Inferential Statistics: SPSS

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## Inferential Statistics: SPSS

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1. Inferential Statistics: SPSS

2. Testing Population Mean • One Sample T-Test • Independent Samples T-Test • Paired Sample T-Test • SPSS • Analyze -> Compare Mean -> …

3. One Sample T-Test • Test mean of one sample against a test value • Variable is either interval or ratio • EX: Test if average total score is more than 55 H0 : μ <= 55 H1 : μ > 55 • If the hypothesis is true then we should reject H0 and accept H1 • Calculate statistic (use SPSS)

4. SPSS Analysis Result t: the calculated T value df: degree of freedom • SPSS uses “Sig.(2-tailed)” or p-value to show test result • SPSS only does Two-tailed • Divide this p-value by 2 to get one-tailed • If p-value is less than α (e.g. 0.05) then the test is significant • Reject H0, accept H1 • Thus the average total score is more than 55 at significance level 0.05

5. Independent Samples T-Test https://statistics.laerd.com/spss-tutorials/independent-t-test-using-spss-statistics.php • Test mean of one sample against another • Assumptions • Independent variable consists of two independent groups. • Dependent variable is either interval or ratio • Dependent variable is approximately normally distributed • Similar variances between the two groups (homogeneity of variances)

6. Independent Samples T-Test • EX: Test if male students get lower total score than female students H0 : μm >= μf H1 : μm < μf • If the hypothesis is true then we should reject H0 and accept H1 • Calculate statistic (use SPSS)

7. Levene’s Test for Equality of Variances • For independent samples T-Test, the calculation for T value is different when: • Both samples have the same variance (σ12 = σ22) AND • The variances are difference (σ12 != σ22) • Use variance test to determine this • See Levene’s Test for Equality of Variances in the table • If the value of Sig. is >= α (e.g. 0.05) then the two variance is equal – use the first row of the result • If the value of Sig. is >= α (e.g. 0.05) then the two variance is NOT equal – use the second row of the result

8. Result According to Levene’s Test, use the first row (Sig. = 0.530 > α) The p-value (2-tailed) is 0.033 < α, thus the average score of male and female students are different The p-value (1-tailed) is 0.033/2 = 0.0165 < α, thus the result is significant Check the Group Statistics, female group has higher mean, thus reject H0 and accept H1 - the research hypothesis is true

9. Paired Sample T-Test https://statistics.laerd.com/spss-tutorials/dependent-t-test-using-spss-statistics.php • Test means of paired samples against each other • Same sample group (or two dependent samples) • Assumptions • Dependent variable is interval or ratio • The differences in the dependent variable between the two related groups are approximately normally distributed. • Independent variable consists of two related groups or "matched-pairs". • No outliers in the differences between the two related groups.

10. Paired Sample T-Test • EX: Test if final score is not different from midterm score of the same group of student H0 : μD = 0 H1 : μD != 0 • If the hypothesis is true then we should accept H0 and reject H1 • Calculate statistic (use SPSS)

11. Result The p-value (2-tailed) is 0.000 < α, thus the result is significant Thus reject H0 and accept H1 - the research hypothesis is false

12. Testing Categorical Data or Proportion One variable – binomial proportion One variable – multiple groups proportion (Goodness of Fit Test) Two variables – Chi-square Test of Independence Two variables – Test of Homogeneity

13. Binomial • Determining the proportion of people in one of two categories is different from a specified amount H0 : pD = p0 H1 : pD != p0 • SPSS assumes numerical data • Recode data into number e.g. M,F -> 1,2 • Analyze->Nonparametric Tests->Legacy Dialogs->Binomial • E.g. the proportion of male student is 0.5 H0 : pD = 0.5 H1 : pD != 0.5

14. Result Careful about the “Test Prop.” SPSS considers the first observation (row) as first group Exact Sig. is 0.04 < α, the result is significant, thus reject H0 and accept H1 - proportion of male students is not 0.5 If tested at 0.6

15. Multiple Groups https://statistics.laerd.com/spss-tutorials/chi-square-goodness-of-fit-test-in-spss-statistics.php • Goodness of Fit Test • Determining the proportion of groups is different from a specified ratio • O: Observed • E: Expected • Analyze -> Nonparametric Tests -> Legacy Dialogs -> Chi-Square • E.g. the proportion of sections is 1:2:1:2:1

16. Result Frequency less than 5 might make the analysis not meaningful The values in the “expected values” ratio correspond to groups in order of appearance in the observation row. Asymp.Sig. = 0.000 < α, the result is significant, thus reject H0 and accept H1 - the proportion is not 1:2:1:2:1

17. Chi-square Test of Homogeneity • Used to determine whether the proportion of one variable is similar when grouped by another variable • two or more groups in each variable H0: p1 = p2 = p3 = … = pn H1: p1 ≠ p2 ≠ p3 ≠ … ≠ pn • Data -> Weight Cases -> Weight cases by -> • Do not weight cases – SPSS uses proportion of total population • Select frequency variable to test dependency • Analyze -> Descriptive Statistics -> Crosstabs • Statistics -> Tick “Chi-square” • Cells -> Tick “Expected” (optional)

18. Result E.g. The proportion of selected of major is similar in both genders of student? H0: pm = pf H1: pm ≠ pf Pearson Chi-Square: Asymp.Sig. 0.010 < α Reject H0 and accept H1 - the proportion is not similar in each gender

19. Chi-square Test of Independence https://statistics.laerd.com/spss-tutorials/chi-square-test-for-association-using-spss-statistics.php • Used to determine whether the effects of one variable depend on the value of another variable (2 variables) • H0: Variable x and variable y are independent of each other • H1: Variable x and variable y are dependent of each other H0: ΣΣ(O - E)2 = 0 H1: ΣΣ(O - E)2  0 • Data -> Weight Cases -> Weight cases by -> • Do not weight cases – SPSS uses proportion of total population • Select frequency variable to test dependency • Analyze -> Descriptive Statistics -> Crosstabs • Statistics -> Tick “Chi-square” • Cells -> Tick “Expected” (optional)

20. Result • E.g. Determine if gender and major are independent based on total score • H0: gender and major are independent of each other • H1: gender and major are dependent of each other • Pearson Chi-Square: Asymp.Sig. 0.00 < α • Reject H0 and accept H1 - the two variables are dependent of each other based on total score

21. One-way ANOVA: SPSS https://statistics.laerd.com/spss-tutorials/one-way-anova-using-spss-statistics.php http://academic.udayton.edu/gregelvers/psy216/spss/1wayanova.htm • Analyze -> Compare Means -> One-way ANOVA • Option -> Tick… • Homogeneity of variance test • Descriptive (optional) • Welch • Post Hoc - used when the result is significant (at least one of the means is different) to find the group with the different mean

22. Example Determine if the means of total score are different in the 5 Sections H0 : μ1 = μ2 = μ3 = μ4 = μ5 H1 : μ1 != μ2 != μ3 != μ4 != μ5 At least one pair is different

23. Result: Descriptives and Variances • Check Levene test • “Sig.” > = 0.05, thus variances are equal in all groups • If not, need to refer to the Robust Tests of Equality of Means Table (Welch) instead of the ANOVA Table

24. Result: ANOVA Table Sig. = 0.013 < α, thus at least one of the group has different means Use Post-Hoc tests To find the pair with different mean

25. Result: Post Hoc Tests • The pair that Sig. < α has different mean • Section 1 and 4 • Section 2 and 4 • Section 2 and 5 • Section 3 and 4 • Section 4 and 5

26. Two-way ANOVA: SPSS https://statistics.laerd.com/spss-tutorials/two-way-anova-using-spss-statistics.php • Analyze -> General Linear Model -> Univariate • Multivariate is MANOVA • Add dependent variable and two or more factors (independent variables) • Option -> tick “Homogeneity tests” (optional “Descriptive”) • Plot -> add one factor (containing more groups) to “Horizontal Axis” and other to “Separate Lines” then click “Add” • To obtain profile plot • Post Hoc to find pair that has different means (similar to One-way ANOVA, optional)

27. Example • Determine the effect of major and gender on the total score H0 : μ1 = μ2 = μ3 = μ4 H1 : μ1 != μ2 != μ3 != μ4

28. Result • Compare Error to Corrected Total • Error should be less than 20% of corrected total • Error is very large compared to corrected total • Total score is effected by other external factors • Gender row Sig. = 0.024 < α, gender has effect on total score • Major row Sig. = 0.575 > α, major has no effect on total score • Major*Gender row Sig. = 0.298 > α, the interaction between two factors has no effect on total score

29. Result: Profile Plot

30. Example Determine the effect of section and gender on the total score