Two-Sample F Test

Statistics > Basic Statistics > 2-Variances


Tests if the variances of two populations are equal.

Many statistical procedures, including the two sample t-test procedures, assume that the two samples are from populations with equal variance. The variance test procedure will test the validity of this assumption.


Dialog box items

Samples in one column:
Choose if the sample data are in a single column, differentiated by factor levels in a second column.

oSamples: Enter the columns containing the sample data.

oFactor and Levels: Enter the columns containing the sample factor, and select the levels.

Samples in different columns:
Choose if the data of the two samples are in separate columns.

oFirst Sample: Enter the column containing one sample.

oSecond Sample: Enter the column containing the other sample

Summarized data:
Choose if you have summary values for the sample size, mean, and standard deviation.

oFirst Sample

-Sample size: Enter the value for the sample size.

-Sample Mean: Enter the value for the sample mean.

-Sample Std Dev: Enter the value for the sample standard deviation.

oSecond Sample

-Sample size: Enter the value for the sample size.

-Sample Mean: Enter the value for the sample mean.

-Sample Std Dev: Enter the value for the sample standard deviation.

The display of outputs of VisualStat.



Data can be entered in one of two ways:

Both samples in a single numeric column with another grouping column (called factor) to identify the population. The grouping column may be categorical, numeric or text.

Each sample in a separate numeric column.

The sample sizes do not need to be equal. Missing values are ignored.



Displays a histogram, a histogram with a normal curve, and a boxplot.

Choose to display a histogram for each variable

Histogram with Normal Curve:
Choose to display a histogram with a normal curve for each variable

Boxplot of data:
Choose to display a boxplot for each variable

Choose the options you want.

oExclude missing values: Check to excludes rows that have missing values.

oInverted Bar: Check to reverse the axes.



Alternative Hypothesis:
Enter Two-sided, Upper One-sided, or Lower One-sided. If you choose an One-sided hypothesis test, an upper or lower confidence bound will be constructed, respectively, rather than a confidence interval.

Confidence Level:
Enter the level of confidence desired. Enter any number between 0 and 100. Entering 90 will result in a 90% confidence interval. The default is 95%.



The data for this case study were collected by Said Jahanmir of the NIST Ceramics Division in 1996 in connection with a NIST/industry ceramics consortium for strength optimization of ceramic strength.

The motivation for studying this data set is to illustrate the analysis of multiple factors from a designed experiment

This case study will utilize only a subset of a full study that was conducted by Lisa Gill and James Filliben of the NIST Statistical Engineering Division

The response variable is a measure of the strength of the ceramic material.

The goals of this case study is to determine if the nuisance factors (lab and batch) have an effect on the ceramic strength (y).


1.Open the DataBook compare.vstz

2.Select the sheet jahanmi2

3.Choose the tab Statistics, the group Basic Statistics and the command 2-Variances

4.Select group Samples in one column

5.In Samples, select Y. In Factors and Levels, select Batch.

6.Click OK


Report window output


Two-Sample F Test


F test to compare two variances

alternative hypothesis: true ratio of variances is not equal to 1


           N1   N2   StDev1  StdDev2  num df  denom df  95% Conf Interval  F-Stat  p-Value  Alt Hypothesis

Y-1 / Y-2  240  240  65.5491  61.8542     239       239   [0.8710; 1.4480]  1.1230   0.3704          Reject




Interpreting the results



Hypotheses: Ho:s1 = s2 vs Ho:s1 ≠ s2

Identify the degrees of freedom (df1 = 240 - 1 = 239 and df2 = 240 - 1 = 239)

Test Statistics: Fo = 1.123

p-value = P(F(df1 = 239, df2 = 239) > Fo = 1.123) = 0.3704


This p-value does not indicate strong evidence in the data to reject the null hypothesis. That is, the data does not have power to discriminate between the population variances of the two populations based on these samples



See Also:

Report | Numeric Formats

Web Resource: NIST e-Handbook of Statistical Methods, 2006 | Probability and statistics EBook