T TESTS?

Degrees of freedom formula

​Df​=N−1 where:Df​=degrees of freedomN=sample size​

Equal Variance (or Pooled) T-Test formula

​T-value= mean1−mean2 ​where:mean1 and mean2=Average values of eachof the sample setsvar1 and var2=Variance of each of the sample setsn1 and n2=Number of records in each sample set​ and, \begin{aligned} &\text{Degrees of Freedom} = n1 + n2 - 2 \\ &\textbf{where:}\\ &n1 \text{ and } n2 = \text{Number of records in each sample set} \\ \end{aligned}​Degrees of Freedom=n1+n2−2where:n1 and n2=Number of records in each sample set​

Example of Degrees of freedom?

Consider a data sample consisting of, for the sake of simplicity, five positive integers. The values could be any number with no known relationship between them. This data sample would, theoretically, have five degrees of freedom. Four of the numbers in the sample are {3, 8, 5, and 4} and the average of the entire data sample is revealed to be 6. This must mean that the fifth number has to be 10. It can be nothing else. It does not have the freedom to vary. So the Degrees of Freedom for this data sample is 4.

What are degrees of freedom?

Degrees of Freedom refers to the maximum number of logically independent values, which are values that have the freedom to vary, in the data sample.

How many types of t tests?

There are three types of t-tests, and they are categorized as dependent and independent t-tests.

What is a t-test?

A t-test is a type of inferential statistic used to determine if there is a significant difference between the means of two groups, which may be related in certain features.

degree of freedom (df) (repeated for clarity and emphasis)

the number of independent pieces of information remaining after estimating one or more parameters

correlated or paired T test

T = (Mean 1 - mean 2) / ( s diff) / square root n mean1 and mean2=The average values of each of the sample sets s(diff)=The standard deviation of the differences of the paired data values n=The sample size (the number of paired differences) n−1=The degrees of freedom​

How to calculate the T Test

Calculating a t-test requires three key data values. They include the difference between the mean values from each data set (called the mean difference), the standard deviation of each group, and the number of data values of each group.

What a large and small t score mean?

A large t-score indicates that the groups are different. A small t-score indicates that the groups are similar.

Equal Variance (or Pooled) T-Test

The equal variance t-test is used when the number of samples in each group is the same, or the variance of the two data sets is similar.

When to use the correlated or paired t test

The correlated t-test is performed when the samples typically consist of matched pairs of similar units, or when there are cases of repeated measures. For example, there may be instances of the same patients being tested repeatedly—before and after receiving a particular treatment. In such cases, each patient is being used as a control sample against themselves. This method also applies to cases where the samples are related in some manner or have matching characteristics, like a comparative analysis involving children, parents or siblings. Correlated or paired t-tests are of a dependent type, as these involve cases where the two sets of samples are related.

What is the T test used for?

The t-test is one of many tests used for the purpose of hypothesis testing in statistics.

Unequal Variance T-Test

The unequal variance t-test is used when the number of samples in each group is different, and the variance of the two data sets is also different. This test is also called the Welch's t-test. The following formula is used for calculating t-value and degrees of freedom for an unequal variance t-test: \begin{aligned}&\text{T-value} = \frac{ mean1 - mean2 }{\frac { var1^2 }{ n1 } + \frac{ var2^2 }{ n2 } } \\&\textbf{where:}\\&mean1 \text{ and } mean2 = \text{Average values of each} \\&\text{of the sample sets} \\&var1 \text{ and } var2 = \text{Variance of each of the sample sets} \\&n1 \text{ and } n2 = \text{Number of records in each sample set} \\ \end{aligned}​T-value=n1var12​+n2var22​mean1−mean2​where:mean1 and mean2=Average values of eachof the sample setsvar1 and var2=Variance of each of the sample setsn1 and n2=Number of records in each sample set​