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## Inferential Statistics: SPSS

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**Testing Population Mean**• One Sample T-Test • Independent Samples T-Test • Paired Sample T-Test • SPSS • Analyze -> Compare Mean -> …**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)**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**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)**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)**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**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**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.**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)**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**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**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**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**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**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**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)**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**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)**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**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**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**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**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**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**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)**Example**• Determine the effect of major and gender on the total score H0 : μ1 = μ2 = μ3 = μ4 H1 : μ1 != μ2 != μ3 != μ4**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**Example**Determine the effect of section and gender on the total score