The document discusses the appropriate use of parametric and nonparametric statistical tests based on the scale of measurement and population distribution. It explains the characteristics of different data types (nominal, ordinal, interval, and ratio) and the conditions required for using parametric tests, including normal distribution and homogeneity of variance. The document provides a decision-making framework for selecting the appropriate statistical tests, detailing alternatives for various input and output variable types.

1. Gonenc DALGIC
Yasar University
PhD in Business Administration

2. When to use which statistical tests:
Parametric or nonparametric??
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3. To find the answer, start with the scale of measurement
• define an attribute
Nominal • e.g. gender, matital status
• rank or order the observations as
scores or categories from low to high
in terms of «more or less»
• e.g. education, attitude/opinion scales
Ordinal
• interval between observations in
terms of fixed unit of measurement
• e.g. measures of temperature
Interval
• The scale has a fundamental zero
point
• e.g. age, income
Ratio
Nonparametric
Nonparametric
*Parametric
*Parametric
*may be used
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4. In addition to scale of measurement, we should look at
the population distribution.
Population is normally distributed
• Nonparametric
• (have to be used)
Not normally distributed population
or no assumption can be made about
the population distribution
• Parametric
• (may be used)
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5. Normal Distribution
 a very common continuous probability distribution
 All normal distributions are symmetric.
 bell-shaped curve with a single peak.
 68% of the observations fall within 1 standard deviation of
the mean
 95% of the observations fall within 2 standard deviations of
the mean
 99.7% of the observations fall within 3 standard deviations
of the mean
 for a normal distribution, almost all values lie within 3
standard deviations of the mean

6. To use parametric tests, stay tuned…
 Interval or ratio data are required.
 Normal distribution is required.
+
Homogeneity of variance
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7. Homogeneity of Variance
 The variance is a measure of the dispersion of the
random variable about the mean. In other words, it
indicates how far the values spread out.
 It refers to that variance within each of population is
equal.
 Homogeneity of Variances is assessed by Levene’s test.
(T-test and ANOVA use Levene’s test.)

8. Parametric or nonparametric – Determination
 In cases where
 the data which are measured by interval or ratio scale come
from a normal distribution
 Population variances are equal
parametric tests are used.
 In cases where
 the data is nominal or ordinal
 the assumptions of parametric tests are inappropriate
nonparametric tests are used.
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9. Parametric or nonparametric – Determination
Type of data
Categorical
Metric
Are the data
approximately
normally
distributed?
No
Yes
Are the
variances of
populations
equal?
Nonparametric Tests
Nonparametric Tests
No Nonparametric Tests
Parametric Tests
Yes
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10. Statistical Test Alternatives: Parametric - Nonparametric
Output variable
Nominal Ordinal Interval - Ratio
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Input variable
Nominal Chi-square
Mann Whitney
Kruskal – Wallis
Unpaired t-test or
Mann Whitney
Paired t-test or Wilcoxon
Analysis of variance or
Kruskal – Wallis
Ordinal
Chi-square
Mann Whitney
Spearman Rank
Linear regression or
Spearman
Interval
Ratio
Logistic
regression
Poisson regression
Pearson’s r,
Linear regression or
Spearman

11. Thank you for your attention.
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