Choosing the right statistics

CHAPTER 19
Choosing the Right Statistics

Three Basic Data Structures
Most research data can be classified into one of
three categories:
• Category 1: A single group of participants with one score
per participant
• Category 2: A single group of participants with two (or
more) variables measured per participant
• Category 3: Two (or more) groups of scores with each
score a measurement of the same variable

Scales of Measurement
Different statistics will be used depending on scales of
measurement
• Ratio and interval scales (numerical scores)
• Height (in inches)
• Weight (in pounds)
• IQ scores
• Ordinal scales (rank or ordered categories of scores)
• Small, medium, or large size t-shirts
• Job applicants: 1st, 2nd, 3rd, etc. rank
• Nominal scales (named categories)
• Gender (male or female)
• Profession (lawyer, doctor, psychologist)

Category 1
A single group of participants with one score per participant
• The goal is to describe individual variables, as they exist naturally,
without attempting to examine relationships between different
variables
• Descriptive statistics are the most commonly used procedures for
these data
• 3 Examples:

Category 2
A single group of participants with two (or more) variables
measured per participant
• The goal is to describe and evaluate the relationship between
variables as they occur naturally

Category 3
Two (or more) groups of scores with each score a
measurement of the same variable
• The goal is to examine relationships between variables by using the
categories of one variable to define groups and then measure a
second variable to obtain a set of scores within each group
• If scores in one group are consistently different from scores in
another group, then the data indicate a relationship between
variables

CHAPTER 19.2
Statistical Procedures for Data from a Single Group of
Participants with One Score Per Participant
(Category 1)

Scores from Ratio or Interval Scales
• Descriptive Statistics
• The mean (Ch.3) and standard deviation (Ch.4) are
the most commonly used
• The median (Ch.3) may also be used as a measure of
central tendency
• Inferential Statistics
• If there is a basis for a null hypothesis, a single-sample
t-test (Ch.9) can be used to test the hypothesis

Scores from Ordinal Scales
• The median is used for describing central tendency
• Proportions can be used to describe the distribution of
individuals across categories
• If there is a basis for a null hypothesis, a chi-square
test for goodness-of-fit (Ch.17) can be used to
evaluate the hypothesis
• The binomial test (Ch.18) can also be used with only
two categories

Scores from a Nominal Scale
• The mode may be used for describing central tendency
• Proportions can be used to describe the distribution of
across categories
• A chi-square test for goodness-of-fit can be used to
evaluate the null hypothesis
• The binomial test can also be used with only two
categories

CHAPTER 19.3
Statistical Procedures for Data from a Single Group of
Participants with Two (or more) Variables Measured for
Each Participant (Category 2)

Two Numerical Variables (Interval/Ratio Scales)
Descriptive Statistics
• The Pearson correlation (Ch.15) describes the degree
and direction of the linear relationship
• The regression equation (Ch. 16) identifies the slope
and Y-intercept for the best-fitting line
Inferential Statistics
• The critical values in Table B6 determine the significance
of the Pearson correlation (Ch.15)
• Analysis of regression determines the significance of the
regression equation (Ch. 16)

Two Ordinal Variables (Ranks/Ordered categories)
• The Spearman correlation (Ch. 15) describes the
degree and direction of monotonic relationship (the
degree to which the relationship is consistently one-
directional)
• The critical values in Table B7 determine the
significance of the Spearman correlation

1 Numerical and 1 Dichotomous Variable
• The point-biserial correlation (Ch. 15) measures the
strength of the relationship
• The data for a point-biserial correlation can be
regrouped into a format suitable for an independent-
measures t-hypothesis test
• The t value determines the significance of the
relationship

2 Dichotomous Variables
• The phi-coefficient (Ch. 15) describes the strength of
the relationship
• The data from a phi-coefficient can be regrouped into a
format suitable for a 2 x 2 chi-square test for
independence
• The chi-square value determines the significance of the
relationship

2 Variables from Any Measurement Scale
• The data can be regrouped as a frequency distribution
matrix
• The frequencies or proportions describe the data
• The chi-square test for independence evaluates the
relationship between variables

3 Variables (Interval or Ratio)
• A partial correlation (Ch.15) describes the direction and
degree of the linear relationship between two variables
while controlling the third variable
• The multiple regression equation (Ch.16) describes the
relationship between two predictor variables and the
variable being predicted
• The statistical significance of the partial correlation can be
evaluated by comparing the sample correlation with the
critical values in Table B6 and df = n-3
• Analysis of regression evaluates the significance of the
multiple regression equation

3 Variables (Numerical and Dichotomous)
• A partial correlation (Ch.15) describes the degree of the
linear relationship between two variables while controlling
the third variable
• The multiple regression equation (Ch.16) describes the
relationship between two predictor variables and the
variable being predicted
• The statistical significance of the partial correlation can be
evaluated by comparing the sample correlation with the
critical values in Table B6 and df = n-3
• Analysis of regression evaluates the significance of the
multiple regression equation

Statistics for Category 2 Data

CHAPTER 19.4
Statistical Procedures for Data Consisting of Two (or
More) Groups of Scores with Each Score a
Measurement of the Same Variable (Category 3)

Numerical Scores (Ratio/Interval)
• For both independent-measures and repeated-measures
studies, the mean and standard deviation can be used
to summarize and describe each group.
• For independent-measures designs, the independent-
measures ANOVA and independent-measures t-test
are used to evaluate the mean difference
• For repeated-measures designs, the repeated-measures
t-test and repeated-measures ANOVA are used to
evaluate the mean difference

Ranks or Ordered Categories (Ordinal scales)
• Ordinal scores can be described by the set of ranks or ordinal
categories within each group.
• The median may be used for both independent-measures and
repeated-measures designs
• For independent-measures designs, the Mann-Whitney U test
evaluates the difference between two groups of scores. The Kruskal-
Wallis test evaluates differences between three or more groups.
• For repeated-measures designs, the Wilcoxon signed ranks test
evaluates the difference between two groups of scores. The
Friedman test evaluates differences among three or more groups.

Scores from a Nominal Scale
• Proportions can be used for each category
• With a relatively small number of nominal categories, the
data can be displayed as a frequency-distribution matrix
• A chi-square test for independence can be used to
evaluate differences between groups for an independent-
measures design

2-Factor Designs with Numerical Scores
(interval/ratio scales)
• The mean and standard deviation can be used to
summarize and describe each group for both
independent-measures and repeated-measures designs
• Independent-measures ANOVA and repeated-
measures ANOVA evaluate the mean differences
between cells

Statistics for Category 3 Data

Choosing the right statistics

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