It is easy, rather easiest to make mistakes that involve statistics. Powerful statistical software can help to remove a lot of errors and simplify the difficulties that surround statistical calculations. However, correct interpretation of the result analysis is always all the more challenging.
Some of the most commonly made statistical mistakes are:
Misinterpretation of overlapping confidence levels: In a situation when multiple means are being compared, the statisticians tend to compare the results from confidence intervals and find out if there is any kind if overlapping in intervals in a situation where the confidence level is 95% for two independent means, there is certainly going to be a difference in their means. In a reverse situation, it might not be true and there may be a difference between the means even when the Confidence Intervals overlap.
Making wrong population inferences: statistics does give the liberty to the researcher to make inferences about the entire population, on the basis of the sample results. There are certain situations when the statistician should avoid making inferences. These situations could be:
1) Capability Analysis: Because capability may vary, data from a single unit of time may not be enough to predict the capability of the process.
2) Acceptance Sampling: Only the samples from one section of the lot are selected for the entire unit.
3) Reliability Analysis: This is a severe case when the failed units are included in an analysis exclusively to produce analysis for the entire population.
Confusing between Correlation and Causation: Even if the term is used interchangeably, more than often, it has to be clear that correlation is not to be confused with causation. If there is a correlation between two variables, it certainly does not indicate that one variable is the cause for change in another variable. If the statistician is using only correlation, this holds all the more true.
Giving similar meaning to statistical and Practical Significance: It is crucial to understand that sometimes statistics helps to find such differences that have nit much of a discernible effect in the practical light. To explain it better, an existing difference does not necessarily mean an important difference. Statisticians should not waste a lot of effort and time in correcting a difference that is visible statistically but does not have much of practical relevance.