PS296 Lecture Notes - Lecture 12: Effect Size, Standard Deviation
Effect Size
-as the sample size (n) increases, the likelihood of being able to reject the null increases
-as a result, sometimes a meaningless difference can be found statistically significant when n
is large
-therefore, we need to consider whether statistically significant tests are also meaningful
-basically, it is how powerful or meaningful a statistic is when sample size is removed
-effect size is a statistic that gives a meaningful indication of how large a mean is or how
different two means are from each other
-a method of quantifying the difference between means
-provides a measure of the different between two means (ex mean under the null and
alternative hypothesis) in standard deviation units
To calculate effect size, we use Cohen's d (d-hat)
dhat = difference between means / standard deviation
-estimated independently of n
Effect size for one sample t test:
dhat = x̅ - μ
s
Document Summary
As the sample size (n) increases, the likelihood of being able to reject the null increases. As a result, sometimes a meaningless difference can be found statistically significant when n is large. Therefore, we need to consider whether statistically significant tests are also meaningful. Basically, it is how powerful or meaningful a statistic is when sample size is removed. Effect size is a statistic that gives a meaningful indication of how large a mean is or how different two means are from each other. A method of quantifying the difference between means. Provides a measure of the different between two means (ex mean under the null and alternative hypothesis) in standard deviation units. To calculate effect size, we use cohen"s d (d-hat) dhat = difference between means / standard deviation. Effect size for one sample t test: dhat = x s. Xbar mu = the difference between the sample mean and population mean.
