Chapter 12 Fraenkel – Statistics in Perspective
Comparing Groups: Quantitative Data - p.243
Techniques
 Researchers should first construct a frequency polygon of each group’s
scores. – Tells us an appropriate central tendency to use: i.e. mean or
median
Recommendation 1: Prepare a frequency polygon of each group’s scores
Recommendation 2: Use these polygons to decide which measure of central
tendency is appropriate to calculate
Interpretation
 In words, describe what the polygons and averages tell the researcher
about the hypothesis – what has my life become? Is anybody really reading
this?
 How big a difference must there be in order to make a difference?
Calculate the effect size
 Technique used to assess the magnitude of a difference between the
means of two groups.
 It, however, does not answer the question of how large it must be for
researchers to consider an obtained difference important.
Recommendation 3: Compare obtained results with data on the means of known
groups.
Recommendation 4: Calculate an effect size. An ES of .50 or larger is IMPORTANT
Use inferential statistics p. 244:
 3rd way of judging the importance of differences between the means of two
groups.
Recommendation 5: Consider using inferential statistics only if you can make a
convincing argument that a difference between means of the magnitude obtain is
important
Recommendation 6: Do not use tests of statistical significance to evaluate the
magnitude of a difference between sample means.
Recommendation 7: Unless random samples were used, interpret probabilities
and/or significance levels as crude indices, not as precise values
Recommendation 8: Report results of inference techniques as confidence
intervals rather than significant levels
Relating variables within a group: Quantitative Data - p.247
Techniques
 Whenever a relationship between quantitative variables within a single
group is examined, the appropriate techniques are the scatterplot and the
correlation coefficient.
 This will help determine which correlation coefficient to use (Pearson r,
assumes a linear relationship, and eta, which describes a curvilinear
Recommendation 9: When analyzing data obtained from a single group,
therefore, researchers should begin by constructing scatterplot.
Recommendation 10: Use scatterplot to determine which correlation coefficient
is appropriate to calculate.
Recommendation 11: Use both scatterplot and correlation coefficient to
interpret the results.
Interpretation
 Interpreting scatterplots and correlations presents problems similar to
those discussed in relation to differences in the mean.
Recommendation 12: Draw a line that bests fits all points in a scatterplot
Recommendation 13: Consider using inferential statistics only if you can give a
convincing argument for the importance of the size of the relationship found in
the sample.
Recommendation 14: Don’t use tests of statistical significance to evaluate the
magnitude of a relationship
Recommendation 15: Unless a random sample was used, interpret probabilities
and or significance levels as crude probabilities
Recommendation 16: Report the results of inference techniques as confidence
intervals rather than as significance levels
Comparing Groups: Categorical Data - p.251
Techniques
 When data are categorical, groups may be compared by reporting either
percentages or frequencies in crossbreak tables
Interpretation



Again, must look at percentages but they can be misleading. Crossbreak
results show actual results.
Drawback with categorical data is that such evaluations are even harder
than with quantitative data.
Because of these difficulties, most research reports using percentages and
crossbreaks rely on the inference techniques to evaluate the magnitude of
relationships.
Recommendation 17: Whenever possible, place all data in crossbreak tables
Recommendation 18: For clarification, calculate a contingency coefficient
Recommendation 19: Do not use tests of statistical significance to evaluate the
magnitude of relationship
Recommendation 20: Unless a random sample was used, interpret probabilities
and/or significance levels as crude indices.
Relating variables within a group: Categorical Data - p.253
This was clearly one of the worst chapters I have ever read. If
anyone of us EVER use anything in this chapter, we should call
each other up a reminisce about all the good times at Two
Summers