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Introduction to t-Static, An estimated standard error is the denominator…
Introduction to t-Static
Alternative to z-Statistic
The basic formula is:
t=M−μ/sM
t Distribution
T distributions are more variable than the normal distribution due to estimation error
Effect Size
Hypothesis Testing with t
An estimated standard error is the denominator of the t formula
The population variance is estimated with the t statistic using the sample variance
When the population standard deviation (σ) is unknown, the t statistic is used
A sample mean and an estimated population mean are compared using the t statistic
The estimated standard error is less precise than the true standard error
A family of t distribution occurs rather than a single t distribution
Each t distribution is determined by its degrees of freedom (df)
df = n-1 (one-sample t test)
Df values increase with sample sizes
The t distribution gets closer to the normal distribution as df rises
A larger distribution results from fewer degrees of freedom
All t distributions are symmetrical with respect to zero
A t distribution's mean = zero
The z-score hypothesis test and t test use the same reasoning
State the null hypothesis first
Describe the alternative hypothesis
Pick an alpha level, which is usually .05
Ascertain the essential t value (using the t table)
Determine the t statistic that was obtained
When within a crucial region, reject H0
Importance is not often indicated by statistical significance
Cohen's d helps assess the size of the treatment impact by measuring the effect size for the t statistic
The sample result is unlikely under H0 if the result is statistically significant