Page 246 - DMGT209_QUANTITATIVE_TECHNIQUES_II

Unit 13: Test of Significance
Tanima Dutta, Lovely Professional University

Unit 13: Test of Significance Notes

CONTENTS
Objectives
Introduction
13.1 Small Sample Tests
13.1.1 T-test
13.1.2 Snedecor’s F-distribution

13.2 Large Sample Test
13.2.1 Z-test (Parametric Test)
13.2.2 Chi-square Test
13.2.3 ANOVA
13.3 Summary
13.4 Keywords
13.5 Review Questions
13.6 Further Readings

Objectives

After studying this unit, you will be able to:
 Discuss the small sample tests;

 Explain the large sample test.
Introduction

Tests for statistical significance are used to estimate the probability that a relationship observed
in the data occurred only by chance; the probability that the variables are really unrelated in the
population. They can be used to filter out unpromising hypotheses. In research reports, tests of
Tanima Dutta, Lovely Professional University
statistical significance are reported in three ways. First, the results of the test may be reported in
the textual discussion of the results. Include:
1. Hypothesis
2. Test statistic used and its value

3. Degrees of freedom
4. Value for alpha (p-value)
Tests for statistical significance are used because they constitute a common yardstick that can be
understood by a great many people, and they communicate essential information about a research
project that can be compared to the findings of other projects. However, they do not assure that
the research has been carefully designed and executed. In fact, tests for statistical significance
may be misleading, because they are precise numbers. But they have no relationship to the
practical significance of the findings of the research.
Finally, one must always use measures of association along with tests for statistical significance.
The latter estimate the probability that the relationship exists; while the former estimate the

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