2.  There are two types of test data and
consequently different types of analysis.
 As the table below shows, parametric data
has an underlying normal distribution which
allows for more conclusions to be drawn as
the shape can be mathematically described.
 Anything else is non-parametric.
 As the table shows, there are different tests
for parametric and non-parametric data.

3.  ANOVA: analysis of variation in an
experimental outcome and
especially of a statistical variance
in order to determine the
contributions of given factors or
variables to the variance.
 Remember: Variance: the square of
the standard deviation
3

4.  Any data set has variability
 Variability exists within groups…
 and between groups
 Question that ANOVA allows us to
answer : Is this variability significant, or
merely by chance?
4

5.  The difference between variation within a
group and variation between groups may
help us determine this.
 If both are equal it is likely that it is due
to chance and not significant.
 H0: Variability w/i groups = variability b/t
groups, this means that 1 = n
 Ha: Variability w/i groups does not =
variability b/t groups, or, 1 n
5

6.  Normal distribution
 Variances of dependent variable are equal in
all populations
 Random samples; independent scores
6

7.  One factor (manipulated variable)
 One response variable
 Two or more groups to compare
7

8.  Similar to t-test
 More versatile than t-test
 Compare one parameter (response variable)
between two or more groups
8

9.  Tedious when many groups are present
 Using all data increases stability
 Large number of comparisons some may
appear significant by chance
9

10. Accept Reject
H0 is true Good Type I
H0 is false Type II Good
©McGraw-Hill Companies, 2010

11. Non-Parametric Techniques

12.  Research Question and Design
 Type of Data
◦ Parametric tests make assumptions about data.
 Parametric tests are not suitable for nominal or ordinal data and
assume equality of variances across samples –homogeneity of
variance.
◦ Non-parametric tests do not make assumptions about data.
 Number of independent Variables
 Number of Conditions
©McGraw-Hill Companies, 2010

13. Parametric Non-parametric
Assumed distribution Normal Any
Assumed variance Homogeneous Any
Typical data Ratio or Interval Ordinal or Nominal
Data set relationships Independent Any
Usual central measure Mean Median
Benefits Can draw more conclusions
Simplicity; Less affected by
outliers
Tests
Correlation test Pearson Spearman
Independent measures, 2
groups
Independent-measures t-test Mann-Whitney test
Independent measures, >2
groups
One-way, independent-
measures ANOVA
Kruskal-Wallis test
Repeated measures, 2
conditions
Matched-pair t-test Wilcoxon test

14. Mann-Whitney U test
Non-parametric test used to compare averages
from two independent samples
Non-parametric equivalent of the independent t
test
Wilcoxon Signed ranks test
Non-parametric test used to compare two
averages from the same sample, or paired or
matched samples
Non-parametric equivalent of the paired-
samples t test
©McGraw-Hill Companies, 2010

15. Kruskal-Wallis test
Non-parametric equivalent of one-way between-subjects
ANOVA; used to compare differences in scores for two or more
groups.
Chi-square (χ2) is the test statistic used for Kruskal-Wallis, so
make a note of it. You should also note the values for df and
Exact Sig.
©McGraw-Hill Companies, 2010

16.  Ordinal data or non-linear relationships.
 The most common of these non-parametric correlations is the
Spearman correlation (rs or rho).
 Spearman’s correlation can be used to look at the relationship between
variables when one or both of the variables are ordinal.
 You should also use it if your data are interval/ratio but there appears to be
a monotonic nonlinear relationship.
A monotonic relationship is simply a relationship that goes in one direction.
©McGraw-Hill Companies, 2010
Suitable for Spearman’s correlat
Not suitable

17. Spearman’s correlation can deal with nonlinear
relationships because it converts scores into
ranks (if they aren’t already ranked) and works
out the linear correlation between the ranks.
An alternative to Spearman’s correlation is
Kendall’s tau (τ). Field (2009) recommends that
Kendall’s tau is used when you have small
samples and large numbers of tied ranks.
©McGraw-Hill Companies, 2010
Non-Parametric Correlation

18. Nominal data represent named discrete categories, people
belong to a group (e.g., male/female) or achieve a certain
outcome (e.g., pass/fail).
All that can be done with this type of data is count it.
When the dependent variable is nominal (e.g., yes/no/don’t
know, pass/fail, option a/b/c/d), you can use chi-square
tests. There are two main chi-square tests that you will
come across:
The chi-square test of goodness-of-fit is used when you
want to examine differences between categories within one
nominal variable.
The chi-square test of association (sometimes also called
the test of independence) is used when you want to examine
the relationship between two nominal variables.
©McGraw-Hill Companies, 2010

19. Independent observations: each participant should
contribute to only one category. The total
frequency in a chi-square test should be the same
as the number of participants.
Expected frequencies: chi-square tests assume
that expected counts will be greater than 5. The
reason for this is that the value of chi-square can
become distorted with small expected frequencies.
Therefore try to use large samples when collecting
data suitable for chi-square analysis.
©McGraw-Hill Companies, 2010