Data considerations for 1 Variance

To ensure that your results are valid, consider the following guidelines when you collect data, perform the analysis, and interpret your results.

The sample data should be selected randomly

In statistics, random samples are used to make generalizations, or inferences, about a population. If your data are not collected randomly, your results may not represent the population. For more information, go to Randomness in samples of data.

The sample data should not be severely skewed, and the sample size should be greater than 40
With the Bonett method, if your sample size is greater than 40, the hypothesis test performs appropriately, even with mildly skewed data. If the sample size is less than 40, graph the data to check for skewness and unusual observations. If the data are from a distribution that has more data at its lower and upper ends than the normal distribution (a distribution with "heavy tails"), use caution when you interpret the results.

Use the chi-square method only if you are certain that the data follow a normal distribution, because any small deviation from normality can greatly affect chi-square method results.

Each observation should be independent from all other observations
The independence of observations is determined by whether one observation provides information about another observation, as follows:
  • If an observation provides no information about the value of another observation, the observations are independent.
  • If an observation provides information about another observation, the observations are dependent. If your observations are dependent, your results may not be valid.
Determine an appropriate sample size
Your sample should be large enough so that the following are true:
  • The estimates have enough precision.
  • The confidence intervals are narrow enough to be useful.
  • You have adequate protection against type I and type II errors.
To determine the appropriate sample size for your hypothesis test, go to Power and Sample Size for 1 Variance.