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Analysis of Variance: ANOVA

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Group 1: control group/ no ind. Var. Group 2: low level of the ind. Var. Group 3: high level of the ind var.

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If you evaluated the differences using a t test: group 1 vs. group 2 group 2 vs. group 3 group 1 vs. group 3

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What is the probability of a type one error somewhere in this analysis?

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Type One error: rejecting the null when there really isn’t any effect of the independent variable. Reject the null

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The probability of a type one error in a single comparison is whatever the probability of a random event is. P <.05 or 5% of the time

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Probability over three comparisons: type one error in comparison one or comparison two or comparison three

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Probability of type one error:.05 +.05 +.05 =.15 or 15% of the time

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This inflation of the type one error rate is known as: Experimentwise error rate

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To hold down the experimentwise error rate we perform an analysis of variance (ANOVA) instead of multiple t tests.

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variance between groups F = --------------------------------------- variance within groups

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Var. between : how much each group mean differs from all other group means.

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Var. within: how much individuals within the groups vary from each other.

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What causes variability between : treatment + random events independent variable confounding factors

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What causes variability within : Random events (individual differences)

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treatment + random events F = ------------------------------------------------ random events

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When the only thing that has caused the groups to differ is random events, F should be a value very close to 1

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variance Sum of squares (SS) Degrees of freedom (df)

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In ANOVA: Variance is known as the mean square (MS)

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Sum of Squares Variance = ------------------------------- degrees of freedom

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Where K represents the number of groups

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