# PSYC209 Lecture 8: Testing Means - One Sample t-Test With Confidence Intervals

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8 Feb 2017
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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 n-1
- 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
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