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 sizes should be greater than 20
If your sample sizes are greater than 20 and the underlying distribution is unimodal and continuous, the hypothesis test performs appropriately even if data are mildly skewed. If your sample sizes are less than 20, you should graph the data to check for skewness and unusual observations. If the data is severely skewed or has many unusual observations, use caution when you interpret the 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 2 Variances