Question

1. When a data distribution is not "normal" why is this concerning for a researcher or statistician? (2 pts)

2. What are the three types of data transformations that can be used when a distribution is skewed to the right? (3 pts)

2b. What is the one transformation discussed that can be applied when the distribution is skewed to the left? (2 pts)

3. List three examples of a non-parametric statistical test? (3 pts)

Answer 1

1. A large number of statistical tests are based on the assumption of normality, so not having data that is normally distributed typically instills a lot of fear.

Many practitioners suggest that if your data are not normal, you should do a nonparametric version of the test, which does not assume normality. From my experience, I would say that if you have non-normal data, you maylook at the nonparametric version of the test you are interested in running. But more important, if the test you are running is not sensitive to normality, you may still run it even if the data are not normal.

2. (a) positive skew: The right tail is longer; the mass of the distribution is concentrated on the left of the figure. The distribution is said to be right-skewed, right-tailed, or skewed to the right, despite the fact that the curve itself appears to be skewed or leaning to the left; right instead refers to the right tail being drawn out and, often, the mean being skewed to the right of a typical center of the data. A right-skewed distribution usually appears as a left-leaning curve. Types of data transformations that can be used when a distribution is skewed to the right

(1) Cube Root

(2) Square Root

(3) Logarithm

2. (b) negative skew: The left tail is longer; the mass of the distribution is concentrated on the right of the figure. The distribution is said to be left-skewed, left-tailed, or skewed to the left, despite the fact that the curve itself appears to be skewed or leaning to the right; left instead refers to the left tail being drawn out and, often, the mean being skewed to the left of a typical center of the data. A left-skewed distribution usually appears as a right-leaning curve.Transformation that can be used when a distribution is skewed to the left

(1) Square

3. The main nonparametric tests are:-

(1) 1-sample sign test. Use this test to estimate the median of a population and compare it to a reference value or target value.

(2) Mann-Whitney test. Use this test to compare differences between two independent groups when dependent variables are either ordinal or continuous.

(3) Kruskal-Wallis test. Use this test instead of a one-way ANOVA to find out if two or more medians are different. Ranks of the data points are used for the calculations, rather than the data points themselves.