Quantitative Reasoning & Analysis




1. The p-value was slightly above conventional threshold, but was described as
“rapidly approaching significance” (i.e., p =.06).
An independent samples t test was used to determine whether student satisfaction
levels in a quantitative reasoning course differed between the traditional classroom
and on-line environments. The samples consisted of students in four face-to-face
classes at a traditional state university (n = 65) and four online classes offered at
the same university (n = 69). Students reported their level of satisfaction on a fivepoint
scale, with higher values indicating higher levels of satisfaction. Since the
study was exploratory in nature, levels of significance were relaxed to the .10 level.
The test was significant t(132) = 1.8, p = .074, wherein students in the face-to-face
class reported lower levels of satisfaction (M = 3.39, SD = 1.8) than did those in the
online sections (M = 3.89, SD = 1.4). We therefore conclude that on average,
students in online quantitative reasoning classes have higher levels of satisfaction.
The results of this study are significant because they provide educators with
evidence of what medium works better in producing quantitatively knowledgeable
2. A results report that does not find any effect and also has small sample size
(possibly no effect detected due to lack of power).
A one-way analysis of variance was used to test whether a relationship exists
between educational attainment and race. The dependent variable of education
was measured as number of years of education completed. The race factor had
three attributes of European American (n = 36), African American (n = 23) and
Hispanic (n = 18). Descriptive statistics indicate that on average, European
Americans have higher levels of education (M = 16.4, SD = 4.6), with African
Americans slightly trailing (M = 15.5, SD = 6.8) and Hispanics having on average
lower levels of educational attainment (M = 13.3, SD = 6.1). The ANOVA was not
significant F (2,74) = 1.789, p = .175, indicating there are no differences in
educational attainment across these three races in the population. The results of
this study are significant because they shed light on the current social conversation
about inequality.
3. Statistical significance is found in a study, but the effect in reality is very small (i.e.,
there was a very minor difference in attitude between men and women). Were the
results meaningful?
An independent samples t test was conducted to determine whether differences
exist between men and women on cultural competency scores. The samples
consisted of 663 women and 650 men taken from a convenience sample of public,
private, and non-profit organizations. Each participant was administered an
instrument that measured his or her current levels of cultural competency. The
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cultural competency score ranges from 0 to 10, with higher scores indicating higher
levels of cultural competency. The descriptive statistics indicate women have
higher levels of cultural competency (M = 9.2, SD = 3.2) than men (M = 8.9, SD =
2.1). The results were significant t (1311) = 2.0, p <.05, indicating that women are
more culturally competent than are men. These results tell us that gender-specific
interventions targeted toward men may assist in bolstering cultural competency.
4. A study has results that seem fine, but there is no clear association to social
change. What is missing?
A correlation test was conducted to determine whether a relationship exists
between level of income and job satisfaction. The sample consisted of 432
employees equally represented across public, private, and non-profit sectors. The
results of the test demonstrate a strong positive correlation between the two
variables, r =.87, p < .01, showing that as level of income increases, job
satisfaction increases as well.



Critically evaluate the two scenarios you selected based upon the following points: Critically evaluate the sample size Critically evaluate the statements for meaningfulness Critically evaluate the statements for statistical significance.
Based on your evaluation, provide an explanation of the implications for social change.


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