Statistical Analysis for Education and Psychology Researchers

relating to ranked data. The three types of data distributions, binomial/nominal, rank and
continuous normal correspond to three main classes of statistics mentioned in the
previous section. For some designs these three types of data distributions are further
divided into independent and related measures. This gives a total of six columns:
binomial independent/related; ranked independent/ related; and continuous normal
independent/related.
To decide on an appropriate statistical test start at the top of the left hand design
column and move down this column until you reach a design and research question that is
consistent with your study design. The type of independent vari-
STATISTICAL INFERENCE ABOUT
DESIGN: COUNT DATA CONTINUOUS
DATA
One. Sample Binomial/Nominal Rank Normal
Research Q:
Association/
relationship

One sample χ^2 test of

Independence (6.1) Phi

Coefficient and Cramer’s

Phi (6.1)

Spearman’s rank order

rs correlation (7.2)

Pearson correlation r

(8.3)

Difference Binomial test difference

between 2 proportions (or

%) (6.2)

One sample Runs test

(7.3)

—

Research Q:

Prediction

(independent

variable is

continuous)

— — Linear Regression

(Response variable is

continuous (8.2))

Two. Sample Independent Related independentRelated IndependentRelated

Research Q:

Comparison/

differences

Fisher’s

exact test

(6.3)

Sign test

(6.5)

Wilcoxon

M-W test

(7.4)

Wilcoxon

Signed

Ranks test

(7.5)

t-test (8.4) t-test

(8.5)

Proportions

test* (6.4)

Association

(class variable

is discrete

forming

groups)

r×2 sample χ^2

test of

homogeneity

(6.1)

— — — — —

Multiple

Samples

(groups) 1

Independent

Independent

Related

variable

(factor)

Independent

Related IndependentRelated

Research Q:

Differences

between

groups (class

variable is

discrete

forming

groups)

— — Kruskal-

Wallis One-

way

ANOVA

(7.6)

Friedman

ANOVA

by Ranks

(7.7)

One-way

ANOVA

(unrelated)

(8.7)

One-way

ANOVA

(related)

(8.8)

Choosing a statistical test 127