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Chapter 9 & 14 - Coggle Diagram
Chapter 9 & 14
correlation — measures and describes the relationship between two different variables; used to make prediction (regression), verify theories, assess validity and reliability, etc.
coefficient of determination — how much variability in one variable can be accounted for by its relationship with another variable
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Types of Correlation
Pearson r correlation — measures the degree of a linear relationship between variables 
sum of products of deviations — used to calculate the covariability of variables (degree to which X and Y vary together)
Spearman correlation — used with data using an ordinal scale, or with variables with a monotonic (one-directional), non-linear relationship; scores are converted to ranks, linear relationship between ranks is assessed with Pearson correlation
special formula for Spearman correlation — used when there are no ties in ranks; D = difference between X and Y rank for each individual
for tied scores, calculate their mean and use it as their final rank
point-biserial correlation — measures relationship between 2 variables, one of which is dichotomous/binomial (has only 2 values); categories are converted to either 0 or 1, then the Pearson correlation is used
phi-coefficient — measures correlation between 2 dichotomous variables; categories for each variable are converted to either 0 or 1, then the Pearson correlation is used
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Measuring Effect Size
estimated d — utilizes both sample mean and sample standard deviation to calculate effect size of treatment
percentage of variance accounted for by the treatment — determines the degree to which a treatment affects variability in a sample
confidence interval — range of values within which the sample mean is and, therefore, the corresponding population parameter is likely to be
t-statistic is calculated similarly to a z-score, but it uses the estimated standard error — incorporates sample standard deviation, rather than the population standard deviation
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does not require knowledge of corresponding population parameters (i.e., mean or variance) for calculation
regression — statistical method for finding the "best-fitting" straight line for a data set; can be used to make predictions for X-values within the range of the original data
regression equation for Y — provides the least-squared-error solution, with the smallest value between the predicted and actual Y values :
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standard error of estimate — measures the standard distance between actual Y values of the data set and predicted Y values provided by the regression line