Final answer:
Non-parametric tests resolve the issue of normality by using data ranks, making the tests robust to outliers and less influenced by the data distribution. These tests include procedures like the test for homogeneity and one-way ANOVA for comparing population distributions and means.
Step-by-step explanation:
Non-parametric tests overcome the problem of normality by ranking the data. These tests do not require the assumption of normal distribution in the population from which the sample is drawn. Non-parametric methods are particularly useful when dealing with small sample sizes or when the distribution of the data is unknown or non-normal. They work by replacing actual data values with their ranks within the dataset and then applying statistical tests to these ranked data. This approach can make the tests more robust to outliers and less sensitive to violations of other assumptions such as homoscedasticity (equal variances) and linearity.
When identifying outliers, statistical tests involving the Interquartile Range (IQR) can be used. If a data value is significantly different from the rest, it may be considered an outlier and could potentially be removed or analyzed separately depending on the context of the research.
Furthermore, when considering non-parametric methods in statistics, additional tests such as tests for homogeneity or one-way ANOVA are used for specific hypotheses related to population distribution and mean comparisons among groups, respectively.