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(hint: write out all the information that you know from the table and
given in the question. Then start with degrees of freedom. This should
get you on your way. Remember: F = a ratio of Mean Squares (MS), MS =
SS/df, SStotal = SSbetween treatments + SSwithin
treatments)
a) A common science-fair project involves testing the effects of music on
the growth of plants. For one of these projects, a sample of 24 newly
sprouted bean plants is obtained. These plants are randoml assigned to
four treatments, with n = 6 in each group. The four conditions are rock,
heavy metal, country, and classical music. The dependent variable is the
height of each plant after 2 weeks. The data from this experiment werer
examined using an ANOVA, and the results are summarized in the following
table. Fill in all the missing values.
b) A researcher studies the effects of need for achievement and task
difficulty on problem solving. A two-factor design is used in which there
are two levels of amount of achievment motivation and four levels of task
difficulty. Each cell consists of n = 6 subjects. The number of errors
each subject made was recorded, and the data were analyzed. The following
table summarizes the results of the ANOVA, but it is not complete. Fill in
the missing values.
Source SS df MS F Between
treatments 90 __3__ __30__ __6__ Within treatments _100_ __20_ 5 Total __190_ _23__
Source SS df MS F Between
treatments 280 __7__ Main effect of
achievement __16_ __1__ __16_ __2__ Main effect of
task _144_ __3__ 48 __6__ Interaction 120 __3__ __40_ __5__ Within treatments _320_ __40_ __8__ Total 600 __47_
3) Know how to do the 1-way between groups ANOVA and 1-way repeated measures ANOVA by hand. I will provide a formula sheet and (parts) of the F-table.
a) An educational psychologist is studying student motivation in elementary school.
A sample of n = 5 students is followed over three years from fourth grade to sixth grade.
Each year the students complete a questionnaire measuring their motivation and enthusiasm
for school. The psychologist would like to know whether there are significant changes in
motivation across the three grade levels. The data from this study are as follows:
What kind of design is this? 1-way repeated measures ANOVA
What kind of statistical analysis should be
performed?1-way repeated measures ANOVA
State the null hypothesis(ses) that you test.
State your conclusions.
b) First-born children tend to develop language skills faster than their younger siblings.
One possible explanation for the phenomenon is that first-borns have undivided attention
from their parents. If this explanation is correct, then it is also reasonable that twins
should show slower language development than single children and that triplets should be
even slower. Davis (1937) found exactly this result. The following hypothetical data
demonstrate the relationship. The dependent variable is a measure of language skill at
age three for each child.
What kind of design is this? 1-way between groups ANOVA
What kind of statistical analysis should be
performed?1-way between groups ANOVA
State the null hypothesis(ses) that you test.
Present your results in an ANOVA table
State your conclusions.
4) Be able to identify the critical information from the SPSS output so that you can make decisions about your null hypotheses (including post hoc and planned comparison output for a 1-way between groups ANOVA).
a) A human factors psychologist studied three computer keyboard designs.
Keyboard A is a standard keyboard, keyboards B and C are new designs.
Three samples of individuals were given material to type on a particular
keyboard, and the number of errors committed by each subject was
recorded. The results of the statistical analysis are presented below.
Based on these results are there differences between the different
keyboards? How do the new keyboard designs compare with the standard
keyboard?
The ANOVA result supports the hypothesis that there is a difference
between keyboard types F(2,12) = 9.13, p < 0.05. The two planned
comparisons show that both new keyboard designs are different from the
standard keyboard design.
b) Individuals who are identified as having an antisocial personality
disorder also tend to have reduced physiological responses to painful or
anxiety-producing stimuli. In everyday terms, these individuals show a
limited physical response to fear, guilt, or anxiety. One way of measuring
the response is with the galvanic skin response (GSR). Normally, when a
person is aroused, there is an increase in perspiration, which causes a
measurable reduction in the electrical resistance on the skin.
The results of the statistical analysis are presented below. In words,
explain the findings of this study.
The results of the ANOVA yeilded a significant main effect of arousal
(stress groups had lower GSR means than baseline)
F(1,36) = 9.12, p < 0.05. There was also a main effect of personality,
with such that normal personality subjects had lower GSR scores than
antisocial personality subjects, F(1,36) = 12.98, p < 0.05. There was
also a significant interaction F(1, 36) = 5.46, p < 0.05. The pattern of
this interaction was that subjects with antisocial personality had rougly
the same GSR levels regardless of stress. Normal personality subjects, on
the other hand, had lower GSR levels when stressed, relative to the
baseline.
5) insert some conceptual questions here ....
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a) Explain why you should never get a negative F-ratio
b) Why should we use planned contrasts or post-hoc tests instead of several t-tests to rule out alternative hypotheses? c) ...