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t Statistic, Correlation & Regression - Coggle Diagram
t Statistic
Overview
The problem with using a z-score for hypothesis testing is that the z-score formula requires more information than is usually available. Namely, we usually do not know the standard deviation for the population.
The estimated standard error (sM) is used as an estimate of the actual standard error (σM) when the sample standard deviation is unknown. It uses the sample variance or sample standard deviation and provides an estimate of the standard distance between a sample mean M and the population mean μ .
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The t statistic is used to test hypotheses about an unknown population mean (μ) when the sample standard deviation is unknown. The formula uses the same structure as the z-score formula (swapping the estimated standard error in the denominator).
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t-distribution
a t distribution is the complete set of t values computed for every possible random sample for a specific sample size (n) or a specific degrees of freedom (df). The t distribution approximates the shape of a normal distribution.
like z distributions, t distributions tend towards normal, especially with larger sample sizes
the degrees of freedom (df) is usually the best determiner of how normal the t distribution is. Larger df = more normal
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Correlation & Regression
Introduction
correlation is a statistical technique that is used to measure and describe the relationship between two variables.
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Pearson Correlation
Pearson correlation measures the degree and the direction of the linear relationship between two variables.
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the sum of products of deviations (SP) measures the amount of covariability between two variables. Similar to SS, the sum of squared deviations
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adding, subtracting, or multiplying(positive) by a constant to X and/or Y value does not change the pattern of data points and does not change the correlation. However, multiplying by a negative constant changes the sign of the correlation
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Alternatives
Ranking Tied Scores: When you are converting scores into ranks for the Spearman correlation, you may encounter two (or more) identical scores. Whenever two scores have exactly the same value, their ranks should also be the same.
When the Pearson correlation formula is used with data from an ordinal scale (ranks), the result is called the Spearman correlation.
The word monotonic describes a sequence that is consistently increasing (or decreasing). Like the word monotonous, it means constant and unchanging.
The point-biserial correlation measures the relationship between two variables in situations in which one variable consists of regular, numerical scores, but the second variable has only two values
a dichotomous variable only has two values. Examples: first-born or later born; graduate or dropout; alive or dead
When both variables (X and Y) measured for each individual are dichotomous, the correlation between the two variables is called the phi-coefficient
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