Chapter 12
Understanding Research Results:
Description and Correlation
Scales of Measurement
 Scales of measurement: A review
• Levels of nominal scale variables
- No numerical, quantitative properties
- Levels are different categories or groups
Scales of Measurement (con’t)
 Scales of measurement: A review
• Variables with ordinal scale levels involve
minimal quantitative distinctions
- Rank order the levels from lowest to
highest
Scales of Measurement (con’t)
 Scales of measurement: A review
• Interval scale variables – quantitative
properties
- Intervals between the levels are equal in
size
- No absolute zero
Scales of Measurement (con’t)
 Scales of measurement: A review
• Ratio scale variables - detailed quantitative
properties
- Equal intervals
- Absolute zero
Analyzing the Results of Research Investigations

Scales of measurement have important implications
• Three basic ways of describing the results
1. Comparing group percentages
2. Correlating scores of individuals on two
variables
3. Comparing group means
Analyzing the Results of Research Investigations
(con’t)
 For all types of data, it is important to understand the
results by carefully describing the data collected
• Frequency distributions
• Graphing frequency distributions
- Directly observe how participants responded
- Examine which scores were the most frequent
- Examine the shape of the distribution of scores
- Identify outliers
- Compare the distributions of different groups
Analyzing the Results of Research Investigations
(con’t)
 Graphing frequency distributions (con’t)
• Pie charts – very useful for nominal scale information
Analyzing the Results of Research Investigations
(con’t)
 Bar graphs use a separate and distinct bar for each
piece of information
Analyzing the Results of Research Investigations
(con’t)
 Frequency polygons – a line is used to represent
frequencies
• Most useful when data are interval or ratio scales
Descriptive Statistics
 Descriptive statistics allow researchers to make precise
statements about the data
• Two statistics are needed to describe the data
- Central tendency
- Variability
Descriptive Statistics (con’t)
 Central tendency
• Mean X M in scientific reports
- Mathematical average
- Appropriate for interval or ratio scale data
• Median Mdn
- Divides the group in half
- Appropriate for ordinal scale data
• Mode
- Most frequent score
- Appropriate for nominal scale data
Descriptive Statistics (con’t)
Descriptive Statistics (con’t)
Descriptive Statistics (con’t)
 Variability - the amount of spread in the distribution of
scores
• Standard deviation = s or SD in reports
• Variance = s2
• Range
Graphing Relationships (con’t)
 Levels of IV are shown on horizontal x-axis
 DV values are shown on the vertical y-axis
y-axis
x-axis
Correlation Coefficients: Describing the Strength
of Relationships
 Correlation coefficient – a statistic that describes how
strongly variables are related to one another
• Pearson Product-Moment correlation coefficient
- Interval or ratio scale data
-r
- Values range from 0.00 to +1.00 and 0.00 to –1.00
Correlation Coefficients: Describing the Strength
of Relationships (con’t)
 Correlation coefficients (con’t)
• Sign of the value indicates direction
• Value indicates the strength
Correlation Coefficients: Describing the Strength
of Relationships (con’t)
 Correlation coefficient – the nearer a correlation is to
1.00 (plus or minus), the stronger the relationship
Correlation Coefficients: Describing the Strength
of Relationships (con’t)
Scatterplots reveal the
pattern of the
relationship
Correlation Coefficients: Describing the Strength
of Relationships (con’t)
 Important considerations
• Restriction of range
• Curvilinear relationship
Effect Size
 Effect size is a general term that refers to the strength of
the association between variables
• A scale of values that is consistent across all types of
studies
• Values range from 0.00 to 1.00
Effect size (con’t)
 Pearson r is one indicator of effect size
• Small effects near r = .15
• Medium effects near r = .30
• Large effects above r = .40
 Squared value of the coefficient r2 - transforms the value
of r to a percentage
• Percent of shared variance between the two variables
Statistical Significance
 Decision about the statistical significance of the results
• Will the results hold up if the experiment is repeated
several times?
• Topic discussed in Chapter 13.
Regression Equations
 Regression equations are calculations used to predict a
score on one variable using a known score on another
variable
Y  a  bX
Y = Score we wish to predict (criterion variable)
X = Score that is known (predictor variable)
Multiple Correlation
 Multiple correlation is uses (symbolized R) is the
correlation between a combined set of predictor variables
and a single criterion variable
• Permits greater accuracy of predictor than if any
single predictor is used alone (never a perfect
predictor)
• R2 = effect size
Y  a  b1X1  b2 X 2 ... bn X n
Partial Correlation and the Third-Variable Problem
 Partial correlation is a way of statistically controlling third
variables
• Correlation between the two variables of interest,
with the influence of the third variable “partialed out
of” the original correlation
Structural Models
 Structural models of relationships among variables using
the nonexperimental method
• An expected pattern of relationships
• Based on a theory of how the variables are causally
related to one another
• Approach called structural equation modeling
• Older but related tool is called path analysis
Structural Models (con’t)
 Arrows depict paths that relate the variables in the model
 Coefficients similar to the weights derived in regression
equations (indicating the strength of the relationship)
The End