Relevant Statistical Tests

Statistical Tests
Graham Tall research@grahamtall.com September 2003
For explanation of types of numbers select: Types of Number

An Aside: The research ethic on the use of statistical evidence is unambiguous:

Not only should evidence AGAINST ones’ hypothesis be used, but if such evidence is found it should be given the same, if not more, weight than evidence FOR one’s hypothesis. Research is not about finding proof but about increasing understanding and negative findings commonly more useful than positive ones.

The reasons for using statistical tests are two fold.

i. They provide a kind of ruler. They give an external measure of the likelihood (the probability) of obtaining a particular result by chance. An intrinsic problem in research is judging whether or not a particular explanation (hypothesis) is sufficient. Triangulation, is the socio-anthropologists researcher’s attempt to judge the value of an explanation, but after all the evidence has been collected, the researcher is left with a ‘gut-feeling’ on which decisions are made and the report is written. Statistical tests are designed to provide, for scientific researchers, a measure of the weight that should be placed on such ‘gut-feelings’. Such tests do not prove something, they indicate the likelihood of the explanation. e.g. One-way Chi square

ii. They allow the researcher to generalise from the sample to the population. Whilst in toto individuals are unique, it is evident that they share with other individuals many of their characteristics, attitudes and abilities. The logic of opinion polls* (used widely in consumer marketing and elections) is that it is not necessary to test, or ask everyone their views - all that is required is to test, or ask, a fair sample of those involved. A fair sample being a range of individuals who, in a microcosm, summarise the population.
* Incidentally, don’t take too seriously the apparent ‘failure’ of the United Kingdom’s 1992 general
        election polls - the failure was in a close race, an inaccuracy of
        probably between, 2% and 5%)

For additional information on testing select: background information

1)    Ratio and Interval Numbers: Correlations calculated by Pearson's r

a)    Comparison of 2 or more sets of scores for the
       same group         Comparison of Mean: Correlated Analysis of Variance (ANOVA)
Correlated t test (if only 2 sets)

b)    Comparison of 2 or more groups of students:
                                 Comparison of Mean:
                                 Comparison of Spread of Scores: Analysis of Variance (ANOVA)
t test (if only 2 groups)
F Ratio test

c)    Comparison of achievement of 2 or more groups
        when correlated scores provide additional
         information on each student's ability:
                                 Comparison of Mean: Analysis of Covariance (ANCOVA)
Regression Analysis (Visual comparison)

d)   Comparison of achievement by 2 or more groups
       of students taking into account other scores.
                                                        (see ANOVA).
                                 Comparison of Mean: Multivariate Analysis of Variance (MANOVA)

e)   Comparison of achievement by 2 or more groups
      of students taking into account other scores
      and a correlated score
                                              (see ANCOVA above).
                                 Comparison of Mean: Multivariate Analysis of Covariance (MANCOVA)

f)   Comparison of achievement by 2 or more groups
      of students who are sub-divided into further
      groups.             Comparison of Mean: Two-way ANOVA
Three-way ANOVA

2) Ordinal Numbers Tests are equivalent to 1a & 1b above	Correlations calculated by Spearman's Rho
a) Comparison of achievement of 2 sets of scores for each student	Wilcoxon Signed Ranks Test
b) Comparison of achievement of 2 groups	Wilcoxon Mann-Whitney U Test

3) Nominal Numbers
a) Comparison of responses by one group to the null hypothesis	One Way Chi-Square Binomial Test Sign Test
b) Comparison of responses of two or more groups	Two Way Chi-Square Fishers Exact Test
c) Comparisons taking into account two or more groups and other factors	Log-Linear Analysis (equivalent to a 3 way Chi-square)

Home Page Research Introduction Research and Statistics Courses Quantitative Advice Index
Types of Number Basic Statistics

1) Ratio and Interval Numbers:	Correlations calculated by Pearson's r
a) Comparison of 2 or more sets of scores for the same group Comparison of Mean:	Correlated Analysis of Variance (ANOVA) Correlated t test (if only 2 sets)
b) Comparison of 2 or more groups of students: Comparison of Mean: Comparison of Spread of Scores:	Analysis of Variance (ANOVA) t test (if only 2 groups) F Ratio test
c) Comparison of achievement of 2 or more groups when correlated scores provide additional information on each student's ability: Comparison of Mean:	Analysis of Covariance (ANCOVA) Regression Analysis (Visual comparison)
d) Comparison of achievement by 2 or more groups of students taking into account other scores. (see ANOVA). Comparison of Mean:	Multivariate Analysis of Variance (MANOVA)
e) Comparison of achievement by 2 or more groups of students taking into account other scores and a correlated score (see ANCOVA above). Comparison of Mean:	Multivariate Analysis of Covariance (MANCOVA)
f) Comparison of achievement by 2 or more groups of students who are sub-divided into further groups. Comparison of Mean:	Two-way ANOVA Three-way ANOVA