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Powering the Statistical Puzzle: Key Elements and Tips

Learn about the essential pieces of the statistical puzzle that contribute to clear hypothesis tests. Discover how power, effect size, sample size, alpha level, and type of statistical test work together to enhance the accuracy and strength of your research findings.

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Powering the Statistical Puzzle: Key Elements and Tips

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  1. April 5, 2019 Power

  2. Pieces of the Statistical Puzzle • There are 5 pieces of the puzzle that work together to create the clearest solutions for your statistical hypothesis tests • Power • Effect Size • Sample Size • Alpha level • Type of Statistical Test

  3. Power • Power is the probability of rejecting a null hypothesis when it should be rejected (1 – b) • In other words, finding a difference that truly exists

  4. Hypothesis Test Decision Table

  5. Power • You always want the greatest amount of power in your statistical test • When conducting a power analysis (analysis prior to research to determine sample size given previous research), we generally try to get 80% power or 80% probability of finding statistically significant results when we should find them

  6. Effect Size • Effect size, in terms of group differences, is the magnitude of the distance between two groups taking standard deviation into consideration • It is a measure of how big a treatment effect is in number of standard deviations

  7. Effect Size • There are many different types of effect size measures for the many types of statistical tests, so we are going to talk globally • Cohen’s d is the difference between two means divided by a pooled standard deviation • (m1 – m2)/s

  8. Effect Size • The Cohen formula is very similar to the statistical test, but sample size has been removed from the equation • Small effect sizes (<.3) indicate relative closeness between the two means • Large effect sizes (>.6) indicate relative distance between two means • The further apart the two means are (greater effect size), the easier it is to achieve statistical significance and have greater power in your test

  9. Small effect size

  10. Large Effect Size

  11. Sample Size • Sample size is a major part of every statistical hypothesis test. • With very large samples, even very small effects will be statistically significant. • A correlation coefficient of .1 can be statistically significantly different from zero, but is it meaningful? • Small samples have difficulty reaching statistical significance

  12. Alpha • Your level of significance, alpha, has a direct effect on power. • The larger your alpha level, the more likely you are to reject the null hypothesis • The larger your alpha level, the more power you have in your study

  13. Graph of changing alpha

  14. Type of Statistical Test • Repeated measures tests have more power because each subject acts as its own control • Fewer observations needed • Between subjects tests have less power • More observations needed

  15. Summary of relationships • Larger effect size, more power • Larger alpha, more power • Larger sample size, more power • Repeated measures tests have more power than between subjects tests

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