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Introduction to the t-Statistic - Coggle Diagram
Introduction to the t-Statistic
t Statistic hypothesis testing tool in which estimated standard error is used in the z-score formula denominator
Step 2-Locate the Critical Region.
Step 3- Calculate the Test Statistic.
Step 1-State the Hypotheses and Select an Alpha Level.
Step 4- Make a Decision Regarding Ho
degree of freedom is a figure in a sample that is independent and can vary
t distibution-complete set of t values computed for every possible random sample for a sample size
estimated Cohen's d figure calculated when substituting sample values in place of population values
percentage of variance accounted for by the treatment measurement of reduction in variability after removing the treatment effect
confidence interval range of values centered around a sample statistic
Every sample from a population can be used to compute a z-score or a t statistic.
The only difference between the t formula and the z-score formula is that the z-score uses the actual population variance,and the t formula uses the corresponding sample variance (or standard deviation) when the population value is not known.
The formula for the t statistic has the same structure as the z-score formula, except that the t statistic uses the estimated standard error in the denominator.
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The t statistic is used to test hypotheses about an unknown population mean,u,when the value of s is unknown.
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 exact shape of a t distribution changes with degrees of freedom.
As with the z-score formula, the t statistic forms a ratio.
An alternative method for measuring effect size is to determine how much of the variability in the scores is explained by the treatment effect.
An alternative technique for describing the size of a treatment effect is to compute an estimate of the population mean after treatment.
A confidence interval is an interval, or range of values centered around a sample statistic.
Directional Hypotheses and One-Tailed Tests
The t statistic is 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.
The t distribution is symmetrical with a mean of zero. To evaluate a t statistic for a sample mean, the critical region must be located in a t distribution.
When a t statistic is used for a hypothesis test, Cohen’s d can be computed to measure effect size.
The structure of the t formula is similar to that of the z-score.