SW 671 # 10

1. SW 671 # 10 Inferential Statistics: Cross-tabulation, Chi-square and Comparing Means

2. Parametric and Non-parametric Tests

3. Non-parametric Tests • Non-parametric tests of significance do not assume a normal distribution • Usually used when variables are represented on the nominal or ordinal scale • Used if one or more of the assumptions for parametric tests is violated

4. Cross-tabs & Chi-squares • Chi-square Goodness-of–Fit Test: interested in finding out whether the data you collected for a sample closely matches the proportion for a larger population. • Chi-square Test-of-Association: interested in finding a relationship between two nominal variables.

5. Presentation of Results • should report the following information • X-squared • df • p • Meaningfulness and Sample Size: no more than 20% of cells can have expected frequency of less than 5

6. Chi-square Alternative: Fisher’s Exact Test • Use if expected frequency size requirements of the chi-square test cannot be met • Use only with 2X2 table and two independent sub-samples • Often used to ascertain a preliminary answer to a research question

7. Chi-square continued • Using Chi-square for Inference • Chi-square with Three or More Variables (Multi-way Frequency Analysis) • Best used when variables are nominal, usually a better test is available if variables are on a higher scale.

8. Inferential Statistics II: Group Differences • The objective in comparing group differences is to determine whether there is a significant difference between two or more established groups. • To accomplish this, means for each group are calculated, followed by using the amount of dispersion (standard deviation), to determine whether statistically significant differences exist.

9. Common parametric statistics • Independent t-tests - when comparing two normally distributed groups • Analysis of Variance (ANOVA) – when comparing three or more normally distributed groups

10. Nonparametric statistics • Mann-Whitney U test – when comparing two non-normal groups • Kruskal-Wallis test – when comparing three or more non-normal groups

11. Be sure not use a series of t-tests in shotgun approach. This will inflate the alpha value (known as family wise error). This is why ANOVA is used when there are three or more groups are being compared. • Other tests include one sample t-test, and the paired t-test (repeated measures ANOVA).

12. One sample t-test is used when the study has only one sample. • It is used to compare a sample’s mean for an interval or ratio level variable with its population’s mean. • Chi-square goodness of fit test is the nonparametric equivalent.

13. Paired T-test (Dependent) t-test • Unlike the one sample t-test, the dependent t-test does not compare a sample’s mean for an interval or ratio level variable with its population’s mean. • It compares mean scores from two samples that are related in some way. • It may be used when we have two connected (matched) samples that we measure once or when we use one sample and measure it on two separate occasions.

14. Error terms become vital to understanding the logic. • The error terms usually refer to the within group variability (spread, deviation). Different tests use different error terms. • Because Dependent t-tests and Repeated measures ANOVA use same subjects you can use smaller samples because of less variability (reduced error term) within subjects.

15. Analysis of Variance • Identical to the t-test, but rather than having two levels (or categories) of a nominal independent variable, there are three or more levels.