Chapter 3: Normality

What is normal distribution?

Describes the way in which data is "spread"

Probability statistics

Describe the likelihood of something happenings based on what we knew about previous outcomes

What does normal distribution look like?

We expect the data to be evenly distributed on each side of the mean, shown as a bell shaped pattern with a distinct peak

Mean

The average number in the data set

Median

The middle number in a set data

Mode

The most common number in a data set

Skewed data

When data is not symmetrical, most scores fall on one end of the distribution, which can distort the data

Positively skewed data

Scores are at the higher end of the range of data, which inflate the mean; the tail goes to the right

Negatively skewed data

Scores are at the lower end of the range of data, which deflate the mean; the tail goes to the left

Kurtosis

How flat or peaked a normal distribution is

3 types of kurtosis

1. Leptokurtic

2. Mesokurtic

3. Platykurtic

Leptokurtic distribution

Very peaked distribution, with little variation in the data

Platykurtic distribution

Very flat distribution, with too much variation across the data

Mesokurtic distribution

A normal curve, bell shaped

What happens when data are not normally distributed?

We may no longer be able to trust the mean score as truly reflecting the data, need to trust alternative tests

Different graphs to measure normality

• histograms

• box plots

• stem and leaf plots

Histogram

A graph with a curve drawn through the data to indicate the trend in the data

Box plot

A graph that shows how the data are spread around the median in a line through a box representing the middle point

Stem and leaf plot

The stem refers to a groups of data (tens, hundreds, etc) and leaf refers to units within that group

Formal statistic methods

Kolmogorov-Smirnov (KS Test) and Shapiro-Wilk (SW)

What are some ways the KS/SW tests are used?

• across single variables

• between group studies

• within groups studies

Dependent variable

The variable being measured

Independent variable

The variable being manipulated

Between groups studies

Where the independent variable is measured between two/more distinct groups of people/cases

Within groups studies

Where the independent variable is measured across one group, in respect to two/more conditions

Outliers

Extreme values that don't appear to belong with the rest of the data

What are some ways to adjust non-normal data?

• removing/adjusting outliers

• transformation

Common methods of transformation of data:

• Logarithmic

• Square root

• Reciprocal

Logarithmic

Useful for positively skewed data

Square root

Used when the data represents a count (rather than a continuous scale)

Reciprocal

Helpful when there is no specific upper limit to the values in the variable

Homogeneity of variance

The assumption that the variance is similar between groups in respect of an outcome

Sphericity

The assumption that the variance between the conditions are similar within groups