![]() ![]() Consult Minitab Help to decide which method to use based on the type of data you have. Minitab offers several methods to test for equal variances. ![]() If you are comparing two or more sample means, as in the 2-Sample t-test and ANOVA, a significantly different variance could overshadow the differences between means and lead to incorrect conclusions. Unequal variances (heteroscedasticity) can affect the Type I error rate and lead to false positives. Equal variances (homoscedasticity) is when the variances are approximately the same across the samples. Statistical tests, such as analysis of variance (ANOVA), assume that although different samples can come from populations with different means, they have the same variance. In simple terms, variance refers to the data spread or scatter. What Is the Assumption of Equal Variance? Non-normal data are fine for some statistical methods, but make sure your data satisfy the requirements for your particular analysis. Look for how your data is distributed (normal or skewed), how the data is spread across the graph, and if there are outliers.įor some processes, such as time and cycle data, the data will never be normally distributed. The data will be displayed as a histogram.When interpreting a graphical summary report for normality: The graphical summary displays four graphs: histogram of data with an overlaid normal curve, boxplot, and 95% confidence intervals for both the mean and the median.Ĭhoose Stat > Basic Statistics > Graphical Summary Minitab’s Descriptive Statistics with the Graphical Summary will generate a nice visual display of your data and calculate the Anderson-Darling & p-value. For a specified data set and distribution, the better the distribution fits the data, the smaller this statistic will be. The statistic is a weighted squared distance from the plot points to the fitted line with larger weights in the tails of the distribution. The Anderson-Darling statistic is a measure of how far the plot points fall from the fitted line in a probability plot. The associated p-value will be larger than your chosen α-level (commonly chosen levels for α include 0.05 and 0.10).The associated Anderson-Darling statistic will be small.Imagine a "fat pencil" lying on top of the fitted line: If it covers all the data points on the plot, the data are probably normal. The plotted points should fall close to the fitted distribution line and pass the “fat pencil” test.Some departure from the straight line at the tails may be okay as long as it stays within the confidence limits. The plotted points will roughly form a straight line.When evaluating the distribution fit for the normality test: The alternative hypothesis states that the population is non-normal.Ĭhoose Stat > Basic Statistics > Normality Test The null hypothesis states that the population is normal. Minitab’s Normality Test will generate a probability plot and perform a one-sample hypothesis test to determine whether the population from which you draw your sample is non-normal. There are several methods to determine normality in Minitab, and I’ll discuss two of the tools in this post: the Normality Test and the Graphical Summary. But if sample sizes are less than 15 and the data are not normally distributed, the p-value may be inaccurate and you should interpret the results with caution. If you don’t have normally distributed data, you might use an equivalent non-parametric test based on the median instead of the mean, or try the Box-Cox or Johnson Transformation to transform your non-normal data into a normal distribution.īut keep in mind that many statistical tools based on the assumption of normality do not actually require normally distributed data if the sample sizes are at least 15 or 20. ![]() Many statistical methods start with the assumption your data follow the normal distribution, including the 1- and 2-Sample t tests, Process Capability, I-MR, and ANOVA. If you don’t, you risk selecting an inappropriate statistical test. Now let’s consider the assumptions of Normality and Equal Variance.īefore you perform a statistical test, you should find out the distribution of your data. I addressed random samples and statistical independence last time. The common data assumptions are: random samples, independence, normality, equal variance, stability, and that your measurement system is accurate and precise. Violating any of these assumptions can result in false positives or false negatives, thus invalidating your results. That’s a very powerful tool, but you must check your assumptions when you make statistical inferences. In Part 1 of this blog series, I wrote about how statistical inference uses data from a sample of individuals to reach conclusions about the whole population. ![]()
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