1.
Exploratory Data Analysis
1.3. EDA Techniques 1.3.5. Quantitative Techniques


Purpose: Test if standard deviations from two populations are equal 
An Ftest ( Snedecor and Cochran, 1983) is used to test if the standard deviations of two populations are equal. This test can be a twotailed test or a onetailed test. The twotailed version tests against the alternative that the standard deviations are not equal. The onetailed version only tests in one direction, that is the standard deviation from the first population is either greater than or less than (but not both) the second population standard deviation . The choice is determined by the problem. For example, if we are testing a new process, we may only be interested in knowing if the new process is less variable than the old process.  
Definition 
The F hypothesis test is defined as:


Sample Output 
Dataplot generated the following output for an Ftest
from the JAHANMI2.DAT data set:
F TEST NULL HYPOTHESIS UNDER TESTSIGMA1 = SIGMA2 ALTERNATIVE HYPOTHESIS UNDER TESTSIGMA1 NOT EQUAL SIGMA2 SAMPLE 1: NUMBER OF OBSERVATIONS = 240 MEAN = 688.9987 STANDARD DEVIATION = 65.54909 SAMPLE 2: NUMBER OF OBSERVATIONS = 240 MEAN = 611.1559 STANDARD DEVIATION = 61.85425 TEST: STANDARD DEV. (NUMERATOR) = 65.54909 STANDARD DEV. (DENOMINATOR) = 61.85425 F TEST STATISTIC VALUE = 1.123037 DEG. OF FREEDOM (NUMER.) = 239.0000 DEG. OF FREEDOM (DENOM.) = 239.0000 F TEST STATISTIC CDF VALUE = 0.814808 NULL NULL HYPOTHESIS NULL HYPOTHESIS HYPOTHESIS ACCEPTANCE INTERVAL CONCLUSION SIGMA1 = SIGMA2 (0.000,0.950) ACCEPT 

Interpretation of Sample Output 
We are testing the hypothesis that the standard deviations for
sample one and sample two are equal. The output is divided into
four sections.


Questions 
The Ftest can be used to answer the following
questions:


Related Techniques 
QuantileQuantile Plot Bihistogram ChiSquare Test Bartlett's Test Levene Test 

Case Study  Ceramic strength data.  
Software  The Ftest for equality of two standard deviations is available in many general purpose statistical software programs, including Dataplot. 