1. S519 Statistical Sessions Wrap up

2. Things we’ve covered Descriptive Statistics Normal Distributions Z-test Hypothesis Testing T-test ANOVA Correlation Linear regression Chi-square

3. Descriptive Statistics Central Tendency – Mean – Median – Mode Variance – Range – Standard deviation – Variance

4. Normal Distributions Skewness Kurtosis

5. Z-test

6. Hypothesis Testing 1.State the hypothesis – Null hypothesis – Research hypothesis Directional Non-directional 2.Set decision criteria 3.Collect data and compute sample statistic 4.Make a decision (accept/reject)

7. T-test

8. Degree of freedom=n-1 TTEST (array1, array2, tails, type) – array1 = the cell address for the first set of data – array2 = the cell address for the second set of data – tails: 1 = one-tailed, 2 = two-tailed – type: 1 = a paired t test; 2 = a two-sample test (independent with equal variances); 3 = a two- sample test with unequal variances

9. ANOVA Analysis of Variance A hypothesis-testing procedure used to evaluate mean differences between two or more treatments (or populations). Advantages: – 1) Can work with more than two samples. – 2) Can work with more than one independent variable

10. ANOVA In ANOVA an independent or quasi- independent variable is called a factor. Factor = independent (or quasi-independent) variable. Levels = number of values used for the independent variable. One factor → “single-factor design” More than one factor → “factorial design”

11. ANOVA Df for independent ANOVA – Between-group degree of freedom=k-1 k: number of groups – Within-group degree of freedom=N-k N: total sample size Df for dependent ANOVA – Between-group degree of freedom=k-1 k: number of groups – Within-group degree of freedom=N-k N: total sample size – Between-subject degree of freedom=n-1 n: number of subjects – Error degree of freedom=(N-k)-(n-1)

12. ANOVA Three different ANOVA: – Independent measures design: Groups are samples of independent measurements (different people) ANOVA: single factor – Dependent measures design: Groups are samples of dependent measurements (usually same people at different times) “Repeated measures” ANOVA: two factors without replication – Factorial ANOVA (more than one factor) ANOVA: two factors with replication

13. Correlation Pearson correlation – CORREL function or Pearson function – Toolpak for more than two variables (matrix) The correlation represents the association between two or more variables It has nothing to do with causality (there is no cause relation between two correlated variables)

14. Correlation r xy valueInterpretation 0.8 ~ 1.0Very strong relationship (share most of the things in common) 0.6 ~0.8Strong relationship (share many things in common) 0.4 ~ 0.6Moderate relationship (share something in common) 0.2 ~ 0.4Weak relationship (share a little in common) 0.0 ~ 0.2Weak or no relationship (share very little or nothing in common)

15. Correlation

16. Linear regression Y’ = bX + a – b = SLOPE() – a = INTERCEPT()

17. Chi-square Non-parametric vs. parametric – O: the observed frequency – E: the expected frequency df=r-1 (r= number of categories)