Assessing Normality
Determine whether a dataset comes from a normal distribution using visual inspection and correlation criteria.
Objective
Goal: Use Normal Probability Plots to assess if sample data comes from a population that is normally distributed.
Many statistical methods (like t-tests) require the data to be approximately normal. This check allows us to verify that assumption.
Normal Probability Plot
A Normal Probability Plot is a graph that plots observed data values against their expected Z-scores (normal scores).
- X-axis: Observed Data Values
- Y-axis: Expected Normal Scores (Z-scores)
Linear Pattern (Normal)
Normal Probability Plot
If the points lie close to the dashed line, the data is approximately normal.
Points follow the straight line closely. Data is likely normal.
Curved Pattern (Not Normal)
Normal Probability Plot
If the points lie close to the dashed line, the data is approximately normal.
Points curve away from the line (e.g., skewness). Data is likely not normal.
Assessment Criteria
1. Linearity Criterion
If the plotted points lies approximately on a straight line, it is reasonable to conclude that the data come from a normally distributed population. Systematic curvature indicates departure from normality.
2. Correlation Criterion
We can calculate the Linear Correlation Coefficient () between the data and the normal scores.
If (from Table VI), then the data is normal.
Critical Value Table (Example)
Try It Yourself
Normality Assessment Tool
r (0.9807) > critical value (0.906)
Points close to the dashed line indicate normality. Curvature suggests skewness.
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