Intro to T-scores

what are the assumptions for hypothesis tests with z-scores

random sampling, independent observations, variability is unchanged by experimental manipulation even if mean is changed, normal distribution of sample means

what is the problem with z-scores

in most cases when we collect a sample, we don’t know the parameters of the population from which it came

what does calculating a z score of a sample rely on

knowing the population standard deviation

what are t scores used for

used to test hypotheses when the population standard deviation is unknown, has the same structured as the z score but uses the estimated Standard error instead of the standard error

what is the formula for t scores

what is the estimated standard error

what are the characteristics of t-distribution

bell shaped, symmetrical, NOT normal, mean of 0, flatter and more spread out tails than normal distribution

what happens when n gets larger in a t distribution

df gets larger and the t distribution gets more normal

what are the two major differences between hypothesis testing with zscores and t-scores

1. The t statistic is used when we don’t know the population variance/standard deviation: We must use the sample variance/standard deviation to estimate 2. The shape of the t distribution is not normal: It changes depending on degrees of freedom and We must use the t-statistic table and the df to determine the critical values

what is the formula for Cohen’s d

what is the effect size r²

it describes the “percentage of variance explained” by the effect

what is the range of effect size r²

Ranges from 0 to 1.0

• 0 < r² < 0.09 = small

• 0.09 < r² < 0.25 = medium

• 0.25 < r² = large

what are the Two methods for calculating r²

Brute Force and Simple Method

what is the formula for calculating r² using the simpler method