PSYC209 Lecture 8: Testing Means  One Sample tTest With Confidence Intervals
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Instructor – Amey Rachel
Textbook – Essential Statistics for the Behavioral Sciences by Gregory Privitera
Z – statistics

 Denominator > standard error
T – statistics
 Inferential statistics used to determine the number of standard deviations in a t
distribution that a sample mean deviates from the mean value or mean difference
stated in the null hypothesis

 Denominator > Estimated standard error
 Has greater variability in the tails because the sample variance is not always equal to the
population variance
 The t distribution shares the same characteristics as the normal distribution. For
example, it’s symmetrical, asymptotic, etc.
 The t distribution is associated with degrees of freedom (df)
o n1
 Compared to z – test, for t – test we do not know the population variance
Effect size
 Gives an estimate of the size of an effect in the population
 Three measures of effect size
o Cohen’s d
o Eta squared and Omega squared > Two measures of proportion variance
Proportion variance is a measure of effect size in terms of the proportion
or percent of variability in a dependent variable that can be explained or
accounted for by a treatment
Treatment is any unique characteristic of a sample or any unique way
that a researcher treats a sample
Cohen’s d
 Most often used
 Measures the number of standard deviations an effect is shifted above or below the
population mean stated by the null hypothesis.

Eta – squared (n2)

 Tends to overestimate the proportion of variance explained by a treatment