Chi Square Statistic Solution

STEP 0: Pre-Calculation Summary
Formula Used
Chi Square Statistic = ((Sample Size-1)*Sample Standard Deviation^2)/(Population Standard Deviation^2)
χ2 = ((N-1)*s^2)/(σ^2)
This formula uses 4 Variables
Variables Used
Chi Square Statistic - Chi Square Statistic is the measure used in chi-square tests to determine if there is a significant association between categorical variables in a contingency table.
Sample Size - Sample Size is the total number of individuals or items included in a specific sample.
Sample Standard Deviation - Sample Standard Deviation is the measure of how much the values in a specific sample vary.
Population Standard Deviation - Population Standard Deviation is the measure of how much the values in an entire population vary.
STEP 1: Convert Input(s) to Base Unit
Sample Size: 10 --> No Conversion Required
Sample Standard Deviation: 15 --> No Conversion Required
Population Standard Deviation: 9 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
χ2 = ((N-1)*s^2)/(σ^2) --> ((10-1)*15^2)/(9^2)
Evaluating ... ...
χ2 = 25
STEP 3: Convert Result to Output's Unit
25 --> No Conversion Required
FINAL ANSWER
25 <-- Chi Square Statistic
(Calculation completed in 00.004 seconds)

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Shri Madhwa Vadiraja Institute of Technology and Management (SMVITM), Udupi
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18 Basic Formulas in Statistics Calculators

P Value of Sample
Go P Value of Sample = (Sample Proportion-Assumed Population Proportion)/sqrt((Assumed Population Proportion*(1-Assumed Population Proportion))/Sample Size)
Sample Size given P Value
Go Sample Size = ((P Value of Sample^2)*Assumed Population Proportion*(1-Assumed Population Proportion))/((Sample Proportion-Assumed Population Proportion)^2)
t Statistic of Normal Distribution
Go t Statistic of Normal Distribution = (Sample Mean-Population Mean)/(Sample Standard Deviation/sqrt(Sample Size))
t Statistic
Go t Statistic = (Observed Mean of Sample-Theoretical Mean of Sample)/(Sample Standard Deviation/sqrt(Sample Size))
Chi Square Statistic
Go Chi Square Statistic = ((Sample Size-1)*Sample Standard Deviation^2)/(Population Standard Deviation^2)
Number of Classes given Class Width
Go Number of Classes = (Largest Item in Data-Smallest Item in Data)/Class Width of Data
Class Width of Data
Go Class Width of Data = (Largest Item in Data-Smallest Item in Data)/Number of Classes
Expectation of Difference of Random Variables
Go Expectation of Difference of Random Variables = Expectation of Random Variable X-Expectation of Random Variable Y
Chi Square Statistic given Sample and Population Variances
Go Chi Square Statistic = ((Sample Size-1)*Sample Variance)/Population Variance
Expectation of Sum of Random Variables
Go Expectation of Sum of Random Variables = Expectation of Random Variable X+Expectation of Random Variable Y
Number of Individual Values given Residual Standard Error
Go Number of Individual Values = (Residual Sum of Squares/(Residual Standard Error of Data^2))+1
F Value of Two Samples given Sample Standard Deviations
Go F Value of Two Samples = (Standard Deviation of Sample X/Standard Deviation of Sample Y)^2
Mid Range of Data
Go Mid Range of Data = (Maximum Value of Data+Minimum Value of Data)/2
F Value of Two Samples
Go F Value of Two Samples = Variance of Sample X/Variance of Sample Y
Smallest Item in Data given Range
Go Smallest Item in Data = Largest Item in Data-Range of Data
Largest Item in Data given Range
Go Largest Item in Data = Range of Data+Smallest Item in Data
Range of Data
Go Range of Data = Largest Item in Data-Smallest Item in Data
Relative Frequency
Go Relative Frequency = Absolute Frequency/Total Frequency

Chi Square Statistic Formula

Chi Square Statistic = ((Sample Size-1)*Sample Standard Deviation^2)/(Population Standard Deviation^2)
χ2 = ((N-1)*s^2)/(σ^2)

What is the importance of Chi Squared test in Statistics?

A chi-squared test is a statistical hypothesis test used in the analysis of contingency tables when the sample sizes are large. In simpler terms, this test is primarily used to examine whether two categorical variables or two dimensions of the contingency table are independent in influencing the test statistic, that is values within the table.
In the standard applications of this test, the observations are classified into mutually exclusive classes. If the null hypothesis that there are no differences between the classes in the population is true, the test statistic computed from the observations follows a chi square frequency distribution. The purpose of the test is to evaluate how likely the observed frequencies would be assuming the null hypothesis is true.

How to Calculate Chi Square Statistic?

Chi Square Statistic calculator uses Chi Square Statistic = ((Sample Size-1)*Sample Standard Deviation^2)/(Population Standard Deviation^2) to calculate the Chi Square Statistic, Chi Square Statistic formula is defined as the measure used in chi-square tests to determine if there is a significant association between categorical variables in a contingency table. Chi Square Statistic is denoted by χ2 symbol.

How to calculate Chi Square Statistic using this online calculator? To use this online calculator for Chi Square Statistic, enter Sample Size (N), Sample Standard Deviation (s) & Population Standard Deviation (σ) and hit the calculate button. Here is how the Chi Square Statistic calculation can be explained with given input values -> 1.361111 = ((10-1)*15^2)/(9^2).

FAQ

What is Chi Square Statistic?
Chi Square Statistic formula is defined as the measure used in chi-square tests to determine if there is a significant association between categorical variables in a contingency table and is represented as χ2 = ((N-1)*s^2)/(σ^2) or Chi Square Statistic = ((Sample Size-1)*Sample Standard Deviation^2)/(Population Standard Deviation^2). Sample Size is the total number of individuals or items included in a specific sample, Sample Standard Deviation is the measure of how much the values in a specific sample vary & Population Standard Deviation is the measure of how much the values in an entire population vary.
How to calculate Chi Square Statistic?
Chi Square Statistic formula is defined as the measure used in chi-square tests to determine if there is a significant association between categorical variables in a contingency table is calculated using Chi Square Statistic = ((Sample Size-1)*Sample Standard Deviation^2)/(Population Standard Deviation^2). To calculate Chi Square Statistic, you need Sample Size (N), Sample Standard Deviation (s) & Population Standard Deviation (σ). With our tool, you need to enter the respective value for Sample Size, Sample Standard Deviation & Population Standard Deviation and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Chi Square Statistic?
In this formula, Chi Square Statistic uses Sample Size, Sample Standard Deviation & Population Standard Deviation. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Chi Square Statistic = ((Sample Size-1)*Sample Variance)/Population Variance
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