The t Test for Independent Means Chapter 8 The t Test for Independent Means Part 1: Oct. 8, 2013

t Test for Independent Means Comparing two samples e.g., experimental and control group Scores are independent of each other Focus on differences betw 2 samples, so comparison distribution is: Distribution of differences between means

The Distribution of Differences Between Means If null hyp is true, the 2 populations (where we get sample means) have equal means If null is true, the mean of the distribution of differences = 0

Pooled Variance Start by estimating the population variance Assume the 2 populations have the same variance, but sample variance will differ… so pool the sample variances to estimate pop variance = df2 = Group2 N2-1 Pooled estimate of pop variance Sample 1 variance Sample 2 variance df total = total N-2

Variance (cont.) Note – check to make sure S2 pooled is between the 2 estimates of S2 We’ll also need to figure S2M for each of the 2 groups:

The Distribution of Differences Between Means Use these to figure variance of the distribution of differences between means (S2 difference) Then take sqrt for standard deviation of the distribution of differences between means (S difference)

T formula and df t distribution/table – need to know df, alpha Where df1 = N1-1 and df2 = N2-1 t observed for the difference between the two actual means = Compare T observed to T critical. If T obs is in critical/rejection region  Reject Null

Example Group 1 – watch TV news; Group 2 – radio news. Is there a significant difference in knowledge based on news source? Research Hyp? Null Hyp?

Example (cont.) M1 = 24, S2 = 4 N1 = 61 M2 = 26, S2 = 6 N2 = 21 Alpha = .01, 2-tailed test, df tot = N-2 = 80 S2 pooled = S2 M1 = S2 M2 = S2 difference = S difference =

(cont.) t criticals, alpha = .01, df=80, 2 tailed t observed = 2.639 and –2.639 t observed = Reject or fail to reject null? Conclusion? APA-style sentence:

Assumptions 1) Each of the population distributions (from which we get the 2 sample means) follows a normal curve 2) The two populations have the same variance This becomes important when interpreting Ind Samples t using SPSS SPSS provides 2 sets of results for ind samples t-test: 1st assumes equal variances in 2 groups 2nd assumes unequal variances You have to check output to see which of these is true SPSS provides “Levine’s test” to indicate whether the 2 groups have equal variance or not. Then, use the results for either equal or unequal variances (depending on results of Levine’s test…)