or in other words you predict that the effect of predators will not depend on guppy gender. To perform the test in SPSS: In Variable View, set up two variables: Gender and Location. Both are categorical, so they must be Nominal, and you need to set up Values. '
25 Enter your data in 2 columns. Each row is a single fish. Go to Analyze Descriptive Statistics Crosstabs. In the popup window, move one of your variables into the Rows window and the other one into the Column window. Click on the Statistics button on the bottom of the Crosstabs window, then click Chisquare in the new popup window. Click Continue, then Okay. Your output should look like this: Case Processing Summary Cases Valid Missing Total N Percent N Percent N Percent Gender * Location % 0.0% % Gender * Location Crosstabulation Location predators refuge Total Gender male female Total ChiSquare Tests Value df Asymp. Sig. (2 sided) Exact Sig. (2 sided) Exact Sig. (1 sided) Pearson ChiSquare 1.250(b) Continuity Correction(a) Likelihood Ratio Fisher's Exact Test LinearbyLinear Association N of Valid Cases 20 a Computed only for a 2x2 table b 2 cells (50.0%) have expected count less than 5. The minimum expected count is How to interpret your output: Ignore the 1st table. The second table (Gender*Location Crosstabulation) has your observed values for each category. You should check this table to make sure your data were entered correctly. In this example, the table correctly reflects that there were 10 of each type of fish, and that 1 male and 3 females were in the predator side of their respective tanks. In the 3rd table, look at the Pearson ChiSquare line. Your Chisquare value is 2 = Your pvalue is p = This suggests that the response to predators was not different between male and female guppies. WHAT TO REPORT: You want to report the 2 value, df, and p, parenthetically, following a statement that describes the patterns in the data. For example: Male and female guppies did not differ in their response to predators (chisquare test of independence, 2 =1.25, df=1, p>0.20)..
For example, enter the following data in three COLUMNS in a new View window.
Statistics with Statview  18 Paired ttest A paired ttest compares two groups of measurements when the data in the two groups are in some way paired between the groups (e.g., before and after on the
More informationSPSS Tests for Versions 9 to 13
SPSS Tests for Versions 9 to 13 Chapter 2 Descriptive Statistic (including median) Choose Analyze Descriptive statistics Frequencies... Click on variable(s) then press to move to into Variable(s): list
More informationA Guide for a Selection of SPSS Functions
A Guide for a Selection of SPSS Functions IBM SPSS Statistics 19 Compiled by Beth Gaedy, Math Specialist, Viterbo University  2012 Using documents prepared by Drs. Sheldon Lee, Marcus Saegrove, Jennifer
More informationSPSS Explore procedure
SPSS Explore procedure One useful function in SPSS is the Explore procedure, which will produce histograms, boxplots, stemandleaf plots and extensive descriptive statistics. To run the Explore procedure,
More informationChapter 5 Analysis of variance SPSS Analysis of variance
Chapter 5 Analysis of variance SPSS Analysis of variance Data file used: gss.sav How to get there: Analyze Compare Means Oneway ANOVA To test the null hypothesis that several population means are equal,
More informationModule 9: Nonparametric Tests. The Applied Research Center
Module 9: Nonparametric Tests The Applied Research Center Module 9 Overview } Nonparametric Tests } Parametric vs. Nonparametric Tests } Restrictions of Nonparametric Tests } OneSample ChiSquare Test
More informationSPSS for Exploratory Data Analysis Data used in this guide: studentp.sav (http://people.ysu.edu/~gchang/stat/studentp.sav)
Data used in this guide: studentp.sav (http://people.ysu.edu/~gchang/stat/studentp.sav) Organize and Display One Quantitative Variable (Descriptive Statistics, Boxplot & Histogram) 1. Move the mouse pointer
More information6 Comparison of differences between 2 groups: Student s Ttest, MannWhitney UTest, Paired Samples Ttest and Wilcoxon Test
6 Comparison of differences between 2 groups: Student s Ttest, MannWhitney UTest, Paired Samples Ttest and Wilcoxon Test Having finally arrived at the bottom of our decision tree, we are now going
More informationThe Dummy s Guide to Data Analysis Using SPSS
The Dummy s Guide to Data Analysis Using SPSS Mathematics 57 Scripps College Amy Gamble April, 2001 Amy Gamble 4/30/01 All Rights Rerserved TABLE OF CONTENTS PAGE Helpful Hints for All Tests...1 Tests
More informationTesting Hypotheses using SPSS
Is the mean hourly rate of male workers $2.00? TTest OneSample Statistics Std. Error N Mean Std. Deviation Mean 2997 2.0522 6.6282.2 OneSample Test Test Value = 2 95% Confidence Interval Mean of the
More informationAn introduction to IBM SPSS Statistics
An introduction to IBM SPSS Statistics Contents 1 Introduction... 1 2 Entering your data... 2 3 Preparing your data for analysis... 10 4 Exploring your data: univariate analysis... 14 5 Generating descriptive
More informationOneWay ANOVA using SPSS 11.0. SPSS ANOVA procedures found in the Compare Means analyses. Specifically, we demonstrate
1 OneWay ANOVA using SPSS 11.0 This section covers steps for testing the difference between three or more group means using the SPSS ANOVA procedures found in the Compare Means analyses. Specifically,
More informationHow to choose a statistical test. Francisco J. Candido dos Reis DGOFMRP University of São Paulo
How to choose a statistical test Francisco J. Candido dos Reis DGOFMRP University of São Paulo Choosing the right test One of the most common queries in stats support is Which analysis should I use There
More informationSPSS: Descriptive and Inferential Statistics. For Windows
For Windows August 2012 Table of Contents Section 1: Summarizing Data...3 1.1 Descriptive Statistics...3 Section 2: Inferential Statistics... 10 2.1 ChiSquare Test... 10 2.2 T tests... 11 2.3 Correlation...
More informationAllelopathic Effects on Root and Shoot Growth: OneWay Analysis of Variance (ANOVA) in SPSS. Dan Flynn
Allelopathic Effects on Root and Shoot Growth: OneWay Analysis of Variance (ANOVA) in SPSS Dan Flynn Just as ttests are useful for asking whether the means of two groups are different, analysis of variance
More informationData Analysis. Lecture Empirical Model Building and Methods (Empirische Modellbildung und Methoden) SS Analysis of Experiments  Introduction
Data Analysis Lecture Empirical Model Building and Methods (Empirische Modellbildung und Methoden) Prof. Dr. Dr. h.c. Dieter Rombach Dr. Andreas Jedlitschka SS 2014 Analysis of Experiments  Introduction
More informationGuide for SPSS for Windows
Guide for SPSS for Windows Index Table Open an existing data file Open a new data sheet Enter or change data value Name a variable Label variables and data values Enter a categorical data Delete a record
More informationSPSS Guide: Tests of Differences
SPSS Guide: Tests of Differences I put this together to give you a stepbystep guide for replicating what we did in the computer lab. It should help you run the tests we covered. The best way to get familiar
More informationProjects Involving Statistics (& SPSS)
Projects Involving Statistics (& SPSS) Academic Skills Advice Starting a project which involves using statistics can feel confusing as there seems to be many different things you can do (charts, graphs,
More informationGeneral Guidelines about SPSS. Steps needed to enter the data in the SPSS
General Guidelines about SPSS The entered data has to be numbers and not letters. For example, in the Gender section, we can not write Male and Female in the answers, however, we must give them a code.
More informationSCHOOL OF HEALTH AND HUMAN SCIENCES DON T FORGET TO RECODE YOUR MISSING VALUES
SCHOOL OF HEALTH AND HUMAN SCIENCES Using SPSS Topics addressed today: 1. Differences between groups 2. Graphing Use the s4data.sav file for the first part of this session. DON T FORGET TO RECODE YOUR
More informationIBM SPSS Statistics 23 Part 4: ChiSquare and ANOVA
IBM SPSS Statistics 23 Part 4: ChiSquare and ANOVA Winter 2016, Version 1 Table of Contents Introduction... 2 Downloading the Data Files... 2 ChiSquare... 2 ChiSquare Test for GoodnessofFit... 2 With
More informationOnce saved, if the file was zipped you will need to unzip it.
1 Commands in SPSS 1.1 Dowloading data from the web The data I post on my webpage will be either in a zipped directory containing a few files or just in one file containing data. Please learn how to unzip
More informationINTERPRETING THE ONEWAY ANALYSIS OF VARIANCE (ANOVA)
INTERPRETING THE ONEWAY ANALYSIS OF VARIANCE (ANOVA) As with other parametric statistics, we begin the oneway ANOVA with a test of the underlying assumptions. Our first assumption is the assumption of
More informationANSWERS TO EXERCISES AND REVIEW QUESTIONS
ANSWERS TO EXERCISES AND REVIEW QUESTIONS PART FIVE: STATISTICAL TECHNIQUES TO COMPARE GROUPS Before attempting these questions read through the introduction to Part Five and Chapters 1621 of the SPSS
More informationMultivariate analysis of variance
21 Multivariate analysis of variance In previous chapters, we explored the use of analysis of variance to compare groups on a single dependent variable. In many research situations, however, we are interested
More informationSPSS Workbook 4 Ttests
TEESSIDE UNIVERSITY SCHOOL OF HEALTH & SOCIAL CARE SPSS Workbook 4 Ttests Research, Audit and data RMH 2023N Module Leader:Sylvia Storey Phone:016420384969 s.storey@tees.ac.uk SPSS Workbook 4 Differences
More informationVariables and Data A variable contains data about anything we measure. For example; age or gender of the participants or their score on a test.
The Analysis of Research Data The design of any project will determine what sort of statistical tests you should perform on your data and how successful the data analysis will be. For example if you decide
More informationChapter 21 Section D
Chapter 21 Section D Statistical Tests for Ordinal Data The ranksum test. You can perform the ranksum test in SPSS by selecting 2 Independent Samples from the Analyze/ Nonparametric Tests menu. The first
More informationJanuary 26, 2009 The Faculty Center for Teaching and Learning
THE BASICS OF DATA MANAGEMENT AND ANALYSIS A USER GUIDE January 26, 2009 The Faculty Center for Teaching and Learning THE BASICS OF DATA MANAGEMENT AND ANALYSIS Table of Contents Table of Contents... i
More informationFactor B: Curriculum New Math Control Curriculum (B (B 1 ) Overall Mean (marginal) Females (A 1 ) Factor A: Gender Males (A 2) X 21
1 Factorial ANOVA The ANOVA designs we have dealt with up to this point, known as simple ANOVA or oneway ANOVA, had only one independent grouping variable or factor. However, oftentimes a researcher has
More informationIBM SPSS Statistics 20 Part 4: ChiSquare and ANOVA
CALIFORNIA STATE UNIVERSITY, LOS ANGELES INFORMATION TECHNOLOGY SERVICES IBM SPSS Statistics 20 Part 4: ChiSquare and ANOVA Summer 2013, Version 2.0 Table of Contents Introduction...2 Downloading the
More informationDEPARTMENT OF HEALTH AND HUMAN SCIENCES HS900 RESEARCH METHODS
DEPARTMENT OF HEALTH AND HUMAN SCIENCES HS900 RESEARCH METHODS Using SPSS Session 2 Topics addressed today: 1. Recoding data missing values, collapsing categories 2. Making a simple scale 3. Standardisation
More informationBasic Data Analysis Using JMP in Windows Table of Contents:
Basic Data Analysis Using JMP in Windows Table of Contents: I. Getting Started with JMP II. Entering Data in JMP III. Saving JMP Data file IV. Opening an Existing Data File V. Transforming and Manipulating
More informationHYPOTHESIS TESTING WITH SPSS:
HYPOTHESIS TESTING WITH SPSS: A NONSTATISTICIAN S GUIDE & TUTORIAL by Dr. Jim Mirabella SPSS 14.0 screenshots reprinted with permission from SPSS Inc. Published June 2006 Copyright Dr. Jim Mirabella CHAPTER
More informationMain Effects and Interactions
Main Effects & Interactions page 1 Main Effects and Interactions So far, we ve talked about studies in which there is just one independent variable, such as violence of television program. You might randomly
More informationDescriptive Statistics
Descriptive Statistics Primer Descriptive statistics Central tendency Variation Relative position Relationships Calculating descriptive statistics Descriptive Statistics Purpose to describe or summarize
More informationChapter 16 Appendix. Nonparametric Tests with Excel, JMP, Minitab, SPSS, CrunchIt!, R, and TI83/84 Calculators
The Wilcoxon Rank Sum Test Chapter 16 Appendix Nonparametric Tests with Excel, JMP, Minitab, SPSS, CrunchIt!, R, and TI83/84 Calculators These nonparametric tests make no assumption about Normality.
More informationBill Burton Albert Einstein College of Medicine william.burton@einstein.yu.edu April 28, 2014 EERS: Managing the Tension Between Rigor and Resources 1
Bill Burton Albert Einstein College of Medicine william.burton@einstein.yu.edu April 28, 2014 EERS: Managing the Tension Between Rigor and Resources 1 Calculate counts, means, and standard deviations Produce
More informationStatistics and research
Statistics and research Usaneya Perngparn Chitlada Areesantichai Drug Dependence Research Center (WHOCC for Research and Training in Drug Dependence) College of Public Health Sciences Chulolongkorn University,
More informationDirections for using SPSS
Directions for using SPSS Table of Contents Connecting and Working with Files 1. Accessing SPSS... 2 2. Transferring Files to N:\drive or your computer... 3 3. Importing Data from Another File Format...
More informationTHE KRUSKAL WALLLIS TEST
THE KRUSKAL WALLLIS TEST TEODORA H. MEHOTCHEVA Wednesday, 23 rd April 08 THE KRUSKALWALLIS TEST: The nonparametric alternative to ANOVA: testing for difference between several independent groups 2 NON
More informationIntroduction to Statistics with SPSS (15.0) Version 2.3 (public)
Babraham Bioinformatics Introduction to Statistics with SPSS (15.0) Version 2.3 (public) Introduction to Statistics with SPSS 2 Table of contents Introduction... 3 Chapter 1: Opening SPSS for the first
More informationSPSS Notes (SPSS version 15.0)
SPSS Notes (SPSS version 15.0) Annie Herbert Salford Royal Hospitals NHS Trust July 2008 Contents Page Getting Started 1 1 Opening SPSS 1 2 Layout of SPSS 2 2.1 Windows 2 2.2 Saving Files 3 3 Creating
More informationSPSS Guide Howto, Tips, Tricks & Statistical Techniques
SPSS Guide Howto, Tips, Tricks & Statistical Techniques Support for the course Research Methodology for IB Also useful for your BSc or MSc thesis March 2014 Dr. Marijke Leliveld Jacob Wiebenga, MSc CONTENT
More informationSPSS TUTORIAL & EXERCISE BOOK
UNIVERSITY OF MISKOLC Faculty of Economics Institute of Business Information and Methods Department of Business Statistics and Economic Forecasting PETRA PETROVICS SPSS TUTORIAL & EXERCISE BOOK FOR BUSINESS
More informationAnalysis of numerical data S4
Basic medical statistics for clinical and experimental research Analysis of numerical data S4 Katarzyna Jóźwiak k.jozwiak@nki.nl 3rd November 2015 1/42 Hypothesis tests: numerical and ordinal data 1 group:
More informationQuantitative Data Analysis: Choosing a statistical test Prepared by the Office of Planning, Assessment, Research and Quality
Quantitative Data Analysis: Choosing a statistical test Prepared by the Office of Planning, Assessment, Research and Quality 1 To help choose which type of quantitative data analysis to use either before
More informationUsing SPSS, Chapter 2: Descriptive Statistics
1 Using SPSS, Chapter 2: Descriptive Statistics Chapters 2.1 & 2.2 Descriptive Statistics 2 Mean, Standard Deviation, Variance, Range, Minimum, Maximum 2 Mean, Median, Mode, Standard Deviation, Variance,
More informationSimple Predictive Analytics Curtis Seare
Using Excel to Solve Business Problems: Simple Predictive Analytics Curtis Seare Copyright: Vault Analytics July 2010 Contents Section I: Background Information Why use Predictive Analytics? How to use
More informationData analysis process
Data analysis process Data collection and preparation Collect data Prepare codebook Set up structure of data Enter data Screen data for errors Exploration of data Descriptive Statistics Graphs Analysis
More informationUsing CrunchIt (http://bcs.whfreeman.com/crunchit/bps4e) or StatCrunch (www.calvin.edu/go/statcrunch)
Using CrunchIt (http://bcs.whfreeman.com/crunchit/bps4e) or StatCrunch (www.calvin.edu/go/statcrunch) 1. In general, this package is far easier to use than many statistical packages. Every so often, however,
More informationTechnology StepbyStep Using StatCrunch
Technology StepbyStep Using StatCrunch Section 1.3 Simple Random Sampling 1. Select Data, highlight Simulate Data, then highlight Discrete Uniform. 2. Fill in the following window with the appropriate
More informationID X Y
Dale Berger SPSS StepbyStep Regression Introduction: MRC01 This stepbystep example shows how to enter data into SPSS and conduct a simple regression analysis to develop an equation to predict from.
More information6. An Introduction to Statistical Package for the Social Sciences
6. An Introduction to Statistical Package for the Social Sciences 53 Nick Emtage and Stephen Duthy This module provides an introduction to statistical analysis, particularly in regard to survey data. Some
More informationSPSS workbook for New Statistics Tutors
statstutor community project encouraging academics to share statistics support resources All stcp resources are released under a Creative Commons licence stcpmarshallowen6a The following resources are
More informationSPSS Workbook 3 Chisquared & Correlation
TEESSIDE UNIVERSITY SCHOOL OF HEALTH & SOCIAL CARE SPSS Workbook 3 Chisquared & Correlation Research, Audit and data RMH 2023N Module Leader:Sylvia Storey Phone:016420384969 s.storey@tees.ac.uk 1 SPSS
More informationRecall this chart that showed how most of our course would be organized:
Chapter 4 OneWay ANOVA Recall this chart that showed how most of our course would be organized: Explanatory Variable(s) Response Variable Methods Categorical Categorical Contingency Tables Categorical
More informationLecture  32 Regression Modelling Using SPSS
Applied Multivariate Statistical Modelling Prof. J. Maiti Department of Industrial Engineering and Management Indian Institute of Technology, Kharagpur Lecture  32 Regression Modelling Using SPSS (Refer
More informationTable of Contents. Preface
Table of Contents Preface Chapter 1: Introduction 11 Opening an SPSS Data File... 2 12 Viewing the SPSS Screens... 3 o Data View o Variable View o Output View 13 Reading NonSPSS Files... 6 o Convert
More informationKSTAT MINIMANUAL. Decision Sciences 434 Kellogg Graduate School of Management
KSTAT MINIMANUAL Decision Sciences 434 Kellogg Graduate School of Management Kstat is a set of macros added to Excel and it will enable you to do the statistics required for this course very easily. To
More informationData analysis. Data analysis in Excel using Windows 7/Office 2010
Data analysis Data analysis in Excel using Windows 7/Office 2010 Open the Data tab in Excel If Data Analysis is not visible along the top toolbar then do the following: o Right click anywhere on the toolbar
More informationThere are six different windows that can be opened when using SPSS. The following will give a description of each of them.
SPSS Basics Tutorial 1: SPSS Windows There are six different windows that can be opened when using SPSS. The following will give a description of each of them. The Data Editor The Data Editor is a spreadsheet
More informationSPSS Bivariate Statistics
SPSS Bivariate Statistics Social Science Research Lab American University, Washington, D.C. Web. www.american.edu/provost/ctrl/pclabs.cfm Tel. x3862 Email. SSRL@American.edu Course Objectives In this tutorial
More informationStudent Guide to SPSS Barnard College Department of Biological Sciences
Student Guide to SPSS Barnard College Department of Biological Sciences Dan Flynn Table of Contents Introduction... 2 Basics... 4 Starting SPSS... 4 Navigating... 4 Data Editor... 5 SPSS Viewer... 6 Getting
More informationAn SPSS companion book. Basic Practice of Statistics
An SPSS companion book to Basic Practice of Statistics SPSS is owned by IBM. 6 th Edition. Basic Practice of Statistics 6 th Edition by David S. Moore, William I. Notz, Michael A. Flinger. Published by
More informationNCSS Statistical Software
Chapter 06 Introduction This procedure provides several reports for the comparison of two distributions, including confidence intervals for the difference in means, twosample ttests, the ztest, the
More informationAnalysis Tools in Geochemistry for ArcGIS
Analysis Tools in Geochemistry for ArcGIS The database that is used to store all of the geographic information in Geochemistry for ArcGIS is Esri s file Geodatabase (fgdb). This is a collection of tables
More informationEPS 625 ANALYSIS OF COVARIANCE (ANCOVA) EXAMPLE USING THE GENERAL LINEAR MODEL PROGRAM
EPS 6 ANALYSIS OF COVARIANCE (ANCOVA) EXAMPLE USING THE GENERAL LINEAR MODEL PROGRAM ANCOVA One Continuous Dependent Variable (DVD Rating) Interest Rating in DVD One Categorical/Discrete Independent Variable
More informationHypothesis Testing. Male Female
Hypothesis Testing Below is a sample data set that we will be using for today s exercise. It lists the heights for 10 men and 1 women collected at Truman State University. The data will be entered in the
More informationChapter Four: Univariate Statistics
Chapter Four: Univariate Statistics Univariate analysis, looking at single variables, is typically the first procedure one does when examining data for the first time. There are a number of reasons why
More informationAdditional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jintselink/tselink.htm
Mgt 540 Research Methods Data Analysis 1 Additional sources Compilation of sources: http://lrs.ed.uiuc.edu/tseportal/datacollectionmethodologies/jintselink/tselink.htm http://web.utk.edu/~dap/random/order/start.htm
More informationChapter 7 Section 7.1: Inference for the Mean of a Population
Chapter 7 Section 7.1: Inference for the Mean of a Population Now let s look at a similar situation Take an SRS of size n Normal Population : N(, ). Both and are unknown parameters. Unlike what we used
More informationSimple Linear Regression in SPSS STAT 314
Simple Linear Regression in SPSS STAT 314 1. Ten Corvettes between 1 and 6 years old were randomly selected from last year s sales records in Virginia Beach, Virginia. The following data were obtained,
More informationChapter 6: t test for dependent samples
Chapter 6: t test for dependent samples ****This chapter corresponds to chapter 11 of your book ( t(ea) for Two (Again) ). What it is: The t test for dependent samples is used to determine whether the
More informationHOW TO USE MINITAB: INTRODUCTION AND BASICS. Noelle M. Richard 08/27/14
HOW TO USE MINITAB: INTRODUCTION AND BASICS 1 Noelle M. Richard 08/27/14 CONTENTS * Click on the links to jump to that page in the presentation. * 1. Minitab Environment 2. Uploading Data to Minitab/Saving
More information4. Descriptive Statistics: Measures of Variability and Central Tendency
4. Descriptive Statistics: Measures of Variability and Central Tendency Objectives Calculate descriptive for continuous and categorical data Edit output tables Although measures of central tendency and
More informationInferential Statistics. Probability. From Samples to Populations. Katie RommelEsham Education 504
Inferential Statistics Katie RommelEsham Education 504 Probability Probability is the scientific way of stating the degree of confidence we have in predicting something Tossing coins and rolling dice
More informationQUANTITATIVE METHODS BIOLOGY FINAL HONOUR SCHOOL NONPARAMETRIC TESTS
QUANTITATIVE METHODS BIOLOGY FINAL HONOUR SCHOOL NONPARAMETRIC TESTS This booklet contains lecture notes for the nonparametric work in the QM course. This booklet may be online at http://users.ox.ac.uk/~grafen/qmnotes/index.html.
More informationBiodiversity Data Analysis: Testing Statistical Hypotheses By Joanna Weremijewicz, Simeon Yurek, Steven Green, Ph. D. and Dana Krempels, Ph. D.
Biodiversity Data Analysis: Testing Statistical Hypotheses By Joanna Weremijewicz, Simeon Yurek, Steven Green, Ph. D. and Dana Krempels, Ph. D. In biological science, investigators often collect biological
More informationTesting for differences I exercises with SPSS
Testing for differences I exercises with SPSS Introduction The exercises presented here are all about the ttest and its nonparametric equivalents in their various forms. In SPSS, all these tests can
More informationChi Square Test. PASSS Research Question 4: Chi Square Test
Chi Square Test Is there a statistically significant relationship between a student s Year 11 truancy and his or her enrolment in full time education after secondary school? A chisquare test is a statistical
More informationBox plots & ttests. Example
Box plots & ttests Box Plots Box plots are a graphical representation of your sample (easy to visualize descriptive statistics); they are also known as boxandwhisker diagrams. Any data that you can
More informationIBM SPSS Statistics for Beginners for Windows
ISS, NEWCASTLE UNIVERSITY IBM SPSS Statistics for Beginners for Windows A Training Manual for Beginners Dr. S. T. Kometa A Training Manual for Beginners Contents 1 Aims and Objectives... 3 1.1 Learning
More information7. Tests of association and Linear Regression
7. Tests of association and Linear Regression In this chapter we consider 1. Tests of Association for 2 qualitative variables. 2. Measures of the strength of linear association between 2 quantitative variables.
More informationData Analysis in SPSS. February 21, 2004. If you wish to cite the contents of this document, the APA reference for them would be
Data Analysis in SPSS Jamie DeCoster Department of Psychology University of Alabama 348 Gordon Palmer Hall Box 870348 Tuscaloosa, AL 354870348 Heather Claypool Department of Psychology Miami University
More informationExamining Differences (Comparing Groups) using SPSS Inferential statistics (Part I) Dwayne Devonish
Examining Differences (Comparing Groups) using SPSS Inferential statistics (Part I) Dwayne Devonish Statistics Statistics are quantitative methods of describing, analysing, and drawing inferences (conclusions)
More informationUsing SPSS 20, Handout 3: Producing graphs:
Research Skills 1: Using SPSS 20: Handout 3, Producing graphs: Page 1: Using SPSS 20, Handout 3: Producing graphs: In this handout I'm going to show you how to use SPSS to produce various types of graph.
More informationStatistical Significance and Bivariate Tests
Statistical Significance and Bivariate Tests BUS 735: Business Decision Making and Research 1 1.1 Goals Goals Specific goals: Refamiliarize ourselves with basic statistics ideas: sampling distributions,
More informationLinear Models in STATA and ANOVA
Session 4 Linear Models in STATA and ANOVA Page Strengths of Linear Relationships 42 A Note on NonLinear Relationships 44 Multiple Linear Regression 45 Removal of Variables 48 Independent Samples
More informationIntroduction to Quantitative Methods
Introduction to Quantitative Methods October 15, 2009 Contents 1 Definition of Key Terms 2 2 Descriptive Statistics 3 2.1 Frequency Tables......................... 4 2.2 Measures of Central Tendencies.................
More informationAn analysis method for a quantitative outcome and two categorical explanatory variables.
Chapter 11 TwoWay ANOVA An analysis method for a quantitative outcome and two categorical explanatory variables. If an experiment has a quantitative outcome and two categorical explanatory variables that
More informationPointBiserial and Biserial Correlations
Chapter 302 PointBiserial and Biserial Correlations Introduction This procedure calculates estimates, confidence intervals, and hypothesis tests for both the pointbiserial and the biserial correlations.
More informationWhen to use Excel. When NOT to use Excel 9/24/2014
Analyzing Quantitative Assessment Data with Excel October 2, 2014 Jeremy Penn, Ph.D. Director When to use Excel You want to quickly summarize or analyze your assessment data You want to create basic visual
More informationChapter 23. Inferences for Regression
Chapter 23. Inferences for Regression Topics covered in this chapter: Simple Linear Regression Simple Linear Regression Example 23.1: Crying and IQ The Problem: Infants who cry easily may be more easily
More informationANOVA Analysis of Variance
ANOVA Analysis of Variance What is ANOVA and why do we use it? Can test hypotheses about mean differences between more than 2 samples. Can also make inferences about the effects of several different IVs,
More informationChapter 11: Chisquare (χ 2 )
Chapter 11: Chisquare (χ 2 ) *This chapter corresponds with Chapter 16 in your text ( What to do when you re not normal ). What it is: Chisquare is a nonparametric statistic. This means that it can be
More informationIBM SPSS Statistics 20 Part 1: Descriptive Statistics
CALIFORNIA STATE UNIVERSITY, LOS ANGELES INFORMATION TECHNOLOGY SERVICES IBM SPSS Statistics 20 Part 1: Descriptive Statistics Summer 2013, Version 2.0 Table of Contents Introduction...2 Downloading the
More informationEPS 625 INTERMEDIATE STATISTICS FRIEDMAN TEST
EPS 625 INTERMEDIATE STATISTICS The Friedman test is an extension of the Wilcoxon test. The Wilcoxon test can be applied to repeatedmeasures data if participants are assessed on two occasions or conditions
More informationSome Critical Information about SOME Statistical Tests and Measures of Correlation/Association
Some Critical Information about SOME Statistical Tests and Measures of Correlation/Association This information is adapted from and draws heavily on: Sheskin, David J. 2000. Handbook of Parametric and
More information