Statistics calculators
Test statistic calculator
# 
Test name 
1  One Sample ZTestCheck that the expected mean is correct, based on a sample average, when you know the standard deviation.

2  One Sample TTestCheck that the expected mean is correct based on the sample average when you don't know the standard deviation

3  Two Sample ZTestCompare the average of two groups, when you know the standard deviation.

4  Two Sample TTest (Pooled variance)Compare the average of two groups, when you don't know the standard deviation, and expect the standard deviation of both groups to be equal.

5  Two Sample TTest (Welch's)Compare the average of two groups, when you don't know the standard deviation, and expect the standard deviation of both groups to be unequal.

6  Two Sample MannWhitney U TestCompare the average of two groups, when you don't know the standard deviation, and expect the standard deviation of both groups to be unequal.

7  Paired TTestCompare the average of two groups, when you don't know the standard deviation, and expect the standard deviation of both groups to be unequal.

8  Paired Wilcoxon Sign Rank TestCompare the average of two groups, when you don't know the standard deviation, and expect the standard deviation of both groups to be unequal.

9  One Way ANOVA TestCheck if the difference between the average (mean) of two or more groups (populations) is significant, using sample data.
ANOVA is usually used when there are at least three groups, since for two groups you can use t tests.

10  ChiSquared Test For Variance 
11  F Test For Variances 
12  ChiSquared Test For Goodness Of FitCheck if the statistical model fits the observations

13  ShapiroWilk TestCheck if the normal distribution model fits the observations

Test 
Assumptions 
Required sample data 
# 
Test name 
Check 
Statistic 

IndIndependent observations 
σYou know the population's standard deviation 
σ_{1}=σ_{2}The standard deviations of both groups are equal 
dYou know the expected difference between the means 
μYou know the expected mean 
xSample average 
nSample size 
sSample standard deviation 

1  One Sample ZTestCheck that the expected mean is correct, based on a sample average, when you know the standard deviation.
 Mean   ✔  ✔  ✔    ✔  ✔  ✔   
2  One Sample TTestCheck that the expected mean is correct based on the sample average when you don't know the standard deviation
 Mean   ✔  ✔  ✘    ✔  ✔  ✔  ✔  
3  Two Sample ZTestCompare the average of two groups, when you know the standard deviation.
 Mean   ✔  ✔  ✔   ✔   ✔  ✔   
4  Two Sample TTest (Pooled variance)Compare the average of two groups, when you don't know the standard deviation, and expect the standard deviation of both groups to be equal.
 Mean   ✔  ✔  ✘  ✔  ✔   ✔  ✔  ✔  
5  Two Sample TTest (Welch's)Compare the average of two groups, when you don't know the standard deviation, and expect the standard deviation of both groups to be unequal.
 Mean   ✔  ✔  ✘  ✘  ✔   ✔  ✔  ✔  
6  Two Sample MannWhitney U TestCompare the median of two groups, when you can't assume normality distribution, the test is robust to outliers.
 Median  
 ✔    ✔    
 ✔ 
7  Paired TTestDetermine how a change has taken effect by considering each individual pair as an observation. The test uses T distribution
 Mean   ✔  Paired         ✔ 
8  Paired Wilcoxon Sign Rank TestDetermine how a change has taken effect by considering each individual pair as an observation. The test uses a ranking methodn
 Mean    Paired         ✔ 
9  One Way ANOVA TestCheck if the difference between the average (mean) of two or more groups (populations) is significant, using sample data.
ANOVA is usually used when there are at least three groups, since for two groups you can use ttests.
 Mean   ✔  ✔         ✔ 
10  ChiSquared Test For Variance  σ   ✔  ✔  ✔      ✔  ✔  
11  F Test For Variances  σ   ✔  ✔       ✔  ✔  
12  ChiSquared Test For Goodness Of FitCheck if the statistical model fits the observations
 Fit  
 ✔         ✔ 
13  ShapiroWilk TestCheck if the normal distribution model fits the observations
 Fit  
✔  ✔         ✔ 
** ✔ yes, ✘ no, empty  irrelevant
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