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Statistics: Chapter Nine - Coggle Diagram
Statistics: Chapter Nine
T Statistic: An alternative for a z statistic. With a z-score, we must know the value of the standard variance of the population which is often not known. As a result, we use the corresponding simple value in its place: a t-statistic.
It is used to test hypotheses about an unknown population mean when the standard deviation is unknown. Same formula except the t statistic uses estimated standard error in the denominator.
T Distribution: Complete set of t values computed for every possible random sample for n or df. The t distribution approximates a normal distribution.
Estimated standard error: Estimate of the real standard error when the value of standard deviation is unknown. Found from sample variance or sample standard deviation and it's an estimate between the sample mean and population mean.
Degrees of Freedom: Describe the number of scores in a sample that are independent and allowed to vary. n-1 is the formula.
As the df gets larger, the shape is closer in shape to a normal z-score distribution.
If your critical value is not listed, look up the critical value for above and below + use the larger
With z-scores, the denominator stays the same since the population variance and standard deviation are all the same while it varies with the t-statistics
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Because the estimated
standard error appears
in the denominator of the
formula, a larger value
produces closer to zero
values for t.
Cohen's d: The measure of effect size in terms of the population mean difference and the population standard deviation. (estimated d)
Percentage of variance accounted for by the treatment is the value after the treatment effect has been accounted for.
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- State the hypothesis & select alpha level. 2. Locate the critical region. 3. Calculate the test statistic. 4. Make decision.