t Statistic
Used for hypothesis testing when the population standard deviation is unknown.
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.
Standard error is estimated by substituting in the formula for standard error.
t=sample mean-population mean/ estimated standard error
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.
Cohen’s d can be computed to measure effect size. d=mean difference/standard deviation
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.
Correlation
Measures the relationship between two variables, X and Y. The relationship is described by direction, form, and strength/consistency.
Direction is either positive or negative.
A positive relationship means that X and Y vary in the same direction. A negative relationship means that X and Y vary in opposite directions. The sign of the correlation (+ or −) specifies the direction.
Most common form for a relationship is a straight line.
The numerical value of the correlation measures the strength or consistency of the relationship.
Most commonly used correlation is the Pearson correlation, which measures the degree of linear relationship.
A correlation of 1.00 indicates a perfectly consistent relationship and 0.00 indicates no relationship at all.
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 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.
The point-biserial correlation is used to measure the strength of the relationship when one of the two variables is dichotomous.