Psych 201: t-test Worksheet Answers

Psych 201: t-Test Worksheet Answers This worksheet will review the t-Test then give you some problems to work. Refer back to the previous handout on t-tests using Excel.

Some Review: Why use the t-Test? When you want to compare the means of two groups. When to use One-tailed or Two-tailed tests? The answer is that it depends on your hypothesis. If your hypothesis states the direction of the difference or relationship, then you use a one-tailed test. Example null hypothesis would include: Females will not score significantly higher than males on the SAT. The null hypothesis (indirectly) predicts the direction of the difference. A two-tailed test would be used to test this null hypothesis: There will be no significant difference in SAT scores between males and females. While it is generally safest to use a two-tailed tests, there are situations where a one-tailed test seems more appropriate. The bottom line is that it is the choice of the researcher whether to use one-tailed or two-tailed research questions. The Formulae: For the independent-measures t, the sample statistic is the sample mean difference (M1M2). The population parameter is the population mean difference (µ1-µ2). The estimated standard error for the sample mean difference is computed by combining the errors for the two sample means. The resulting formula is: t=

(M 1 − M 2 ) − (µ 1 − µ 2 ) s(M1 − M 2 )

Where the estimated standard error is:

s(M1 − M 2 ) =

s 2p n1

+

s 2p n2

The pooled variance in the formula, s 2p , is the weighted mean of the two sample variances:

T-Test worksheet

Dr. Sullivan

1

s 2p =

SS1 + SS 2 df 1 + df 2

This t-statistic has degrees of freedom determined by the sum of the df values for the two samples:

df = df 1 + df 2 = (n1 − 1) + (n2 − 1) For hypothesis testing, the null hypothesis normally states that there is no difference between the two population means: H 0 : µ1 = µ 2 or µ1 − µ 2 = 0

Appropriate use and interpretation of the t statistic require that the data satisfy the homogeneity of variance assumption. This assumption stipulates that the two populations have equal variances. An informal test of this assumption can be made by simply comparing the two sample variances. If the two sample variances are approximately equal, the t test is justified.

T-Test worksheet

Dr. Sullivan

2

Problem 1: Dr. Jittery is exploring the effects of caffeine on college students. Though caffeine is widely used to defer sleep and increase the available time per day to perform homework or improve attention in class, too much caffeine may have negative effects. Dr. Jittery believes fine motor control may be a good measure of the hypothesized negative effect, and creates a maze-tracing task that will allow her to collect data on how accurately subjects can move a pointer through the maze. A counter will be kept to measure the number of times the subject bumps the pointer into a wall of the maze. Her hypothesis is that too much caffeine will affect the accuracy of the maze tracing. Null Hypothesis: Caffeine will have no effect on the number of bumps Alternative Hypothesis: Caffeine will have an effect on the number of bumps. She selects an alpha level of 0.05 and 8 subjects for each condition (No Espresso vs 6 Espressos). The df (degrees of freedom) are __14___ and the critical t value will be ___2.145_____ (based upon the table in the book). She runs her subjects and the following data is produced: No Espresso 4 5 0 4 2 4 1 4

6 Cups of Espresso 8 10 9 8 8 11 10 9

Using Excel, we calculate the t-test assuming equal variances and get the following: t-Test: Two-Sample Assuming Equal Variances

Mean Variance Observations Pooled Variance Hypothesized Mean Difference Df t Stat P(T