PSYC2009 Study Guide - Quiz Guide: Bonferroni Correction, Standard Deviation, Effect Size
Comparing Multiple Means
• Compare means between 2 or more groups
• To reduce the likelihood of a type 1 error, a Bonferroni correction is used when comparing
means
• A Between-groups t-statistic is used and can be calculates
• Step-by step process:
1. Calculate the difference between each groups means
2. Calculate overall variance of all the groups, , where k is the number of
samples
3. Calculate estimated standard deviation of the error,
4. Calculate Bonferroni-corrected significance level
• K = no. of comparisons
5. Find
using table A.3
• Row: value of df - N - k
• Column under two-tailed using Bonferroni-corrected CL
• If asked for normal approximation, find
, which is the z-score where area
beyond z =
6. Calculate the width of the confidence interval, w
7. Calculate confidence interval
• Interpret confidence interval
• If 0 is included, then the two groups are not significantly different
• If 0 is not included, then the two groups are significantly different
• Calculation proves not too different to standard confidence interval calculation, after
Bonferroni-correction is done
Effect size for multiple means
• Cohen's d: most common measure of effect size
• To calculate:
1. Use means and standard deviations calculated for Bonferroni-corrected calculations:
2. Judge size of d using standard benchmarks:
• Small: d = 0.2
• Medium: d = 0.5
• Large: d = 0.8
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Document Summary
Comparing multiple means: compare means between 2 or more groups, to reduce the likelihood of a type 1 error, a bonferroni correction is used when comparing means, a between-groups t-statistic is used and can be calculates. Step-by step process: samples: calculate the difference between each groups means. If 0 is included, then the two groups are not significantly different. If 0 is not included, then the two groups are significantly different: calculation proves not too different to standard confidence interval calculation, after. Effect size for multiple means: cohen"s d: most common measure of effect size, to calculate, use means and standard deviations calculated for bonferroni-corrected calculations: (cid:1856)=