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Chapter 8

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:

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Chapter 8

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

  2. 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

  3. 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

  4. 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

  5. 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:

  6. The Distribution of Differences Between Means • Use these to figure variance of the distribution of differences between means (S2difference) • Then take sqrt for standard deviation of the distribution of differences between means (S difference)

  7. 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

  8. 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?

  9. 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 = • S2M1 = • S2 M2 = • S2 difference = • S difference =

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

  11. 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…)

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