PSYC 2260 Lecture Notes - Lecture 14: Null Hypothesis, Parametric Statistics, Normal Distribution
26 Jun 2018
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PSYC 2260 Introduction to Research Methods in Psychology Chapter 14
Chapter 14 Strategies When Population Distributions Are not Normal
14.1 Assumptions in the Standard Hypothesis-Testing Procedure
Sometime data violates the conditions for accuracy (‘assumption’)
- Assumption of normality in normal population
- Assumption of equal variations in the population
In many situations, minor violations do not have dramatic effects on the accuracy of statistical
test
Recall assumption are for unknown population parameters, not sample
- T-test, ANOVA, correlation, and regression use sample to estimate the population
- More or less depend on assumptions for accuracy
What happens when assumptions are severely violated?
- Critical cut-off pints for ‘significant’ can go up or can go down
- Problem: you don’t know which way they will go
How you check to see if you have met the assumption? Why is this problematic?
- Make a histogram for the sample. If it’s not drastically different from normal, the
researchers assume that the population it come from is roughly normal
- The samples, especially if they are small, can have quite different shapes and variances from
the populaitons
Situation you doubt the assumption
- Ceiling or floor effect
- When sample has outliers
Outlier has a huge effect
- T-test, ANOVA…..rely on squared deviations from the mean
- Outlier is so far from mean, an outlier has a huge influence when you square its deviation
from the mean
- A single outlier, if it is extreme enough, can drastically distort the results of a study
14.2 Data Transformation
find more resources at oneclass.com
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PSYC 2260 Introduction to Research Methods in Psychology Chapter 14
Data transformation: mathematical procedure (such as taking the square root) used on each
score in a sample, usually done to make the sample distribution closer to the normal
- Do it when the scores in the sample do not appear to come from a normal population
- In order to use familiar and sophisticated hypothesis-testing procedures.
Legitimate
- Done when it is done to all scores
- Not for satisfied researcher’s expectation
- The underlying meaning of the distance between scores is arbitrary
Kinds of data transformations
a) For positive view (skew): skewed to the right is the most common situation
- Square-root transformation
Moderate numbers become only slightly lower but high numbers become much
lower
- Log transformation
Has stronger effect
Is better used for distribution that are very strongly skewed to the right
- Inverse transformation
Corrects distribution with an even stronger skew to the right the a log
transformation
Each score is divides into 1. E.g. X=10 1/10 = 0.1
b) For negative view (skew)
- Must “reflect” the data then use the square root transformation , log, and inverse
- Subtract all scores from some high number
Handout MAR27
14.3 Rank-Order Tests
Another way to cope with non-normal distribution
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Chapter 14 strategies when population distributions are not normal. Sometime data violates the conditions for accuracy ( assumption") In many situations, minor violations do not have dramatic effects on the accuracy of statistical test. Recall assumption are for unknown population parameters, not sample. T-test, anova, correlation, and regression use sample to estimate the population. More or less depend on assumptions for accuracy. Critical cut-off pints for significant" can go up or can go down. Problem: you don"t know which way they will go. If it"s not drastically different from normal, the researchers assume that the population it come from is roughly normal. The samples, especially if they are small, can have quite different shapes and variances from the populaitons. T-test, anova rely on squared deviations from the mean. Outlier is so far from mean, an outlier has a huge influence when you square its deviation from the mean.
