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Introduction to the t Statistic/Correlation and Regression - Coggle Diagram
Introduction to the t Statistic/Correlation and Regression
Problem with z-Scores
The main problem with using z-scores for hypothesis testing is that they require the population standard deviation, which is usually unknown.
t Statistic
Used to test hypotheses about a population mean (μ) when the population standard deviation (σ) is unknown
Degrees of Freedom
Refers to the number of scores in a sample that are free to vary, which is calculated as n – 1. They are important in t statistics because they affect how well the sample variance estimates the population variance.
t Distribution
The complete set of t values calculated from all possible random samples of a given size. The t distribution is bell-shaped, symmetrical, and centered at zero, but it is flatter and more spread out due to increased variability.
Cohen's d
A measure of effect size that describes the magnitude of a treatment effect in terms of standard deviation units.
Confidence Interval
A range of values centered around a sample mean that is used to estimate the unknown population mean.
The Characteristics of a Relationship
Direction of the Relationship
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.
The Form of the Relationship
Describes the shape of the pattern between two variables
The Pearson Correlation
The most common method for measuring the strength and direction of a linear relationship between two variables. It tells us how well the data points fit a straight line.
The Spearman Collection
A statistical method used to measure the strength and direction of the relationship between two variables when the data are in ordinal form
The Phi-Coefficient
Used to measure the correlation between two dichotomous variables, or variables with only two categories
The Linear Equation
Expresses the relationship between two variables, X and Y, in the form Y = bX + a, where b is the slope and a is the Y-intercept.
Regression
Statistical technique used to find the best-fitting straight line that describes the relationship between two variables.
Standard Error of Estimate
Measures how accurately a regression equation predicts Y values
The Sum of Products of Deviations
This is used in calculating the Pearson correlation and measures the covariability between two variables—how much they change together.
The Strength or Consistency of the Relationship
Refers to how closely the data points follow a clear pattern, especially in a linear relationship