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

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 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

2 CONTENT Introduction... 3 Description of the dataset... 4 Step 1: Preparing the Dataset... 6 Goal: Label the variables... 6 Goal: Checking outliers... 6 Goal: Checking assumptions for regression analysis... 7 Step 2: Descriptive statistics... 9 Goal: Distribution and means... 9 Step 3: Correlations and reliability analysis Goal: Correlations between variables Goal: Test reliability Goal: Recoding variables Step 4: Making a new sum variable Goal: Making a sum variable Step 5: Technique Choice Goal: Choosing the analysis technique Step 6: The control variables Goal: T-Test Independent Samples Goal: Linear Regression Goal: One-way Anova Goal: One-way Anova (2) Step 7: Testing the hypothesis Goal: Kruskal Wallis Test Goal: Linear Regression (2) Goal: Paired samples t-test Goal: Cross-table with Chi-square Goal: Mann-Whitney U-test Goal: Manova Goal: Two-way Anova Appendix Tables for Univariate and bivariate analyses

3 INTRODUCTION What to do before you start... When you start working in SPSS, it is useful to tick the box which makes sure the computer code of the analyses you make is also saved in the output. This might not immediately be clear to you. However, it is very insightful for your tutor. You can do this by going to: Edit>Options > tab Viewer > tick the box Display commands in the log in the bottom left. The techniques that are discussed in the chapter control variables are also usable for testing your hypotheses and the same goes for the analyses that are described in testing your hypotheses. The only reason these techniques are discussed in these chapters is due to the structure of the dataset used in this guide. Recommended literature Field, A. Discovering statistics using SPSS. Sage. ISBN: Huizingh, E. Applied statistics with SPSS. Sage. ISBN: Keller, G. Statistics for Management and Economics (7th International Student Edition), Thomson. ISBN: Recommended literature for more advanced and specialized techniques: Janssens, W., Wijnen, K., De Pelsmacker, P., & Van Kenhove, P. (2008) Marketing Research with SPSS. Pearson Education Limited. ISNB: > e.g. logistic regression, factor analysis, SEM, cluster analysis, Scaling techniques Tabachnick, B. G., and Fidell, L. S. (2007). Using Multivariate Statistics, 5th ed. Boston: Allyn and Bacon. ISBN-10: ; ISBN-13: > e.g. multiple regressions, experimental designs (ANOVAs), and time series analyses Lattin, J., Carroll, J.D., & Green, P.E. (2003). Analyzing Multivariate Data. Toronto: Thomson Learning. ISBN > e.g., Roles of third variables in the linear model, Hierarchical linear models, Principal components analysis, Factor analysis, Latent class analysis, Conjoint analysis, Choice models, Multidimensional scaling. 3

6 STEP 1: PREPARING THE DATASET GOAL: LABEL THE VARIABLES The goal of this section is learning how you can label variables so you can understand what your variables mean later on. This can be done by clearly labeling your variables and naming the categories of each variable. TECHNIQUE Click the tab variable view in the bottom left corner of your SPSS file and type a description of your variables in the column labels. After this you click a cell in the column values which allows you to specify each category of your variable. Example: click in the column values on gender and type a 1 in the value box and man in label, then press add. Do the same for woman and press add again. Important! When discussing your analyses and findings, never mention terms like variable A1, W2, etc. (like we did in this guide), but mention their full description. This is because other people (clients for example) do not know what A1, W2 means. GOAL: CHECKING OUTLIERS Every statistical technique is based on several assumptions and in order to draw the right conclusion from the results these assumptions must be met. TECHNIQUE: OUTLIERS When using statistics it is important to always check your data for possible outliers (extreme values on the dependent or independent variable). It s possible that these 6

7 extreme values are the result of a mistake in the data input. However, these values might also be correct. These outliers violate the normality assumption and therefore a nonparametric test is has to be chosen in these cases. Outliers can be detected by plotting boxplots, histograms, probability plots or scatterplots. GOAL: CHECKING ASSUMPTIONS FOR REGRESSION ANALYSIS The assumptions that will be covered here are relevant for regression analysis: 1. The sample should be based on independent observations. 2. There is a linear relationship between the dependent and the independent variable. 3. The residuals are normally distributed. These assumptions also hold for the One-way ANOVA and multiple regression analysis. The assumptions regarding independent observations and normality also apply to T-tests. Nonparametric tests are not restricted by these assumptions. TECHNIQUE: INDEPENDENT OBSERVATIONS The respondents in the dataset must be determined in dependent of each other, and there cannot be any relation between the observed scores between respondents. This also means the expected correlation between the residuals of a regression analysis are zero (independence assumption). In the case of dependence the estimated standard error will be smaller than the actual standard error which leads to inefficient estimates of the regression coefficients. TECHNIQUE: LINEAR RELATIONSHIP There should be a linear relationship between the dependent and the independent variable. For every set of values of the independent variable the expected mean residuals should be equal to zero. A systematic deviation of this assumption indicates the relationship is not linear. Detection of this problem can be done by making a scatterplot where the residuals (on the y-axis) are plotted against another variable (on the x-axis). If a linear relationship exists, the residuals will be spread randomly around their average (which is zero). However, when the scatterplot shows a non-linear relationship another type of relationship might be applicable (e.g. logistic relationship). TECHNIQUE: NORMALITY ASSUMPTION There are several methods to test for non-normality. Examples include graphical ways of examining normality and statistical tests. The easiest way is to plot a histogram of the residuals, which is particularly relevant for large samples. When a more accurate analysis is required one can use P-P plots (normal probability plot). This is basically a scatterplot that shows the cumulative probability of a stand normal distribution plotted against the cumulative probabilities of the observed distribution. If the normality assumption is 7

8 satisfied, the dots on the P-P plot will be in a straight line. The normality assumption is violated if there is a systematic deviation from the line which will lead to wrong estimates for the confidence intervals and p-values. An important note here is that when sample size is sufficiently large (about 200) and the amount of independent variables is small (less than 5), the central limit theorem says that the estimates of confidence intervals and p-values will be accurate again, even though the normality assumption is violated. 8

9 STEP 2: DESCRIPTIVE STATISTICS GOAL: DISTRIBUTION AND MEANS Use SPSS to calculate the number of males and females whom participated in the study and their average age. Furthermore, compute the distribution of education level and provide the medians of the ordinal variables education level and A1, and the averages for the quasi interval variables A2, A3, W1 and W2. TECHNIQUE Analyze > Descriptive Statistics > Frequencies. Put the variables gender, age, education level, A1, A2, W1,W2 in the right box and click Statistics. Next, tick the boxes mean, median, std. deviation, minimum and maximum and click continue. 9

10 Click Charts and tick the box Histograms (with normal curve) and click continue and OK. SPSS OUTPUT Amount of male and female participants: Gender Frequency Percent Valid Percent Cumulative Percent Valid man ,6 47,6 47,6 woman ,4 52,4 100,0 Total ,0 100,0 This table shows that 107 participants were male (47,6%) and 118 were female (52,4%). Furthermore, it shows that everyone answered what their gender was, since there is no row called missing. Descriptive statistics: Statistics Age Education Gender A1 A2 A3 W1 W2 N Valid Missing Mean 41,26 2,47 1,52 3,61 4,22 4,52 3,83 3,81 Median 42,00 2,00 2,00 3,00 4,00 4,00 4,00 4,00 Std. Deviation 13,203,987,501 1,475 1,627 1,593 1,839 1,651 Minimum Maximum

11 HOW TO REPORT DESCRIPTIVE STATISTICS The table above shows the descriptive statistics that were required. Keep in mind that when you report a mean, you should also report the standard deviation (SD). Distribution of education level: The sample consists of 107 (47,6%) men and 118 (52,4%) women, with an average age of 41 (Mage= 41,26, SD =13,20). Table 1 shows the means of variables A2, A3, W1 and W2. Furthermore, education level was approximately normally distributed (see figure 1) ranging from primary school to Ph.D.-level. The median of education level was 2,00 (secondary school) and the median of A1 3,00 (often). Figure 1. Distribution of education level Table 1. Descriptive statistics for variables A2,A3,W1 and W2 A2 A3 W1 W2 Mean 4,22 4,52 3,83 3,81 Standard deviation 1,63 1,59 1,84 1,65 11

12 STEP 3: CORRELATIONS AND RELIABILITY ANALYSIS Two constructs in the model (autonomy and job satisfaction) are measured with multiple questions. Before proceeding with the analysis, it might be useful to check whether or not the questions correlate with each other and if they do, make a new sum variable that depicts the whole construct up in one score. GOAL: CORRELATIONS BETWEEN VARIABLES How are the questions measuring job satisfaction related? Can they be summed up? If yes, how would you do this? TECHNIQUE: CORRELATION First, you have to check whether or not the questions measuring job satisfaction (W1,W2 and W3) correlate with each other. Use Analyze>Correlate>Bivariate and put the three variables in the right box and press OK. SPSS-OUTPUT Correlations W1 W2 W3 W1 Pearson Correlation 1,000 -,103 -,089 Sig. (2-tailed),122,186 N 225, W2 Pearson Correlation -,103 1,000,897** Sig. (2-tailed),122,000 N , W3 Pearson Correlation -,089,897** 1,000 Sig. (2-tailed),186,000 N ,000 **. Correlation is significant at the 0.01 level (2-tailed). NB. A correlation table actually provides the same information twice since the information is the same across the diagonal. Therefore, you only need half of the table to find your answer. The table shows that W2 does not significantly correlates with W1 (p is larger then 0,05; p=0,122). It also seems W3 does not correlate with W1 (p=0,186). However, W3 and W2 do correlate significantly (p is smaller than 0,05, namely p=0,000). 12

13 HOW TO REPORT THIS? A correlation analysis showed that W1 and W2 did not significantly correlate (r= -0,103, p=0,122). The variables W2 and W3 did correlate significantly (r= 0,897, p <.001). When people have more fun while working, they will be more satisfied with their work, and vice versa. Considering you can only sum up the variables that correlate significantly, it appears only W2 and W3 can be recoded into a sum variable. GOAL: TEST RELIABILITY The final test you have to perform to check whether or not a sum variable may be computed is Cronbach s alpha. This value should be as high as possible (ranging from 0 to 1), but a value of at least 0,6 is required. TECHNIQUE: CRONBACH S ALPHA Analyze > Scale > Reliability analysis. Move the three variables of job satisfaction to the right box and press Statistics. In the top right corner, tick the box under descriptives for : item, scale en scale if item deleted. Press continue and OK. 13

14 SPSS-OUTPUT Reliability Statistics Cronbach's Alpha N of Items,442 3 SPSS shows a value for Cronbach s Alpha of 0,442 when combining all three questions for job satisfaction (W1, W2 & W3). However, the minimum to allow for summing up the variables is a Cronbach s Alpha of 0,6. When examining the rest of the output of SPSS you find the last column Cronbach s Alpha if item deleted which shows the value of Cronbach s Alpha if one of the questions is omitted. For example, if you don t consider W1 the Cronbach s Alpha shoots up to 0,945 which is significantly above the minimum of 0,6 which means W2 and W3 can be summed to one variable. However, when you delete W2 the Cronbach s Alpha goes down to -0,193. The same goes for deleting W3 (Cronbach s Alpha = -0,229). Both of these options only reduce the Cronbach s Alpha of 0,44 that we found before. We can conclude that W2 & W3 can be summed, but W1 cannot (the same conclusion we reached with correlations). Item-Total Statistics Scale Mean if Item Deleted Scale Variance if Item Deleted Corrected Item- Total Correlation W1 7,99 10,174 -,099,945 W2 8,01 5,491,540 -,193 a W3 7,64 5,481,563 -,229 a Cronbach's Alpha if Item Deleted a. The value is negative due to a negative average covariance among items. This violates reliability model assumptions. You may want to check item codings. Important! A negative value for Cronbach s Alpha means something went wrong. One of the possibilities is that you included two variables with mirrored answer options (e.g. 1 means never with one variable, while 1 means always with the other variables). In order to calculate a valid Cronbach s Alpha in this case you should recode the variables in such a way that they all have the same scale (also see: recoding variables). 14

15 HOW TO REPORT THIS Reliability analysis on the three questions measuring job satisfaction showed that W2 and W3 together had a α = When W1 was also included, the α was reduced to 0,44. Therefore, a sum variable was computed using only W2 and W3. GOAL: RECODING VARIABLES How are the questions about autonomy related? Can they be summed to one variable? In this case several steps are of importance. The variables A2 and A3 are interval while A1 is ordinal. Therefore, only A2 and A3 can be summed since you can only sum interval variables. However, the categories for A2 and A3 are opposites (A2 starts with never, while A3 starts with always). This means one of these questions has to be recoded in such a way that they can be summed. TECHNIQUE: RECODE Recode variable A3 in such a way that 1=never and 7=always Transform > Recode into different variables. Important! NEVER choose Recode into same variable since if something goes wrong you will have lost your original data! Move the variable you want to recode to the right box and fill in the new name for your variable (RecA3) under output variable and press change. Next, press Old and New Values. 15

16 Since the old A3 had: 1=always and 7=never and the new A3 should be: 1=never and 7=always, you should fill in 1 at Old Value and 7 at New Value and press add. After that you fill in 2 at Old Value and 6 at New Value and press add. Continue until you recoded all seven levels, then press continue and OK. You have now recoded the variable in such a way that the new variable has: 1= never and 7=always. TECHNIQUE: CRONBACH S ALPHA In order to calculate the Cronbach s Alpha of A2 and A3 you can follow the procedure described in question 3a but instead of W1,W2 and W3 you use the variables A2 and RecA3. SPSS provides the following output: Reliability Statistics Cronbach's Alpha N of Items,871 2 The Cronbach s Alpha is α = 0,871 which is higher than the minimum of 0,6. This means we can conclude the variables A2 and RecA3 can be summed into one variable. Regarding the other variables in the dataset: you can use the same procedure described here. 16

17 STEP 4: MAKING A NEW SUM VARIABLE GOAL: MAKING A SUM VARIABLE After you found out which variables can be summed, you can use SPSS to calculate a new variable for you. First, this will be done for the questions about job satisfaction and after that for the questions about autonomy. TECHNIQUE: SUMMING THE VARIABLES In order to sum W2 and W3: Transform > Compute Variable. Fill in a new name for the variable you are about to make in the field Target Variable. For example: SumW2W3 (to clearly identify this as the sum of W2 and W3; which is also nice if someone else uses your dataset in the future). Next, you can indicate in the right field that you want to sum the two variables: (W2+W3) and click OK. After this you can see your new variable in the dataset (both in the Variable view and the Data view ). TECHNIQUE: AVERAGE Make a new variable for the combination of A2 and RecA3 by taking the average of the two variables. Instead of making a new variable by summing the two (which was done above), the average of the variables is taken instead. We can do this by first summing the variables and then dividing by the number of variables (2 here). An advantage of this method when comparing it to summing the variables is that the 7-point scale is left intact this way which makes the result easier to interpret. Transform > Compute Variable. 17

18 Fill in the new name for the variable you are about to make in the field Target Variable. For example: AvA2A3 and fill the formula for averaging the scores in next (A2+RecA3)/2 and press OK. You can see your new variable in the dataset. 18

19 STEP 5: TECHNIQUE CHOICE GOAL: CHOOSING THE ANALYSIS TECHNIQUE In order to answer the following questions the same steps will be taken each time: 1. What statistical technique is necessary? (You can use the tables in the appendix for this) 2. How can you perform the technique in SPSS and how does the most important output look? 3. How do you report the results? TECHNIQUE: BIG THREE A method for choosing the right technique is the Big Three which are three questions about the data you are using. These questions will also be discussed later on. 1. How many variables are involved in the analysis? One: univariate analysis (descriptive statistics) Two: bivariate analysis (inferential statistics) > Two: multivariate analysis (inferential statistics) 2. What is the data type of the involved variable(s)? Independent variable (X): nominal, ordinal or interval (ratio) Dependent variable (Y): nominal, ordinal or interval (ratio) 3. Asymmetric vs. symmetric? (only for 2 or more variables) Asymmetric: when variables have a different data types or you want to explain the dependent variable based on the independent variable (causal relationship) Symmetric: when there is no need for predicting causal relationships and the variables are of the same data type. HOW TO REPORT THIS? It is important to know that directly copying SPSS output to your report is NOT allowed! You should use the values found in the SPSS output and report them in your own words by using the ABCD-Formula: A. What was the goal? (= WHAT) B. How did you do this? (= HOW) C. Was the test significant? Report this in the right way! (= RESULT) D. What can be concluded from the results? ( = CONCLUSION) In this formula, part A and D must be described in such a way that anyone can understand it. However, part B and C are for people who know about statistics. The best way of reporting the analyses is described in more detail in the results. Even though the letters A until D are also used in the results section, you should never use these in your research paper. 19

20 STEP 6: THE CONTROL VARIABLES GOAL: T-TEST INDEPENDENT SAMPLES The next step is checking the influence of the control variables that were included in the model (in this example: age, gender, religion and education level) on the most important dependent variable (job satisfaction). TECHNIQUE: INDEPENDENT SAMPLES T-TEST Needed technique: the variable gender is nominal and job satisfaction is interval. Furthermore, gender consists of two categories; male and female (k=2). Therefore, we need to use an independent samples t-test to find out whether or not gender influences job satisfaction. SPSS output: Analyze > Compare Means > Independent samples t-test Please make sure you add the new sum variable of job satisfaction in the box Test variable and gender in the box Grouping variable. Press Define groups and fill in a 1 for Group 1 and a 2 for Group 2. Press Continue and then OK. 20

21 SPSS-OUTPUT. Group Statistics Gender N Mean Std. Deviation Std. Error Mean SumW2W3 man 107 7,8037 3,31503,32048 woman 118 8,1525 3,07631,28320 Independent Samples Test Levene's Test for Equality of Variances t-test for Equality of Means F Sig. t df Sig. (2- tailed) Mean Std. Error Difference Difference 95% Confidence Interval of the Difference Lower Upper Sum W2W3 Equal variances assumed Equal variances not assumed,791,375 -, , ,34880, ,18852, , ,551, ,34880, ,19174,49413 HOW TO REPORT THIS? Remember, you cannot use these inconvenient tables in your results section. Please explain the results in words. A. In order to analyze whether or not the average job satisfaction of men is different from the average job satisfaction of women, (=WHAT) B. we performed an independent samples t-test with gender and job satisfaction. (=HOW) C. The independent samples t-test was not significant, t(223) = -0,82, p = 0,414 (=RESULT) D. The average job satisfaction of men (M= 7,8, SD=3,32) does not differ from the average job satisfaction of women (M = 8,1, SD = 3,08). (=CONCLUSION) 21

22 GOAL: LINEAR REGRESSION TECHNIQUE The variables age and job satisfaction are both measured on interval data type. Therefore, we have to use regression analysis in order to examine the influence of age on job satisfaction. Analyze > Regression > Linear Regression Put the sum variable job satisfaction in the dependent field, and age in the independent field, then press OK. SPSS-OUTPUT Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1,022 a,001 -,004 3,19600 a. Predictors: (Constant), Age 22

23 Model Sum of Squares df ANOVA b Mean Square F Sig. 1 Regression 1, ,142,112,738 a Residual 2277, ,214 Total 2278, a. Predictors: (Constant), Age b. Dependent Variable: SumW2W3 Model Unstandardized Coefficients Coefficients a B Std. Error Beta Standardized Coefficients 1 (Constant) 8,210,701 11,719,000 t Sig. Age -,005,016 -,022 -,334,738 a. Dependent Variable: SumW2W3 HOW TO REPORT THIS A. In order to analyze whether or not the age of employees influences their job satisfaction, (=WHAT) B. we performed a regression analysis with age regressed on job satisfaction. (=HOW) C. The regression analysis was not significant, R 2 =0,001, F(1,223) =.11, p =.738. (=RESULT) D. The age of employees does not influence job satisfaction, B = -0,005, t = 11.72, p = (=CONCLUSION). Important! Whenever you use more independent variables (e.g. four) in a so-called multivariate linear regression, the F-test (in the ANOVA table) will display the overall significance of the influence of all these variables together on the dependent variable. If you want to know what variables have a specific effect, you can find this information in the table Coefficients. This is because it is possible that only two of the four regressors have a significant effect which leads to an overall significant F-test. Because this case only considers one independent variable, the significant F-test also means our sole predictor significantly predicts the dependent variable. 23

24 GOAL: ONE-WAY ANOVA TECHNIQUE The variable education level is ordinal while job satisfaction is interval. Unfortunately, there is no statistical test available for this combination of variables. However, in this case it is the easiest to assume the variable education level is nominal (remember, you can always make the transition to a lower data type, but never from low to high). This means you get an independent variable of more than two categories which leads to a one-way ANOVA. SPSS output: Analyze > Compare Means > One-way ANOVA Input the sum variable for job satisfaction in the dependent list and education level in factor. Tick the box descriptives under Options which provides the means of all treatment levels of the independent variable. SPSS- OUTPUT SumW2W3 Sum of Squares df Mean Square F Sig. Between Groups 17, ,672,554,646 Within Groups 2261, ,235 Total 2278,

25 Descriptives SumW2W3 95% Confidence Interval for Mean Lower Upper N Mean Std. Deviation Std. Error Bound Bound Minimum Maximum Primary school 43 8,35 3,309,505 7,33 9, Secondary school 72 8,01 3,270,385 7,25 8, College 72 7,62 2,971,350 6,93 8, University 38 8,21 3,354,544 7,11 9, Total 225 7,99 3,190,213 7,57 8, HOW TO REPORT THIS? A. In order to analyze whether or not the job satisfaction of employees differs per education level, (=WHAT) B. we performed a One-way ANOVA of education level on job satisfaction. ( = HOW) C. This One-way ANOVA was not significant, F(3, 221) = 0,55, p = 0,65 ( = RESULT) D. The education level of employees does not influence their job satisfaction. ( = CONCLUSION) GOAL: ONE-WAY ANOVA (2) TECHNIQUE Needed technique: the variable religion is nominal (with more than two categories, so k>2) and job satisfaction is interval. Therefore, we have to use a One-way ANOVA to find out whether or not religion influences job satisfaction. SPSS output: Analyze > Compare Means > One-way ANOVA. 25

26 Input the sum variable for job satisfaction in the dependent list and relgion in factor. Tick the box descriptives under Options which displays the means of your treatment levels, then press OK. SPSS-OUTPUT ANOVA Descriptives SomW2W3 95% Confidence Interval for Mean N Mean Std. Deviation Std. Error Lower Bound Upper Bound Minimum Maximum reformed 14 8,21 3,017,806 6,47 9, catholic 28 7,93 3,344,632 6,63 9, hindoeism 48 8,44 3,814,551 7,33 9, muslim 48 8,15 2,552,368 7,40 8, jewish 46 8,11 3,261,481 7,14 9, atheist 28 7,61 3,095,585 6,41 8, other 13 6,00 2,309,641 4,60 7, Total 225 7,99 3,190,213 7,57 8, SumW2W3 Sum of Squares df Mean Square F Sig. Between Groups 67, ,303 1,114,355 Within Groups 2211, ,143 Total 2278, HOW TO REPORT THIS A. In order to analyze whether or not the job satisfaction of employees differs per religion, (=WHAT) B. we performed a One-way ANOVA of religion on job satisfaction. ( = HOW) C. This One-way ANOVA was not significant, F(6, 218) = 1,11, p = 0,355 ( = RESULT) D. The religion of employees does not influence their job satisfaction. ( = CONCLUSION) 26

27 STEP 7: TESTING THE HYPOTHESIS After checking the control variables, it is now time to examine the effect of the independent variable on the dependent variable. This will be done by using the aforementioned hypothesis. Unfortunately it is not possible to test the influence of a nominal variable on an ordinal variable due to a mistake in an earlier version of this SPSS guide involving the conceptual model and the dataset. Therefore, an example that was NOT included in the conceptual model will be used to show how this test is performed, even though there is no theoretical grounding for this research question. The variables that are referred to here are religion and autonomy. Does religion have an influence on the degree of autonomy people experience during their job? One of the questions for autonomy (A1) is ordinal and religion is nominal with more than two categories (K=7). Therefore, a Kruskal-Wallis test has to be performed here. GOAL: KRUSKAL WALLIS TEST What is the effect of religion on the variable How often is it necessary to explain yourself beforehand to a superior about the tasks that have to be performed? (A1) TECHNIQUE The variable religion is nominal (k>2) and autonomy A1 is ordinal. Therefore the Kruskal- Wallis test is used to determine the influence of religion on autonomy. Analyze > Nonparametric Tests > K Independent Samples Put the autonomy variable A1 in Test Variable List and religion in Grouping Variable, then click Define Range. Because religion has seven categories, you fill in a 1 at minimum and a 7 at maximum. Then press Continue and OK. 27

28 SPSS-OUTPUT Test Statistics a,b A1 Chi-Square 2,520 df 6 Asymp. Sig.,866 a. Kruskal Wallis Test b. Grouping Variable: religie HOW TO REPORT THIS A. In order to analyze whether people with a different religion differ in the degree of experience autonomy, (= WHAT) B. we performed a Kruskal-Wallis test with religion on autonomy. (= HOW) C. This Kruskal-Wallis test was not significant, Chi-Square(6) = 2,52, p = 0,866 (=RESULT) D. People with a different religion do not differ in experienced autonomy. (=CONCLUSION) NB When the test is significant you can find frequency tables for the observed autonomy per religion through the crosstabs option. You can report these to show the significant difference. 28

29 GOAL: LINEAR REGRESSION (2) What is the effect of the sum variable of autonomy on job satisfaction? TECHNIQUE The sum variable of autonomy and job satisfaction are both interval variables, therefore we can use a regression analysis to examine the influence of autonomy on job satisfaction. Analyze > Regression > Linear SPSS-OUTPUT Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1,919 a,844,843 1,26341 a. Predictors: (Constant), MeanA2A3 29

30 ANOVA b Model Sum of Squares df Mean Square F Sig. 1 Regression 1923, , ,746,000 a Residual 355, ,596 Total 2278, a. Predictors: (Constant), MeanA2A3 b. Dependent Variable: SumW2W3 Coefficients a Model Unstandardized Coefficients B Std. Error Beta Standardized Coefficients 1 (Constant),545,230 2,364,019 MeanA2A3 1,934,056,919 34,709,000 a. Dependent Variable: SumW2W3 t Sig. HOW TO REPORT THIS? A. In order to analyze whether or not a higher autonomy leads to a higher job satisfaction, (=WHAT) B. we performed a regression analysis of autonomy on job satisfaction, (=HOW) C. The results of this regression, R 2 = 0,84, F(1,224) = , p =.000 reveal a significant effect. There is a positive relationship between autonomy and job satisfaction B = 1.93, t(224) = 34,70, p <.001. (=RESULT) D. A higher autonomy of employees does lead to a significantly higher job satisfaction. (CONCLUSION) 30

31 GOAL: PAIRED SAMPLES T-TEST Imagine that Solar Energy Plc decided to raise the autonomy of their employees based on past research within the company. A year after these changes have taken place, job satisfaction is measured again. Test whether or not job satisfaction has risen the past year. Mind you, the measurement of the second year has not yet been summed, make sure this is allowed. TECHNIQUE Before we can compare the original sum variable of job satisfaction with the new one, a sum variable for the second year has to be made (in the same way as the First one). Check if W2later and W3later correlate significantly (which is in fact true, see table below) and if the Cronbach s Alpha is sufficiently high to sum the variables (which is in fact true; Cronbach s Alpha is 0,974, see table below). Next, you can sum the variables in the same way as assignment 3a: (W2later+W3later). SPSS-OUTPUT Correlations W2later W3later W2later Pearson Correlation 1,000,950 ** Sig. (2-tailed),000 N 225, W3later Pearson Correlation,950 ** 1,000 Sig. (2-tailed),000 N ,000 **. Correlation is significant at the 0.01 level (2- tailed). **. Correlation is significant at the 0.01 level (2- tailed). Reliability Statistics Cronbach's Alpha N of Items,

32 TECHNIQUE We are dealing with two related samples that have to be compared here, because every person answered the same questions twice. The first time he/she answered the questions influence the second time he/she answered the questions which means the samples are related and we have to use the paired sample t-test. Analyze > Compare Means > Paired samples t-test Drag the old job satisfaction variable (SumW2W3) to variable 1 and the new job satisfaction variable (SumW2laterW3later) to variable 2, then press OK. NB. You could input additional pairs of variables here if you wanted to. However, since we only have one pair here, this is not relevant for this analysis. SPSS-OUTPUT Paired Samples Statistics Mean N Std. Deviation Std. Error Mean Pair 1 SumW2W3 7, ,190,213 SumW2laterW3later 9, ,042,203 Paired Samples Test Pair 1 SumW2W3 - SumW2laterW3later Paired Differences Mean Std. Std. Error Deviation Mean 95% Confidence Interval of the Difference Lower Upper t df Sig. (2- tailed) -1,91111,43416, , , , ,000 32

33 HOW TO REPORT THIS? A. In order to analyze whether or not job satisfaction has risen in the last year, (=WHAT) B. we performed a paired samples t-test on the original job satisfaction variable and the new one. (=HOW) C. The paired samples t test was significant, t(224) = -66,03, p <.001 (=RESULT) D. Job satisfaction did significantly rise this year, from M=7,99 to M=9,90 a year later (=CONCLUSION).* *it is important to note here that it is not possible to proof whether or not the increase is due to the increase in autonomy based on this test! Another test would have to be performed which includes both measurement moments of autonomy too. GOAL: CROSS-TABLE WITH CHI-SQUARE Imagine another question was posed regarding job satisfaction, namely are you satisfied with your job? 1=yes, 2=no and we wanted to find out whether or not gender influences this question? Perform the appropriate analysis and report the results. TECHNIQUE The relevant variables are both nominal, therefore a Chi-square with cross table has to be used. Analyze > Descriptive Statistics > Crosstabs Drag gender to Row and the T (the other question about job satisfaction) to Column. Then press Statistics in the top right and click the box Chi-square. Press Continue and then Cells, tick the boxes Row and Column in the Percentages heading. Then press Continue and OK. 33

34 SPSS-OUTPUT gender * T Crosstabulation T 1 2 Total gender man Count % within geslacht 94,4% 5,6% 100,0% % within T 87,8% 5,5% 47,6% women Count % within geslacht 11,9% 88,1% 100,0% % within T 12,2% 94,5% 52,4% Total Count % within geslacht 51,1% 48,9% 100,0% % within T 100,0% 100,0% 100,0% Chi-Square Tests Value Pearson Chi-Square 152,954 a 1,000 Continuity Correction b 149,669 1,000 Likelihood Ratio 179,621 1,000 df Asymp. Sig. (2- sided) Exact Sig. (2- sided) Fisher's Exact Test,000,000 Linear-by-Linear Association N of Valid Cases ,274 1,000 a. 0 cells (,0%) have expected count less than 5. The minimum expected count is 52,31. b. Computed only for a 2x2 table Exact Sig. (1- sided) NB. If the value in an SPSS table is shown with an E in it, double click the table in the SPSS output and widen the column of Value a bit. HOW TO REPORT THIS? A. In order to analyze whether or not man and women differ concerning their job satisfaction, (=WHAT) B. we performed a cross table with Chi-square with gender and job satisfaction (1=yes, 2=no) (=HOW) C. The Chi-square test was significant, Chi-Square(1) = 152,95, p <.001. (=RESULT) D. Men are more often satisfied with their job (94,4%) than women (11,9%). (=CONCLUSION) 34

35 GOAL: MANN-WHITNEY U-TEST Imagine one of the researchers working on this report is bored and wants to know if gender influences education level. Even though it is not in the conceptual model and he has no theory to suspect there is a difference (and how the difference would look), he still decides to find out if there is a relationship. Therefore, we have to find out if there is a difference between men and women concerning their education level. TECHNIQUE We are dealing with a nominal independent variable (gender, k = 2) and an ordinal dependent variable education level, which means a Mann-Whitney U-test is appropriate. SPSS output: Analyze > Nonparametric tests > 2 independent samples Input education level in the Testing variable box and gender in the Grouping variable one. Press define groups and indicate Group 1 equals 1 and Group 2 equals 2. Press Continue and then OK. 35

36 SPSS-OUTPUT Ranks Education level gender N Mean Rank Sum of Ranks , , , ,00 Total 225 Test Statistics a Education level Mann-Whitney U 5485,000 Wilcoxon W 11263,000 Z -1,768 Asymp. Sig. (2-tailed),077 a. Grouping Variable: gender The test shows that the Mean Ranks appear to differ from each other (105 vs 120), but using a α =.05 the difference is not significant. Since you can observe a trend in this case, you could describe the effect as marginally significant. NB All p-values above.10 cannot be described as such. Since it is not possible to determine the medians of both groups (namely the median of men and women) in this menu, you have to determine these yourself in SPSS. In order to do this, first select only the male subjects in your dataset. Go to Data > Select Cases. Press the button if condition is satisfied under select and press if next. Indicate that you only want to select people that scored a 1 on the variable gender: gender=1 and press Continue, then OK. NB Always make sure you filter out unselected cases (option in the Output section) which will make sure the unselected cases are not deleted but simply kept out of the analyses. 36

37 You can now get the median of education level through Analyze > Frequencies. Since only men are selected at the moment, the median only applies to the male group, which will indicate the median is 2 (secondary school). In order to determine the median of women, you go back to data > select cases > if... and indicate that you want to use people that scored 2 now: gender = 2 and press Continue, then OK. If you ask SPSS to determine the median through Frequencies, the median of the female group will be displayed, which is 3 (College). HOW TO REPORT THIS? A. In order to analyze if men and women differ regarding their education level, (= WHAT) B. we performed a Mann-Whitney U-test. (=HOW) C. This test was marginally significant, MWU = 5485, p =.077. (=RESULT) D. Men have a lower education level (MR = 105.3; median = Secondary school) than women (MR = 120.0; median = College). (= CONCLUSION) GOAL: MANOVA If you want to examine multiple dependent variables at once as a researcher, you can use the Multivariate Analysis of Variance (MANOVA). This is especially useful when one or more of your variables are not interval and can be used to answer questions like: do job satisfaction and autonomy of employees differ per age category? 37

38 TECHNIQUE: MANOVA We are dealing with two dependent variables and 1 independent variable. All variables are measured on the interval data type. Analyze >General Linear Model > Multivariate The dependent variables SumW2W3 and mean A2A3 are put in Dependent variables and age in Fixed factor. Press Model and tick Full factorial with Sum of squares Type III, then press continue. Press Options, in order to get extra means with the analyses tick Descriptive statistics, Parameter estimates and Homogeneity test. Press Continue, then OK. 38

39 SPSS-OUTPUT Multivariate Tests c Effect Value F Hypothesis df Error df Sig. Intercept Pillai's Trace, ,792 a 2, ,000,000 Wilks' Lambda, ,792 a 2, ,000,000 Hotelling's Trace 5, ,792 a 2, ,000,000 Roy's Largest Root 5, ,792 a 2, ,000,000 leeftijd Pillai's Trace,318,752 90, ,000,948 Wilks' Lambda,705,754 a 90, ,000,946 Hotelling's Trace,384,755 90, ,000,945 Roy's Largest Root,251 1,000 b 45, ,000,481 a. Exact statistic b. The statistic is an upper bound on F that yields a lower bound on the significance level. c. Design: Intercept + age 39

40 Source Dependent Variable Tests of Between-Subjects Effects Type III Sum of Squares df Mean Square F Sig. Corrected Model SumW2W3 269,302 a 45 5,984,533,993 MeanA2A3 64,011 b 45 1,422,565,987 Intercept SumW2W , , ,815,000 MeanA2A3 2379, , ,908,000 leeftijd SumW2W3 269, ,984,533,993 MeanA2A3 64, ,422,565,987 Error SumW2W3 2009, ,227 MeanA2A3 450, ,516 Total SumW2W , MeanA2A3 3847, Corrected Total SumW2W3 2278, MeanA2A3 514, a. R Squared =,118 (Adjusted R Squared = -,104) HOW TO REPORT THIS? When interpreting a MANOVA, first look at multivariate effects. These describe if the independent variables have an effect on all dependent variables. Four different statistics are used to interpret this, (Pillai's Trace and Wilk's Lambda, Roy's largest root and Hotelling's Trace) which all use a slightly different calculation. Normally, it is best to use Wilk s Lambda because it shows the amount of unexplained variance (the opposite of the R 2 ). Only if a multivariate effect was found specific univariate effects are relevant. You can do this in the table with univariate results that automatically comes after the multivariate table, and look at the relevant independent variables there. 40

41 A. In order to analyze whether or not the degree of job satisfaction and autonomy of employees differs per age (=WHAT) B. we performed a Multivariate Analysis of Variance. (=HOW) C. This test was not significant at all, F (90,356)= 0,754, p =0,946. (=RESULT) D. Apparently there is no difference in job satisfaction and autonomy for employees of different ages. Therefore, it is unnecessary to interpret the univariate analysis. (= CONCLUSION) GOAL: TWO-WAY ANOVA Besides the One-Way ANOVA there is also the Two-Way ANOVA which is used when you want to perform an analysis of variance with two independent variables. In this case, autonomy and need for structure were chosen as the independent variables. Both variables will be split based on the median ( median split ). The dependent variable is, again, job satisfaction. The question is whether or not there is a difference in job satisfaction for employees with a high or low autonomy and employees with a high or low need for structure. TECHNIQUE: SPLITTING This test is often used when you have two independent variables on nominal data type. An example of this could be an experiment in which you manipulated power (high vs low) and valence (win vs lose) and want to find out how these factors influence negotiating behavior. In this case it is unnecessary to split, since they are already nominal! However, in this case it is needed to split the two independent variables based on their medians. The median can be found through Descriptives and splitting them goes as follows: Transform > Compute Variable Indicate how you want to name the new variable in Target Variable and press if. This allows you to specify how you want to split the variable. Press Continue and provide a new value for the variable. After splitting both variables in two groups, the Two-Way ANOVA can be performed. 41

42 42

43 TECHNIQUE: TWO-WAY ANOVA Analyze > General Linear Model > Univariate Input the (in)dependent variables and press Model. Specify the model as Full factor with sum of squares Type III, then press Continue. 43

44 Tick the box descriptive statistics at Options so the marginal and cellmeans are displayed. Then press Contrast and change the factors to simple contrasts, don t forget to press Change and press continue. There are several contrasts you can use here. More information about this can be found in advanced statistics books. Next, indicate that you want a plot of the main effect as well as the interaction effect in the Plot section. Then press Continue and OK. 44

45 SPSS-OUTPUT Descriptive Statistics Dependent Variable:SumW2W3 SplitA SplitS Mean Std. Deviation N Low Autonomy Low Need for Structure 5,26 1, High Need for Structure 5,33 1, Total 5,30 1, High Autonomy Low Need for Structure 8,37, High Need for Structure 11,05 1, Total 10,61 1, Total Low Need for Structure 6,04 2, High Need for Structure 8,98 3, Total 7,99 3, Dependent Variable:SumW2W3 Tests of Between-Subjects Effects Source Type III Sum of Squares df Mean Square F Sig. Corrected Model 1698,749 a 3 566, ,682,000 Intercept 9081, , ,048,000 SplitA 784, , ,946,000 SplitS 76, ,463 29,124,000 SplitA * SplitS 68, ,869 26,232,000 Error 580, ,625 Total 16631, Corrected Total 2278, a. R Squared =,745 (Adjusted R Squared =,742) 45

46 Test Results Dependent Variable:SumW2W3 Source Sum of Squares df Mean Square F Sig. Contrast 784, , ,946,000 Error 580, ,625 HOW TO REPORT THIS? Before you report anything (in a Two-Way design) about the main effect of both variables, it is important to first look at the interaction effects. When the two lines in the graph cross each other, an interaction effect is usually present. This means the effect of autonomy on job satisfaction is influenced by their need for structure. Employees with a high autonomy and a high need for structure have a higher job satisfaction than employees with high autonomy and a low need for structure. Use the sample means to describe this effect! A. In order to analyze the influence of autonomy and need for structure on job satisfaction of employees, (=WHAT) B. we performed a 2 (autonomy: low vs. high) x 2 (need for structure: low vs. high) ANOVA on job satisfaction. (=HOW) C. Both main effects proved to be significant. A high autonomy leads to a higher job satisfaction (M = 10.61) than low autonomy (M = 5.30), F(1,221)= 298,95, p < 0,001. Also, a high need for structure leads to more job satisfaction (M = 8.98) than a low need for structure (M = 6.04), F (1,221)= 29,124, p < 0,001. The interaction effect also appeared significant, F (1,221)= 26,232, p < 0,001. However, for people with a low score for autonomy, it does not matter if they have a high need for structure, because in both cases they have a low score for job satisfaction (Mlow need for structure = 5.26 en M high need for structure = 5.33). Furthermore, for people with a high score for autonomy, need for structure does make a 46

47 difference regarding their score for job satisfaction. Especially people with a high need for structure are very satisfied with their job (M = 11.05) when compared to people with a low need for structure(m = 8.37). (=RESULT) D. The most important conclusion is that the need for structure is not influential for people with a low score for autonomy. However, for people with a high score on autonomy, this effect is present; especially people with a high need for structure are very satisfied with their job. (=CONCLUSION) Figure 1. Autonomy and need for structure on job satisfaction Low need for structure High need for structure 2 0 Low autonomy High autonomy 47

48 APPENDIX TABLES FOR UNIVARIATE AND BIVARIATE ANALYSES Univariate analyses Nominal Ordinal Interval Central tendency Mode Median Mean Distribution Range (not very precise) Standard deviation Bivariate analyses: symmetric vs. asymmetric Asymmetric when: 1) variables have different measurement scales OR 2) predict DV based on IV Symmetric bivariate analyses (X X) X X Nominal Ordinal Interval Nominal Cross table with Chisquare test of independence Ordinal Spearman Rank correlation coefficient Interval Pearson correlation coefficient 48

### 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

### 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 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,

### 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

### Data Analysis for Marketing Research - Using SPSS

North South University, School of Business MKT 63 Marketing Research Instructor: Mahmood Hussain, PhD Data Analysis for Marketing Research - Using SPSS Introduction In this part of the class, we will learn

### 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...

### 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)

### The Chi-Square Test. STAT E-50 Introduction to Statistics

STAT -50 Introduction to Statistics The Chi-Square Test The Chi-square test is a nonparametric test that is used to compare experimental results with theoretical models. That is, we will be comparing observed

### 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

### Instructions for SPSS 21

1 Instructions for SPSS 21 1 Introduction... 2 1.1 Opening the SPSS program... 2 1.2 General... 2 2 Data inputting and processing... 2 2.1 Manual input and data processing... 2 2.2 Saving data... 3 2.3

### DESCRIPTIVE STATISTICS. The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses.

DESCRIPTIVE STATISTICS The purpose of statistics is to condense raw data to make it easier to answer specific questions; test hypotheses. DESCRIPTIVE VS. INFERENTIAL STATISTICS Descriptive To organize,

### Data Analysis Tools. Tools for Summarizing Data

Data Analysis Tools This section of the notes is meant to introduce you to many of the tools that are provided by Excel under the Tools/Data Analysis menu item. If your computer does not have that tool

### 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

### Introduction to Regression and Data Analysis

Statlab Workshop Introduction to Regression and Data Analysis with Dan Campbell and Sherlock Campbell October 28, 2008 I. The basics A. Types of variables Your variables may take several forms, and it

### 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 Data. Organizing Data Files in SPSS. Descriptive Statistics

Analysis of Data Claudia J. Stanny PSY 67 Research Design Organizing Data Files in SPSS All data for one subject entered on the same line Identification data Between-subjects manipulations: variable to

### Data exploration with Microsoft Excel: analysing more than one variable

Data exploration with Microsoft Excel: analysing more than one variable Contents 1 Introduction... 1 2 Comparing different groups or different variables... 2 3 Exploring the association between categorical

### An introduction to using Microsoft Excel for quantitative data analysis

Contents An introduction to using Microsoft Excel for quantitative data analysis 1 Introduction... 1 2 Why use Excel?... 2 3 Quantitative data analysis tools in Excel... 3 4 Entering your data... 6 5 Preparing

### 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

### 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 7: Simple linear regression Learning Objectives

Chapter 7: Simple linear regression Learning Objectives Reading: Section 7.1 of OpenIntro Statistics Video: Correlation vs. causation, YouTube (2:19) Video: Intro to Linear Regression, YouTube (5:18) -

### 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

### Assumptions. Assumptions of linear models. Boxplot. Data exploration. Apply to response variable. Apply to error terms from linear model

Assumptions Assumptions of linear models Apply to response variable within each group if predictor categorical Apply to error terms from linear model check by analysing residuals Normality Homogeneity

### ASSIGNMENT 4 PREDICTIVE MODELING AND GAINS CHARTS

DATABASE MARKETING Fall 2015, max 24 credits Dead line 15.10. ASSIGNMENT 4 PREDICTIVE MODELING AND GAINS CHARTS PART A Gains chart with excel Prepare a gains chart from the data in \\work\courses\e\27\e20100\ass4b.xls.

### 1. What is the critical value for this 95% confidence interval? CV = z.025 = invnorm(0.025) = 1.96

1 Final Review 2 Review 2.1 CI 1-propZint Scenario 1 A TV manufacturer claims in its warranty brochure that in the past not more than 10 percent of its TV sets needed any repair during the first two years

### Multiple Regression in SPSS This example shows you how to perform multiple regression. The basic command is regression : linear.

Multiple Regression in SPSS This example shows you how to perform multiple regression. The basic command is regression : linear. In the main dialog box, input the dependent variable and several predictors.

### 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

### NCSS Statistical Software Principal Components Regression. In ordinary least squares, the regression coefficients are estimated using the formula ( )

Chapter 340 Principal Components Regression Introduction is a technique for analyzing multiple regression data that suffer from multicollinearity. When multicollinearity occurs, least squares estimates

### 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

Bowerman, O'Connell, Aitken Schermer, & Adcock, Business Statistics in Practice, Canadian edition Online Learning Centre Technology Step-by-Step - Excel Microsoft Excel is a spreadsheet software application

### business statistics using Excel OXFORD UNIVERSITY PRESS Glyn Davis & Branko Pecar

business statistics using Excel Glyn Davis & Branko Pecar OXFORD UNIVERSITY PRESS Detailed contents Introduction to Microsoft Excel 2003 Overview Learning Objectives 1.1 Introduction to Microsoft Excel

### DESCRIPTIVE STATISTICS AND EXPLORATORY DATA ANALYSIS

DESCRIPTIVE STATISTICS AND EXPLORATORY DATA ANALYSIS SEEMA JAGGI Indian Agricultural Statistics Research Institute Library Avenue, New Delhi - 110 012 seema@iasri.res.in 1. Descriptive Statistics Statistics

### 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

### COMPARISONS OF CUSTOMER LOYALTY: PUBLIC & PRIVATE INSURANCE COMPANIES.

277 CHAPTER VI COMPARISONS OF CUSTOMER LOYALTY: PUBLIC & PRIVATE INSURANCE COMPANIES. This chapter contains a full discussion of customer loyalty comparisons between private and public insurance companies

### UNDERSTANDING THE INDEPENDENT-SAMPLES t TEST

UNDERSTANDING The independent-samples t test evaluates the difference between the means of two independent or unrelated groups. That is, we evaluate whether the means for two independent groups are significantly

### Data Analysis. Using Excel. Jeffrey L. Rummel. BBA Seminar. Data in Excel. Excel Calculations of Descriptive Statistics. Single Variable Graphs

Using Excel Jeffrey L. Rummel Emory University Goizueta Business School BBA Seminar Jeffrey L. Rummel BBA Seminar 1 / 54 Excel Calculations of Descriptive Statistics Single Variable Graphs Relationships

### Statistics Review PSY379

Statistics Review PSY379 Basic concepts Measurement scales Populations vs. samples Continuous vs. discrete variable Independent vs. dependent variable Descriptive vs. inferential stats Common analyses

### 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

### SPSS Resources. 1. See website (readings) for SPSS tutorial & Stats handout

Analyzing Data SPSS Resources 1. See website (readings) for SPSS tutorial & Stats handout Don t have your own copy of SPSS? 1. Use the libraries to analyze your data 2. Download a trial version of SPSS

### Section Format Day Begin End Building Rm# Instructor. 001 Lecture Tue 6:45 PM 8:40 PM Silver 401 Ballerini

NEW YORK UNIVERSITY ROBERT F. WAGNER GRADUATE SCHOOL OF PUBLIC SERVICE Course Syllabus Spring 2016 Statistical Methods for Public, Nonprofit, and Health Management Section Format Day Begin End Building

### Statistical Analysis Using SPSS for Windows Getting Started (Ver. 2014/11/6) The numbers of figures in the SPSS_screenshot.pptx are shown in red.

Statistical Analysis Using SPSS for Windows Getting Started (Ver. 2014/11/6) The numbers of figures in the SPSS_screenshot.pptx are shown in red. 1. How to display English messages from IBM SPSS Statistics

### Introduction Course in SPSS - Evening 1

ETH Zürich Seminar für Statistik Introduction Course in SPSS - Evening 1 Seminar für Statistik, ETH Zürich All data used during the course can be downloaded from the following ftp server: ftp://stat.ethz.ch/u/sfs/spsskurs/

### 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

### 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

### SPSS Manual for Introductory Applied Statistics: A Variable Approach

SPSS Manual for Introductory Applied Statistics: A Variable Approach John Gabrosek Department of Statistics Grand Valley State University Allendale, MI USA August 2013 2 Copyright 2013 John Gabrosek. All

### The Statistics Tutor s Quick Guide to

statstutor community project encouraging academics to share statistics support resources All stcp resources are released under a Creative Commons licence The Statistics Tutor s Quick Guide to Stcp-marshallowen-7

T O P I C 1 2 Techniques and tools for data analysis Preview Introduction In chapter 3 of Statistics In A Day different combinations of numbers and types of variables are presented. We go through these

### Chapter 7. One-way ANOVA

Chapter 7 One-way ANOVA One-way ANOVA examines equality of population means for a quantitative outcome and a single categorical explanatory variable with any number of levels. The t-test of Chapter 6 looks

### Students' Opinion about Universities: The Faculty of Economics and Political Science (Case Study)

Cairo University Faculty of Economics and Political Science Statistics Department English Section Students' Opinion about Universities: The Faculty of Economics and Political Science (Case Study) Prepared

### Chapter 13 Introduction to Linear Regression and Correlation Analysis

Chapter 3 Student Lecture Notes 3- Chapter 3 Introduction to Linear Regression and Correlation Analsis Fall 2006 Fundamentals of Business Statistics Chapter Goals To understand the methods for displaing

### Simple Linear Regression Inference

Simple Linear Regression Inference 1 Inference requirements The Normality assumption of the stochastic term e is needed for inference even if it is not a OLS requirement. Therefore we have: Interpretation

### One-Way Analysis of Variance

One-Way Analysis of Variance Note: Much of the math here is tedious but straightforward. We ll skim over it in class but you should be sure to ask questions if you don t understand it. I. Overview A. We

### Basic Statistics and Data Analysis for Health Researchers from Foreign Countries

Basic Statistics and Data Analysis for Health Researchers from Foreign Countries Volkert Siersma siersma@sund.ku.dk The Research Unit for General Practice in Copenhagen Dias 1 Content Quantifying association

### DISCRIMINANT FUNCTION ANALYSIS (DA)

DISCRIMINANT FUNCTION ANALYSIS (DA) John Poulsen and Aaron French Key words: assumptions, further reading, computations, standardized coefficents, structure matrix, tests of signficance Introduction Discriminant

CHAPTER 9 ADD-INS: ENHANCING EXCEL This chapter discusses the following topics: WHAT CAN AN ADD-IN DO? WHY USE AN ADD-IN (AND NOT JUST EXCEL MACROS/PROGRAMS)? ADD INS INSTALLED WITH EXCEL OTHER ADD-INS

### Biostatistics: Types of Data Analysis

Biostatistics: Types of Data Analysis Theresa A Scott, MS Vanderbilt University Department of Biostatistics theresa.scott@vanderbilt.edu http://biostat.mc.vanderbilt.edu/theresascott Theresa A Scott, MS

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

### Analysis of categorical data: Course quiz instructions for SPSS

Analysis of categorical data: Course quiz instructions for SPSS The dataset Please download the Online sales dataset from the Download pod in the Course quiz resources screen. The filename is smr_bus_acd_clo_quiz_online_250.xls.

### 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

### A Basic Guide to Analyzing Individual Scores Data with SPSS

A Basic Guide to Analyzing Individual Scores Data with SPSS Step 1. Clean the data file Open the Excel file with your data. You may get the following message: If you get this message, click yes. Delete

### 5 Correlation and Data Exploration

5 Correlation and Data Exploration Correlation In Unit 3, we did some correlation analyses of data from studies related to the acquisition order and acquisition difficulty of English morphemes by both

### Multivariate analyses

14 Multivariate analyses Learning objectives By the end of this chapter you should be able to: Recognise when it is appropriate to use multivariate analyses (MANOVA) and which test to use (traditional

### Mathematics within the Psychology Curriculum

Mathematics within the Psychology Curriculum Statistical Theory and Data Handling Statistical theory and data handling as studied on the GCSE Mathematics syllabus You may have learnt about statistics and

### Profile analysis is the multivariate equivalent of repeated measures or mixed ANOVA. Profile analysis is most commonly used in two cases:

Profile Analysis Introduction Profile analysis is the multivariate equivalent of repeated measures or mixed ANOVA. Profile analysis is most commonly used in two cases: ) Comparing the same dependent variables

EC151.02 Statistics for Business and Economics (MWF 8:00-8:50) Instructor: Chiu Yu Ko Office: 462D, 21 Campenalla Way Phone: 2-6093 Email: kocb@bc.edu Office Hours: by appointment Description This course

### Exercise 1.12 (Pg. 22-23)

Individuals: The objects that are described by a set of data. They may be people, animals, things, etc. (Also referred to as Cases or Records) Variables: The characteristics recorded about each individual.

### Introduction to StatsDirect, 11/05/2012 1

INTRODUCTION TO STATSDIRECT PART 1... 2 INTRODUCTION... 2 Why Use StatsDirect... 2 ACCESSING STATSDIRECT FOR WINDOWS XP... 4 DATA ENTRY... 5 Missing Data... 6 Opening an Excel Workbook... 6 Moving around

### Testing Group Differences using T-tests, ANOVA, and Nonparametric Measures

Testing Group Differences using T-tests, ANOVA, and Nonparametric Measures Jamie DeCoster Department of Psychology University of Alabama 348 Gordon Palmer Hall Box 870348 Tuscaloosa, AL 35487-0348 Phone:

### TIPS FOR DOING STATISTICS IN EXCEL

TIPS FOR DOING STATISTICS IN EXCEL Before you begin, make sure that you have the DATA ANALYSIS pack running on your machine. It comes with Excel. Here s how to check if you have it, and what to do if you

### Moving from SPSS to JMP : A Transition Guide

WHITE PAPER Moving from SPSS to JMP : A Transition Guide Dr. Jason Brinkley, Department of Biostatistics, East Carolina University Table of Contents Introduction... 1 Example... 2 Importing and Cleaning

### Survey Research Data Analysis

Survey Research Data Analysis Overview Once survey data are collected from respondents, the next step is to input the data on the computer, do appropriate statistical analyses, interpret the data, and

### Gamma Distribution Fitting

Chapter 552 Gamma Distribution Fitting Introduction This module fits the gamma probability distributions to a complete or censored set of individual or grouped data values. It outputs various statistics

### Working with SPSS. A Step-by-Step Guide For Prof PJ s ComS 171 students

Working with SPSS A Step-by-Step Guide For Prof PJ s ComS 171 students Contents Prep the Excel file for SPSS... 2 Prep the Excel file for the online survey:... 2 Make a master file... 2 Clean the data

### Normality Testing in Excel

Normality Testing in Excel By Mark Harmon Copyright 2011 Mark Harmon No part of this publication may be reproduced or distributed without the express permission of the author. mark@excelmasterseries.com

### Reporting Statistics in Psychology

This document contains general guidelines for the reporting of statistics in psychology research. The details of statistical reporting vary slightly among different areas of science and also among different

### Class 19: Two Way Tables, Conditional Distributions, Chi-Square (Text: Sections 2.5; 9.1)

Spring 204 Class 9: Two Way Tables, Conditional Distributions, Chi-Square (Text: Sections 2.5; 9.) Big Picture: More than Two Samples In Chapter 7: We looked at quantitative variables and compared the

### Silvermine House Steenberg Office Park, Tokai 7945 Cape Town, South Africa Telephone: +27 21 702 4666 www.spss-sa.com

SPSS-SA Silvermine House Steenberg Office Park, Tokai 7945 Cape Town, South Africa Telephone: +27 21 702 4666 www.spss-sa.com SPSS-SA Training Brochure 2009 TABLE OF CONTENTS 1 SPSS TRAINING COURSES FOCUSING

### How To Run Statistical Tests in Excel

How To Run Statistical Tests in Excel Microsoft Excel is your best tool for storing and manipulating data, calculating basic descriptive statistics such as means and standard deviations, and conducting

### Lecture 2: Descriptive Statistics and Exploratory Data Analysis

Lecture 2: Descriptive Statistics and Exploratory Data Analysis Further Thoughts on Experimental Design 16 Individuals (8 each from two populations) with replicates Pop 1 Pop 2 Randomly sample 4 individuals

### SPSS-Applications (Data Analysis)

CORTEX fellows training course, University of Zurich, October 2006 Slide 1 SPSS-Applications (Data Analysis) Dr. Jürg Schwarz, juerg.schwarz@schwarzpartners.ch Program 19. October 2006: Morning Lessons

### DESCRIPTIVE STATISTICS & DATA PRESENTATION*

Level 1 Level 2 Level 3 Level 4 0 0 0 0 evel 1 evel 2 evel 3 Level 4 DESCRIPTIVE STATISTICS & DATA PRESENTATION* Created for Psychology 41, Research Methods by Barbara Sommer, PhD Psychology Department

### TI-Inspire manual 1. Instructions. Ti-Inspire for statistics. General Introduction

TI-Inspire manual 1 General Introduction Instructions Ti-Inspire for statistics TI-Inspire manual 2 TI-Inspire manual 3 Press the On, Off button to go to Home page TI-Inspire manual 4 Use the to navigate

### When to Use a Particular Statistical Test

When to Use a Particular Statistical Test Central Tendency Univariate Descriptive Mode the most commonly occurring value 6 people with ages 21, 22, 21, 23, 19, 21 - mode = 21 Median the center value the

### Types of Data, Descriptive Statistics, and Statistical Tests for Nominal Data. Patrick F. Smith, Pharm.D. University at Buffalo Buffalo, New York

Types of Data, Descriptive Statistics, and Statistical Tests for Nominal Data Patrick F. Smith, Pharm.D. University at Buffalo Buffalo, New York . NONPARAMETRIC STATISTICS I. DEFINITIONS A. Parametric

: Table of Contents... 1 Overview of Model... 1 Dispersion... 2 Parameterization... 3 Sigma-Restricted Model... 3 Overparameterized Model... 4 Reference Coding... 4 Model Summary (Summary Tab)... 5 Summary

### 2. Simple Linear Regression

Research methods - II 3 2. Simple Linear Regression Simple linear regression is a technique in parametric statistics that is commonly used for analyzing mean response of a variable Y which changes according

### 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

### www.kellogg.northwestern.edu/kis/tek/ongoing/spss.htm

First version: October 11, 2004 Last revision: January 14, 2005 KELLOGG RESEARCH COMPUTING Introduction to SPSS SPSS is a statistical package commonly used in the social sciences, particularly in marketing,

### Good luck! BUSINESS STATISTICS FINAL EXAM INSTRUCTIONS. Name:

Glo bal Leadership M BA BUSINESS STATISTICS FINAL EXAM Name: INSTRUCTIONS 1. Do not open this exam until instructed to do so. 2. Be sure to fill in your name before starting the exam. 3. You have two hours

### SPSS (Statistical Package for the Social Sciences)

SPSS (Statistical Package for the Social Sciences) What is SPSS? SPSS stands for Statistical Package for the Social Sciences The SPSS home-page is: www.spss.com 2 What can you do with SPSS? Run Frequencies

### Using Excel for Statistics Tips and Warnings

Using Excel for Statistics Tips and Warnings November 2000 University of Reading Statistical Services Centre Biometrics Advisory and Support Service to DFID Contents 1. Introduction 3 1.1 Data Entry and