Transcript Lecture 6
Independent Sample T-test • Classical design used in psychology/medicine • N subjects are randomly assigned to two groups (Control * Treatment). • After treatment, the individuals are measured on the dependent variable. • A test of differences in means between groups provides evidence for the treatment's effect. Measures of Variation • A lot of statistical techniques (using interval data) use measures of variation in some manner • What is the difference between a standard deviation, the standard error of the mean, and the standard error of the difference between means? Or How are they related? Look in the glossary to help you answer these questions? Using Measures of Variation • Leaned how to measure variation in data, i.e., variance, standard deviation (Ch.4) • Used the normal curve & SD to calculate z-scores and probabilities (Ch.5) • Used the normal curve & the z-score & the SE of the mean to calculate confidence intervals (Ch.6) • Used the concept of the confidence interval and the standard error of the differences between means to calculate the t-test (Ch.7) • Use the sum of squares Σ(X – Mean)2 [sum of the squared differences from the mean] in ANOVA Null Hypothesis • The two groups come from the same population or that the two means are equal • μ 1 = μ2 Levels of Significance • What does an α = .05 level of significance mean? • We decide to reject the null if the probability is very small (5% or less) that the sample difference is a product of sampling error. • The observed difference is outside the 95% confidence interval of the difference Choosing a Level of Significance • Convention • Minimize type I error – Reject null hypothesis when the null is true • Minimize type II error – fail to reject null when the null is false • Making alpha smaller reduces the likelihood of making a type I error • Making alpha larger reduces the probability of a type II error Independent Sample T-test Formula t= X1 X 2 s X1 X 2 N1s1 N 2 s2 N1 N 2 2 2 s x1 x2 2 N1 N 2 N N 1 2 Assumptions of the t-test • 1. All observations must be independent of each other (random sample should do this) • 2. The dependent variable must be measured on an interval or ratio scale • 3. The dependent variable must be normally distributed in the population (for each group being compared). (NORMALITY ASSUMPTION) [this usually occurs when N is large and randomly selected] • 4. The distribution of the dependent variable for one of the groups being compared must have the same variance as the distribution for the other group being compared. (HOMOGENEITY OF VARIANCE ASSUMPTION) Don’t worry about these assumptions to much, but • Point 1: statistical tools are attempting to quantify and analyze very complex social/political phenomenon • Point 2: For these test to be accurate they relay on simplifying the world with many assumptions that might not be true • Point 3: social science researchers violate these assumptions quite often, but try to be honest about it • Point 4: there are sometimes ways of testing and adjusting for violations SPSS & the Independent Sample T-Test Group Statistics VAR00001 VAR00002 1.00 2.00 N 10 10 Mean 102.0000 98.0000 Std. Error Mean 10.03328 9.63789 Std. Deviation 31.72801 30.47768 Independent Samples Test Levene's Test for Equality of Variances F VAR00001 Equal variances ass umed Equal variances not as sumed .073 Sig. .789 t-tes t for Equality of Means t df Sig. (2-tailed) Mean Difference Std. Error Difference 95% Confidence Interval of the Difference Lower Upper .288 18 .777 4.00000 13.91242 -25.22892 33.22892 .288 17.971 .777 4.00000 13.91242 -25.23230 33.23230