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t Statistic (Computed using the estimated standard error. The t statistic…
t Statistic
Computed using the estimated standard error. The t statistic is used as a substitute for a z-score that cannot be computed when the population variance or standard deviation is unknown.
First calculate the sample variance (or standard deviation) as a substitute for the unknown population value.
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Hypothesized mean produces an extreme value for t, you conclude that the hypothesis was wrong.
The critical t values depend on the value for df associated with the t test. As df increases, the shape of the t distribution approaches a normal distribution.
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Another measure of effect size is , which measures the percentage of the variability that is accounted for by the treatment effect.
An alternative method for describing the size of a treatment effect is to use a confidence interval for μ. A confidence interval is a range of values that estimates the unknown population mean.
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Correlation
Measures the relationship between two variables, X and Y. The relationship is described by direction, form, and strength/consistency.
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Most commonly used correlation is the Pearson correlation, which measures the degree of linear relationship.
The Spearman correlation measures the consistency of direction in the relationship between X and Y—that is, the degree to which the relationship is one-directional, or monotonic.
Evaluating the strength of a relationship, you square the value of the correlation. The resulting value, r squared, is called the coefficient of determination because it measures the portion of the variability in one variable that can be determined using the relationship with the second variable.
A partial correlation measures the linear relationship between two variables by eliminating the influence of a third variable by holding it constant.
The point-biserial correlation is used to measure the strength of the relationship when one of the two variables is dichotomous.