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T-Statistics- used as an alternative for a z-score when the standard…
T-Statistics- used as an alternative for a z-score when the standard deviation (or variance) is unknown. The estimated sample standard deviation (or variance) is used instead
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We typically use the sample variance formula in t-statistics because they are unbiased and some types of t-statistics require variance.
When every sample is displayed, T-distributions have more variability and are flatter than z-distributions, but become more normal with larger sample size and df. T-statistics also have their own unit normal table.
The estimated sample variance is also used in the "estimated D" which is the Cohen's D formula for accounting for effect size.
Hypothesis testing with t-statistics assumes that the sample must consist f independent observations and that the population is normal.
A hypothesis test can be preformed with t-statistics using only the null hypothesis and a sample. You do not need to know the population mean and variance.
We use degrees of freedom (n-1) to make sure the sample variance approximates the population variance. The higher the df (and the sample size) the more accurate you will be.
Alternative methods of considering effect size include are using an r squared formula for determining variability in the treated scores and finding the confidence interval, the range of values which estimates the population mean.
In hypothesis testing, similar to z-scores, researchers must determine whether to use a one tailed or two tailed test to determine the critical region.