Inferential Analysis

We have just reviewed descriptive analysis, which includes descriptive statistics such as range, minimum, maximum, and frequency. It also includes measures of central tendency such as mean, median, mode, and standard deviation tells us what our data look like. Once you have appropriately described your data, then you can move on to making inferences based on your data.


Inferential Analysis

Inferential analysis uses statistical tests to see whether a pattern we observe is due to chance or due to the program or intervention effects. Research often uses inferential analysis to determine if there is a relationship between an intervention and an outcome as well as the strength of that relationship.  

This section provides an overview of things to consider before starting inferential analysis, examples of common statistical tests, and the meaning of statistical significance.

The first step in inferential analysis: One of the first steps in inferential analysis is to answer the question what does the distribution of data look like? The type of test you choose will be guided by the distribution of the data. Distributions fall into two categories, normal and non-normal. You should always check the distribution of your data before beginning inferential analysis.

Normal Distribution: This type of distribution looks like the Bell Curve. The graph below is an example of what a normal distribution looks like.

Normal Distribution

 

If you look at your distribution, you could draw a curve over the distribution that would fit your data. If your distribution looks like the one in the image below (or close to it) your distribution is normal. This type of distribution shows us that the majority of the data is clustered around one number or value. Usually if the data is normal, we choose from statistical tests called parametric tests.

Normal Distribution

Non-Normal Distributions There are several ways a distribution can be non-normal. A small sample size or unusual sets of responses are common reasons that data may not be normally distributed. Usually if the data is non-normal, we choose from a set of statistical tests called non-parametric tests.

We will review the two types of non-normal distributions listed below.

Skewed: This type of distribution does not take the shape of the familiar Bell Curve and can be skewed positively or negatively.

The bar chart below shows negatively skewed data; the majority of the scores are at the higher end of possible scores.

Negatively Skewed distribution

The bar chart below shows positively skewed data; the majority of the scores are at the lower end of possible scores.

Positively Skewed Distribution


Kurtosis: This describes when a distribution is either too peaked (pointy) or too flat.



Kurtosis



flat distribution



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