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Stats Week 4 - Coggle Diagram
Stats Week 4
Correlation and Regression
Correlation
a statistical technique that is used to measure and describe the relationship between two variables
positive correlation
the two variables tend to change in the same direction
negative correlation
the two variables tend to go in opposite directions
perfect correlation
is always identified by a correlation of 1.00 and indicates a perfectly consistent relationship
Pearson correlation
measures the degree and the direction of the linear relationship between two variables
linear relationship
how well the data points fit a straight line
sum of products of deviations
is used to measure variability for a single variable
outliers
One or two extreme data points, often called outliers, can have a dramatic effect on the value of a correlation
restricted range
a correlation that is computed from scores that do not represent the full range of possible values
coefficient of determination
measures the proportion of variability in one variable that can be determined from the relationship with the other variable
Correlation Matrix
The results from multiple correlations are most easily reported in a table called a correlation matrix, using footnotes to indicate which correlations are significant
Spearman Correlation
When the pearson correlation formula is used with data from an ordinal scale (ranks), the result is called the Spearman Correlation
monotonic relationship
a consistently one-directional relationship between two variables
Point-Biserial Correlation
Comparing independent-measures t-test and special version of Pearson correlation
dichotomous variable or a binomial variable
A variable with only two values
Phi-Coefficient
When both variables (X and Y) measured for each individual are dichotomous
Introduction to the t Statistic
estimated standard error
used as an estimate of the real standard error
T-Statistic
is used to test hypotheses without an unknown population mean
t distribution
is the complete set of t values computed for every possible random sample for a specific sample size or a specific degrees of freedom and the t distribution approximates the shape of a normal distribution
Degrees of freedom
describe the number of scores in a sample that are independent and free to vary
Assumptions of the t Test
The values in the sample must consist of independent observations
The population sampled must be normal
confidence interval
is an interval, or range of values centered around a sample statistic
percentage of variance accounted for by the treatment
A measure of effect size that determines what portion of the variability in the scores can be accounted for by the treatment effect.
Linear Equations and Regression
Linear Equation
an equation between two variables that gives a straight line when plotted on a graph
slope
determines how much the Y variable changes when X is increased by one point
Y-intercept
value of a in the general equation
Regression
The statistical technique for finding the best-fitting straight line for a set of data is called
regression line
the resulting straight line
Analysis of Regression
The process of testing the significance of a regressing equation is called analysis of regression. The regression analysis uses an F-ratio to determine whether the variance predicted by regression equation is significantly greater than would be expected if there were no relationship between X and Y
Standard Error Of Estimate
gives a measure of the standard distance between the predicted Y values on the regression line and the actual Y values in the data