This document discusses statistical tests for different types of data and research questions. It explains that there are parametric tests that assume a normal distribution, like the t-test, z-test, and F-tests, and non-parametric tests that don't make distribution assumptions, like chi-square, Mann-Whitney, and Wilcoxon. It provides examples of the types of data and questions each test is suited for, such as using t-tests for comparing two means, chi-square for nominal associations, and Spearman's rank for ordinal correlations. Finally, it presents a summary table outlining which statistical tests to use for different sample characteristics and levels of measurement.

5. Lesson Objectives

6. 1. The scale of measurement
2. Type of question being asked
 There are two types of tests
 A. Parametric
 B. Non parametric

7.  Parametric: decision making method
where the distribution of the sampling
statistic is known
 Non-Parametric: decision making method
which does not require knowledge of the
distribution of the sampling statistic

8. What kind of data you have?
Nominal
Ordinal
NUMERICAL
Continuous
Nonparametric
Categorical data
Parametric
(mean)
Ex: height / length / weight
(Assuming a normal distribution on n>30)
Ex: Frequency: Yes / No
Race
Gender
Ex: Middle (1) / Moderate(2) Severe (3)
Comparing groups (samples)
How to checK Normality ?

9. These tests test the hypothesis about means or variances.
They share three common features
1. Hypothesis refers to population parameters: the population mean (in
the case of t and Z tests) or Population variance (in case of F tests)
2. They are concerned with the interval or ratio scale data e.g. weight,
blood pressure, IQ, per capita income, measurements of clinical
improvement and so on.
3. They make certain assumptions about the distribution of the data of
interest in the population
. T test, Z test and F tests are examples of Parametric tests

10.  These tests do not test the hypothesis
concerning parameters,
 they do not assume that the population is
normally distributed and are also called
distribution free test.
 They are used to test the nominal or ordinal
scale data.
 They are less powerful than parametric tests.

11.  the various forms of chi-square tests
 the Fisher Exact Probability test
 the Mann-Whitney Test,
 the Wilcoxon Signed-Rank Test,
 the Kruskal-Wallis Test,
 the Friedman Test.
 McNemar test

12.  Concerning nominal scale data only one kind of question
has been asked
 DO the proportions of observations falling in different
categories differ significantly from the proportions that
would be expected by chance?.
 The appropriate test for such questions is the chi square
test

13.  Regarding ordinal scale data only one kind of question
 Is there an association between ordinal position on one
ranking and ordinal position on another ranking.
 The appropriate technique here is Spearman rank
order correlation

14. Four general kinds of questions have been discussed.
 Questions concerning means
1. what is the true mean of the population ?.
2. Is one sample mean significantly different from one or more other
sample means?.
 Questions concerning Variances:
3. Are the variances in two samples significantly different.
 Questions concerning Association:
4. To what degree are two variables correlated?.

15. three ways of answering questions concerning means of interval or ratio scale data.
 1. Questions concerning means
A. when the question involves only one or two means or making only one comparison , a t
test will be used.
e.g. Estimation of a population mean ?, testing a hypothesis about population mean?,
comparing two sample means with each other .
B. if n > 100 or if the standard deviation of the population is known a Z test may be used.
 2. Questions concerning Variances:
C. Are the variances in two samples significantly different.
 3. Questions concerning Association:
D. To what degree are two variables correlated?.

16.  When the question involves more than two means or
making more than one comparison the appropriate
technique is Analysis of variance (ANOVA), together
with F test, followed by post hoc test of various types (if
ANOVA has found some significant results)

17.  T o evaluate the strength and direction of the
relationship, pearson product- moment
correlation is used.
 To make predictions about the value of one variable on
the basis of other Regression techniques are used.

19. Summary Table of Statistical Tests
Level of
Measurement
Sample Characteristics Correlation
1
Sample
2 Sample K Sample (i.e., >2)
Independent Dependent Independent Dependent
Categorical
or Nominal
Χ2 or
bi-
nomial
Χ2 Macnarmar’
s Χ2
Χ2 Cochran’s Q
Rank or
Ordinal
Mann
Whitney U
Wilcoxin
Matched
Pairs Signed
Ranks
Kruskal Wallis
H
Friendman’s
ANOVA
Spearman’s
rho
Parametric
(Interval &
Ratio)
z test
or t test
t test
between
groups
t test within
groups
1 way ANOVA
between
groups
1 way
ANOVA
(within or
repeated
measure)
Pearson’s r
Factorial (2 way) ANOVA