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Unformatted text preview: Independent samples ttest We “know” nothing! Use two samples. NHST: Null Hypothesis Significance Testing The “Prequel” – zscores and the normal distribution “NHST” – ztest, single sample ttest “NHST Part 2 – The Sequel” – dependent ttest, independent ttest “NHST Part 3 – ANOVA” – coming soon to a lecture near you “NHST The Final Installment” – Factorial ANOVA, power and effect size ttests • Single sample ttest: One set of scores from one group of people. • Dependent samples ttest: Two sets of scores from one group of people. • Independent samples ttest: Two sets of scores from two groups of people. We “know” nothing! Use Two Samples • Population 1 – Estimate μ 1 from sample 1 (M 1 ) • Examples: males, ethnic majority, introverts, treatment group • Population 2 – Estimate μ 2 from sample 2 (M 2 ) • Examples: females, ethnic minority, extroverts, control group NOTE! Your independent variable is your two samples: IV = gender (1 = males, 2 = females) IV = ethnicity (1 = minority, 2 = majority) IV = personality (1 = introvert, 2 = extrovert) IV = treatment (1 = treatment, 2 = control) Estimate variance Homogeneity of Variance assumption: Population 1 variance (σ 2 1 ) = Population 2 variance (σ 2 2 ) BUT we have TWO estimates of variance, one from sample 1 and one from sample 2. s 2 1 and s 2 2 NOTE! s 2 1 = s 2 2 Estimate variance BUT we have TWO estimates of variance, one from sample 1 and one from sample 2. s 2 1 and s 2 2 We use both of them to estimate the population variance. We pool the variance . Pooled variance s 2 pooled = (df 1 /df total )s 2 1 + (df 2 /df total )s 2 2 df 1 = degrees of freedom for sample 1 s 2 1 = variance of sample 1 df 2 = degrees of freedom for sample 2 s 2 2 = variance of sample 2 df total = df 1 + df 2 Comparison Distribution Distribution of Means from Population 1 (we will estimate using sample 1 mean and pooled variance) Distribution of Means from Population 2 (we will estimate using sample 2 mean and pooled variance) Comparison Distribution For the ttest for independent samples we calculate the difference between sample 1 mean and sample 2 mean. (M 1 – M 2 ) We will compare the difference between sample means to the Distribution of Differences Between Means (all possible differences between means). Comparison Distribution Distribution of Means from Population 1...
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 Spring '11
 VictoriaHarmon
 Normal Distribution, Variance, Statistical hypothesis testing, Student's ttest, Mdifference Sdifference

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