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

Save this PDF as:

Size: px
Start display at page:

## 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 Two-sample t-test p. 8 Paired T-test p. 10 Comparing two groups using non-parametric statistics Mann Whitney U test p. 11 Comparing three or more groups using parametric statistics One-way ANOVA and post-hoc tests p. 13 Comparing three or more groups using non-parametric statistics Kruskal-Wallis test p. 15 For studies with two independent variables Two-way 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

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: &

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, stem-leaf 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.

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 Mann-Whitney 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 two-sample t-test 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 T-test. 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. (2-tailed) t-test 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 t-value of the t-test, the degrees of freedom of the test, and the p-value which is labeled Sig. (2-tailed). Before you look at the results of the t-test, 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 p-value 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 t-test. If you logtransformed the data and re-ran 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. (2-tailed) t-test 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 t-test. For the t-test, 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 t-value, 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 t-test 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 low-light 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 T-test. Highlight both of your variables and hit the arrow to put them in the Paired-Variables box. They will show up as Low-High. 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. (2-tailed)

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 ( Mann-Whitney U ). The p-value is labeled as Asymp. Sig. (2- tailed). Ranks Density Island N Mean Rank Sum of Ranks A B Total 40 Test Statistics(b) Density Mann-Whitney 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 p-value = 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 U-value, 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 One-way 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 post-hoc paired comparisons. They are called post-hoc, because you conduct the tests after you have completed an ANOVA and it shows where significant differences lie among the groups. One of the Post-hoc 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 One-way 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 post-hoc 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 non-parametric 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 p-value in the ANOVA table ( Sig. ). If this p-value is > 0.05, then there are no significant differences among any of the means. If the p-value 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 (I-J) 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 F-value, df, and p from the ANOVA. Following statements that describe the differences between specific groups, you should report the p-value from the post-hoc test only. (NOTE: there is no F-value or df associated with the post-hoc tests only a p-value!) 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 Mann-Whitney U test was a non-parametric version of a t-test, a Kruskal-Wallis test is the non-parametric 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 non-parametric statistics by reviewing the information on Page 11. To run the Kruskal-Wallis test: Go to Analyze Nonparametric Tests K Independent Samples. Note: Remember for the Mann-Whitney 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 Kruskal-Wallis 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 chi-square value and it is reported in the first row of the second table. The p-value is labeled as Asymp. Sig. (2-tailed). Ranks density Location A B C Total N Mean Rank Test Statistics(a,b) density Chi-Square df 2 Asymp. Sig..004 a Kruskal Wallis Test b Grouping Variable: Location In the table above, the p-value = 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 Kruskal-Wallis test does not have an easy way to do post-hoc analyses. So, if you have a significant effect for the overall Kruskal-Wallis, you can follow that up with a series of two-group comparisons using Mann-Whitney U tests. In this case, we would follow up the Kruskal-Wallis with three Mann-Whitney 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 chi-square 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 Two-way ANOVA, a parametric statistical test. The two-way 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 non-parametric 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 two-way ANOVA, you might want to first run a t-test on bill size just between species, then a t-test 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 two-way ANOVA can be in telling you more about the patterns in your data. Now run a two-way ANOVA on the same data. The procedure is much the same as for a One-way 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 2-way 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 2-way 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 Between-Subjects 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 p-value 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 bill-size 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 t-test) and neither sex has a consistently larger bill when considered across both species. The main effects terms in a 2-way ANOVA basically ignore the interaction term and give similar results to the t-tests you may have performed earlier. So, the p-value 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

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 pop-up 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 ( between-subjects ) 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. Between-Subjects 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 two-way 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 Between-Subjects 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 2-way 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 y-axis and the continuous independent variable (Body Size) on the x-axis. 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 F-value, 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 F-value, 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 non-predator areas? You are interested in whether predators influence guppy behavior. So you put guppies in a tank that is divided into a predator-free 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 Chi-Square 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 Chi-square. 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 Chi-Square value, df, and p-value 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 chi-square 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 predator-free 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 pop-up 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 Chi-square in the new pop-up 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 Chi-Square Tests Value df Asymp. Sig. (2- sided) Exact Sig. (2- sided) Exact Sig. (1- sided) Pearson Chi-Square 1.250(b) Continuity Correction(a) Likelihood Ratio Fisher's Exact Test Linear-by-Linear 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 Chi-Square line. Your Chi-square value is 2 = Your p-value 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 (chi-square 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 t-test A paired t-test 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

### SPSS 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

### A 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

### SPSS Explore procedure

SPSS Explore procedure One useful function in SPSS is the Explore procedure, which will produce histograms, boxplots, stem-and-leaf plots and extensive descriptive statistics. To run the Explore procedure,

### Chapter 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 One-way ANOVA To test the null hypothesis that several population means are equal,

### Module 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 } One-Sample Chi-Square Test

### SPSS 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

### 6 Comparison of differences between 2 groups: Student s T-test, Mann-Whitney U-Test, Paired Samples T-test and Wilcoxon Test

6 Comparison of differences between 2 groups: Student s T-test, Mann-Whitney U-Test, Paired Samples T-test and Wilcoxon Test Having finally arrived at the bottom of our decision tree, we are now going

### The 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

### Testing Hypotheses using SPSS

Is the mean hourly rate of male workers \$2.00? T-Test One-Sample Statistics Std. Error N Mean Std. Deviation Mean 2997 2.0522 6.6282.2 One-Sample Test Test Value = 2 95% Confidence Interval Mean of the

### An 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

### One-Way ANOVA using SPSS 11.0. SPSS ANOVA procedures found in the Compare Means analyses. Specifically, we demonstrate

1 One-Way 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,

### How to choose a statistical test. Francisco J. Candido dos Reis DGO-FMRP University of São Paulo

How to choose a statistical test Francisco J. Candido dos Reis DGO-FMRP University of São Paulo Choosing the right test One of the most common queries in stats support is Which analysis should I use There

### SPSS: 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 Chi-Square Test... 10 2.2 T tests... 11 2.3 Correlation...

### Allelopathic Effects on Root and Shoot Growth: One-Way Analysis of Variance (ANOVA) in SPSS. Dan Flynn

Allelopathic Effects on Root and Shoot Growth: One-Way Analysis of Variance (ANOVA) in SPSS Dan Flynn Just as t-tests are useful for asking whether the means of two groups are different, analysis of variance

### Data 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

### Guide 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

### SPSS Guide: Tests of Differences

SPSS Guide: Tests of Differences I put this together to give you a step-by-step 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

### Projects 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,

### General 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.

### SCHOOL 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

### Once 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

### INTERPRETING THE ONE-WAY ANALYSIS OF VARIANCE (ANOVA)

INTERPRETING THE ONE-WAY ANALYSIS OF VARIANCE (ANOVA) As with other parametric statistics, we begin the one-way ANOVA with a test of the underlying assumptions. Our first assumption is the assumption of

### ANSWERS 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 16-21 of the SPSS

### Multivariate 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

### SPSS Workbook 4 T-tests

TEESSIDE UNIVERSITY SCHOOL OF HEALTH & SOCIAL CARE SPSS Workbook 4 T-tests Research, Audit and data RMH 2023-N Module Leader:Sylvia Storey Phone:016420384969 s.storey@tees.ac.uk SPSS Workbook 4 Differences

### Variables 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

### Chapter 21 Section D

Chapter 21 Section D Statistical Tests for Ordinal Data The rank-sum test. You can perform the rank-sum test in SPSS by selecting 2 Independent Samples from the Analyze/ Nonparametric Tests menu. The first

### January 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

### Factor 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

### DEPARTMENT 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

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

### HYPOTHESIS TESTING WITH SPSS:

HYPOTHESIS TESTING WITH SPSS: A NON-STATISTICIAN 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

### Main 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

### Descriptive Statistics

Descriptive Statistics Primer Descriptive statistics Central tendency Variation Relative position Relationships Calculating descriptive statistics Descriptive Statistics Purpose to describe or summarize

### Chapter 16 Appendix. Nonparametric Tests with Excel, JMP, Minitab, SPSS, CrunchIt!, R, and TI-83-/84 Calculators

The Wilcoxon Rank Sum Test Chapter 16 Appendix Nonparametric Tests with Excel, JMP, Minitab, SPSS, CrunchIt!, R, and TI-83-/84 Calculators These nonparametric tests make no assumption about Normality.

### Bill 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

### Statistics 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,

### Directions 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...

### THE KRUSKAL WALLLIS TEST

THE KRUSKAL WALLLIS TEST TEODORA H. MEHOTCHEVA Wednesday, 23 rd April 08 THE KRUSKAL-WALLIS TEST: The non-parametric alternative to ANOVA: testing for difference between several independent groups 2 NON

### Introduction 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

### SPSS 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

### SPSS Guide How-to, Tips, Tricks & Statistical Techniques

SPSS Guide How-to, 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

### SPSS 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

### Analysis 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:

### Quantitative 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

### Using 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,

### Simple 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

### Data 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

### Using 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,

### Technology Step-by-Step Using StatCrunch

Technology Step-by-Step 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

### ID X Y

Dale Berger SPSS Step-by-Step Regression Introduction: MRC01 This step-by-step example shows how to enter data into SPSS and conduct a simple regression analysis to develop an equation to predict from.

### 6. 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

### SPSS 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 stcp-marshallowen-6a The following resources are

### SPSS Workbook 3 Chi-squared & Correlation

TEESSIDE UNIVERSITY SCHOOL OF HEALTH & SOCIAL CARE SPSS Workbook 3 Chi-squared & Correlation Research, Audit and data RMH 2023-N Module Leader:Sylvia Storey Phone:016420384969 s.storey@tees.ac.uk 1 SPSS

### Recall this chart that showed how most of our course would be organized:

Chapter 4 One-Way 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

### Lecture - 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

Table of Contents Preface Chapter 1: Introduction 1-1 Opening an SPSS Data File... 2 1-2 Viewing the SPSS Screens... 3 o Data View o Variable View o Output View 1-3 Reading Non-SPSS Files... 6 o Convert

### KSTAT MINI-MANUAL. Decision Sciences 434 Kellogg Graduate School of Management

KSTAT MINI-MANUAL 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

### Data 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

### There 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

### SPSS 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

### Student 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

### An 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

### NCSS Statistical Software

Chapter 06 Introduction This procedure provides several reports for the comparison of two distributions, including confidence intervals for the difference in means, two-sample t-tests, the z-test, the

### Analysis 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

### EPS 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

### Hypothesis 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

### Chapter 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

### Chapter 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

### Simple 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,

### Chapter 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

### HOW 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

### 4. 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

### Inferential Statistics. Probability. From Samples to Populations. Katie Rommel-Esham Education 504

Inferential Statistics Katie Rommel-Esham Education 504 Probability Probability is the scientific way of stating the degree of confidence we have in predicting something Tossing coins and rolling dice

### QUANTITATIVE METHODS BIOLOGY FINAL HONOUR SCHOOL NON-PARAMETRIC TESTS

QUANTITATIVE METHODS BIOLOGY FINAL HONOUR SCHOOL NON-PARAMETRIC 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.

### Biodiversity 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

### Testing for differences I exercises with SPSS

Testing for differences I exercises with SPSS Introduction The exercises presented here are all about the t-test and its non-parametric equivalents in their various forms. In SPSS, all these tests can

### Chi 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 chi-square test is a statistical

### Box plots & t-tests. Example

Box plots & t-tests Box Plots Box plots are a graphical representation of your sample (easy to visualize descriptive statistics); they are also known as box-and-whisker diagrams. Any data that you can

### IBM 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

### 7. 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.

### Data 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 35487-0348 Heather Claypool Department of Psychology Miami University

### Examining 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)

### Using 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.

### Statistical Significance and Bivariate Tests

Statistical Significance and Bivariate Tests BUS 735: Business Decision Making and Research 1 1.1 Goals Goals Specific goals: Re-familiarize ourselves with basic statistics ideas: sampling distributions,

### Linear Models in STATA and ANOVA

Session 4 Linear Models in STATA and ANOVA Page Strengths of Linear Relationships 4-2 A Note on Non-Linear Relationships 4-4 Multiple Linear Regression 4-5 Removal of Variables 4-8 Independent Samples

### Introduction 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.................

### An analysis method for a quantitative outcome and two categorical explanatory variables.

Chapter 11 Two-Way 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

### Point-Biserial and Biserial Correlations

Chapter 302 Point-Biserial and Biserial Correlations Introduction This procedure calculates estimates, confidence intervals, and hypothesis tests for both the point-biserial and the biserial correlations.

### When 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

### Chapter 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

### ANOVA 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,

### Chapter 11: Chi-square (χ 2 )

Chapter 11: Chi-square (χ 2 ) *This chapter corresponds with Chapter 16 in your text ( What to do when you re not normal ). What it is: Chi-square is a nonparametric statistic. This means that it can be