Independent Sample T-test Often used with experimental designs 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?

Using Measures of Variation Leaned how to measure variation in data, i.e., variance, standard deviation (Ch.4) Used the normal curve & standard deviation to calculate z-scores and probabilities (Ch.5) Used the normal curve & the z-score & the Standard error 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)

Standard Error of the Differences between Means Similar to the idea behind the SE of the mean Lets say that in the population men and women IQ scores are (on average) equal. If we took a 1000 pairs of sample means for men and women, calculated the difference between those means and plotted those 1000 differences, the plot would look like a normal curve.

Some differences will be at or near zero Some will be a little below or above zero A few will be noticeably different from zero Even though the true population difference between men and women IQs is zero, because of sampling error, we will get differences that are above or below zero. What if we don’t know the true population difference? Create confidence intervals to estimate what the true population difference is

Null Hypothesis The two groups come from the same population or that the two means are equal μ 1 = μ 2

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

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)

Independent Sample T-test Formula t =

Let’s play with some fake data Go to our webpage Open the IQ SPSS file

SPSS & the Independent Sample T-Test

Now a hand calculation with more fake data t =

Real world example Matland (1994) – available on WebCampus 528 high school students in Norway Students given documents (speeches) from the Conservative and Labor party. 50% of the speeches were associated with a male name the other a female name. Hypothesis: Norway has so many female politicians that students should evaluate speeches/candidates equally