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What's t.test?

Feb 28, 2024

What's t.test?

Solution by Steps

step 1

Understand the purpose of a t-test: A t-test is a statistical test used to compare the means of two groups or to compare a sample mean to a known value when the population variance is unknown

step 2

Identify the type of t-test: There are different types of t-tests, including the one-sample t-test, independent two-sample t-test, and paired sample t-test. The choice depends on the experimental design and data

step 3

Formulate the null hypothesis (

H_0

) and alternative hypothesis (

H_a

): The null hypothesis typically states that there is no effect or no difference, while the alternative hypothesis states that there is an effect or a difference

step 4

Calculate the t-statistic: The t-statistic is calculated using the sample data. For a one-sample t-test, the formula is:

t = \frac{\bar{x} - \mu}{s / \sqrt{n}}

where

\bar{x}

is the sample mean,

\mu

is the population mean,

s

is the sample standard deviation, and

n

is the sample size

step 5

Determine the degrees of freedom (df): For a one-sample t-test,

df = n - 1

. For an independent two-sample t-test,

df

is calculated based on the sample sizes and variances of the two groups

step 6

Find the critical value(s) and compare with the t-statistic: Using the degrees of freedom and the desired significance level (commonly 0.05), find the critical value(s) from the t-distribution table. Compare the calculated t-statistic to the critical value(s) to determine if the null hypothesis can be rejected

step 7

Interpret the results: If the t-statistic is greater than the critical value (in absolute terms) and the p-value is less than the significance level, reject the null hypothesis. Otherwise, do not reject the null hypothesis

Answer

The t-test is a method for testing whether there is a significant difference between means or whether a sample mean significantly differs from a known value, based on the t-distribution.

Key Concept

t-test

Explanation

A t-test is used to determine if there are significant differences between the means of two groups or between a sample mean and a known population mean, especially when the population variance is unknown. It involves calculating a t-statistic and comparing it to a critical value from the t-distribution.