The pooled variance is the weighted average of the two sample variances taken from the two populations. The variance is determined by taking the weighted estimates for each sample set. Divide the mean square of the two sample sets by the degrees of freedom of the two sample sets. The Pooled Variance Calculator calculates the pooled variance, standard deviation, standard error, and degrees of freedom for the data set. .
The model for estimating the population variance is as follows: :
\(S_p^2 = \dfrac{(n -1)S_1^2 + (n_2 - 1)S_2^2}{n_1 + n_2 - 2}\)
in which:
S = variance of the data set
n= Range of factorials
let pooled pattern trendy deviations of populations be 2 and three respectively. the dimensions of both the sample dataset are 10 and 20, then and widespread deviation of the dataset, and the usual deviation of the dataset?
Given:
pattern size (n1) = 10
pattern size (n2) = 20
pattern standard deviation (S1) = 2
pattern standard deviation (S2) = 3
\(S_p^2 = \dfrac{(n -1)S_1^2 + (n_2 - 1)S_2^2}{n_1 + n_2 - 2}\)
\(S_p^2 = \dfrac{(10 -1)(2)^2 + (20 - 1)(3)^2}{10 + 20 - 2}\)
\(S_p^2 = \dfrac{207}{28}\)
\(S_p^2 = 7.3929\)
The expected population standard deviation for the two samples is 7.3929. You can calculate the standard deviation by taking the square root of the variance. .
\(S_p^2 = 7.3929\)
Taking beneath the root of both sides
\(sqrt{(S_p)^2} = sqrt{7.3929}\)
S_p = 2.719
The Standard Deviation for the Standard Deviation is calculated after the values of the variables are obtained. The variance of the pooled samples shows the variance of the values of the data set.
\(SE = S_{{\bar x_1 - \bar x_2}} = S_p \sqrt{\dfrac{1}{n_1} + \dfrac{1}{n_2}}\)
\(SE = 2.719 \sqrt{\dfrac{1}{10} + \dfrac{1}{20}}\)
\(SE = 2.719 \sqrt{0.15}\)
\(SE = 1.0531\)
The standard errors is calculated with the aid of the Pooled Variance Calculator to locate the predicted error inside the dataset values.
\(df = n_1 + n_2 - 2\)
\(df = 10 + 20 - 2\)
\(df = 28\)
The standard error is calculated with the help of the Competition Cap The degrees of freedom of the data set are the degrees of freedom that affect the data set The variable is a fixed variable. The T-Test Calculator calculates the degrees of freedom for the values in a data set relative to the sample values.
Let's take a look at how the Combined Test works. Some of the steps are easy for consumers to understand.
Input:
Ouput:
