Soc 3306a Lecture 7: Inference and Hypothesis Testing T-tests and ANOVA

Hypothesis Tests When sample is non-random or have non- normal distribution, use Chi-square test Non-parametric (can not generalize) More powerful method is inferential test Through the use of parametric statistics Assumptions: random sampling, normal distribution and relatively equal variances

Inference When assumptions met, can use sample statistics to generalize to population Test Ho (null hypothesis) of “no difference” Find evidence for H1 (alternate or research hypothesis) Caution: when using very large samples, even trivial differences become significant Always check actual mean differences too

Alpha Levels N<1000, alpha =.05 N>1000, alpha =.01 or.001 Your p-value is the probability associated with the statistic you used Smaller p-value = stronger evidence for your research hypothesis Eg. p-value of <.001 means that you would find that result less than 1 in 1000 times Strong evidence for research hypothesis in population

Single Sample T-Test Figure 1 For use when population value is known  This is entered as the “test value” Is the sample significantly different form the population? Can use to test differences in means Requires a DV at interval-ratio level data For nominal level (%) need to use the binomial test (non-parametric)

Independent Samples T-Test Figure 2 For testing differences in two sample means DV = interval-ratio is entered as “test variable” IV is your “grouping variable” – binary Can be nominal or ordinal Need to “define groups” (enter the codes for the categories (2 groups) to be tested) Also look at confidence interval of difference

Oneway ANOVA (F-test) Figure 3 To test for differences in 3 or more means DV is I-R and IV is nominal/ordinal level Assumptions: relatively equal variances and group sizes but F is fairly “robust” Levene statistic to test for equal variances Post Hoc tests  Bonferroni: confidence intervals of differences  Tukey B: to examine means Can also ask for “Means Plots” - graph

Univariate Analysis of Variance Figure 4 Like oneway ANOVA but more flexible and informative (see Babbie Ch. 14 for detail) Can use for 1 or more IV’s at a time Tests “main effects” and when used for 2+ IV’s, tests “interaction effects” (“Two-way”) Produces regression-like output and can also be combined with regression to examine coefficients and plots (“ANCOVA”)