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Chapters 9 & 15 (T-Statistic (Formula: sample mean - population mean /…
Chapters 9 & 15
T-Statistic
Used instead of a z-score for hypothesis testing when the population standard deviation (or variance) is unknown.
To compute the t statistic, you must first calculate the sample variance (or standard deviation) as a substitute for the unknown population value. Then, the standard error is estimated by substituting s^2 in the formula for standard error. Lastly, a t statistic is 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.
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T Distribution
The distribution of t statistics is symmetrical and centered at zero like a normal distribution. A t distribution is flatter and more spread out than the normal distribution, but approaches a normal shape as df increases.
Confidence Interval: a range of values that estimates the unknown population mean. The confidence interval uses the t equation, solved for the unknown mean
r^2
A measure of effect size that determines what portion of the variability in the scores can be accounted for by the treatment effect.
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Correlation
Direction
A relationship can be 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.
Positive Correlation: the two variables tend to change in the same direction: as the value of the X variable increases from one individual to another, the Y variable also tends to increase; when the X variable decreases, the Y variable also decreases.
Negative Correlation: the two variables tend to go in opposite directions. As the X variable increases, the Y variable decreases. That is, it is an inverse relationship.
Form
The most common form for a relationship is a straight line. However, special correlations exist for measuring other forms. The form is specified by the type of correlation used. For example, the Pearson correlation measures linear form.
Strength
The numerical value of the correlation measures the strength or consistency of the relationship. A correlation of 1.00 indicates a perfectly consistent relationship and 0.00 indicates no relationship at all. For the Pearson correlation, r=1.00 (or −1.00) means that the data points fit perfectly on a straight line.
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Spearman Correlation
A correlation calculated for ordinal data. Also used to measure the consistency of direction for a relationship.
Partial Correlation
measures the relationship between two variables while controlling the influence of a third variable by holding it constant
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