Normality of Distribution

Parametric Statistics require that the variables being studied are..

Normally Distributed

Step 1 of Distribution

Look at all the possible values and then see how many times they repeat (put them from smallest to largest)

Frequency Table

Listing every possible value in the 1st column of numbers the frequency of each value as the 2nd column

Step 2 of Distribution

Create an ungrouped frequency distribution

Ungrouped Frequency Distribution

Researchers list all categories of the variable on which they have data and tally each datum on the listing

Step 3 of Distribution

Group ages into ranges of value (must be exhaustive: each age will fit into at least one category)

Theoretical Normal Curve

Expression of Statistical Theory (mean, median and mode are equal) (symmetrical, unimodal, and continuous values)

Skewness (aka asymmetrical) 

Any frequency distribution that is not symmetrical 

In a skewed distribution, the mean/median/mode are

Not Equal

What does skewness interfere with?

Validity of the many statistical analyses

Positively Skewed

Largest portion of data is below the mean (the mean is greater than the median which is greater than the mode)

Negatively Skewed

Largest portion of data is above the mean (The mean is less than the median which is less than the mode)

Kurtosis

Explains the degree of the peak of the frequency distribution (related to the spread/variance of scores)

Leptokurtic

Extremely peaked distribution

Mesokurtic

Intermediate degree of kurtosis 

Platykurtic 

Relatively flat distribution

Extreme kurtosis can affect the validity of

Statistical analysis because the scores have little variance

What does kurtosis of zero indicate?

Curve = Mesokurtic

What does kurtosis values above zero indicate?

Curve = Leptokurtic

What does kurtosis values below zero indicate?

Curve = Platykurtic

What should be assessed prior to statistical analysis?

Skewness and Kurtosis

What skewness and kurtosis values are severe and impacts outcomes from parametric analysis techniques?

≥ +1 or ≤ -1 (Since it is this severe, nonparametric testing should be considered)

Shapiro-Wilk’s W Test

Assesses whether a variable’s distribution is skewed and/or kurtotic

How does the Shapiro-Wilk’s W Test have the ability to calculate both skewness and kurtosis?

By comparing the shape of the variable’s frequency distribution to that of a perfect normal curve