Discussion 3: Descriptive Statistics, Ordinal Scale, and Dichotomous Variable
D3.4.1 Using Outputs 4.1a and 4.1b: (a) What is the mean visualization test score? (b) What
is the skewness statistic for math achievement test? What does this tell us? (c) What is the
minimum score for the mosaic pattern test? How can that be?
a) The mean for the visualization test score is 5.2433.
b) The skewness of the math achievement test is .044. This informs us that the variable is
not actually skewed.
c) The minimum score for the mosaic pattern test is -4.0. The score appears as if it may be
an error. Based on the codebook, it indicates that the visualization scores range from -4 to
16, in this instance -4 confirms that an individual has scored no less than the lowest score
that can be achieved. The negative value can be a result of a consequence for predicting
incorrectly (Morgan et al., 2019).
D3.4.2.Using Output 4.1b: (a) For which variables that we called scale, is the skewness
statistic more than 1.00 or less than –1.00? (b) Why is the answer important? (c) Does this
agree with the boxplot for Output 4.2? Explain.
a) The scale values represent variables of which levels are ordered and the variables are
normally distributed with equal intervals among the levels. The output shows the
descriptive statistics for each variable that are considered ordinal and scale. The variables
are listed within the left column of the output and the descriptive statistics are listed
within the top rows. The variable competence has a skewness statistic of less than -1 as it
is -1.634.
b) Skewness calculates to which degree of distribution varies from the normal curve.
Distribution whose right tail is more extended than the left can be identified as right
skewed and the distribution whose left tail is more extended than right can be identified
as left skewed.
c) The box plot provided demonstrates that the four outliers, participants that are numbered
4,5,6, 8, and 10. This suggests that the information is not normally distributed. The
variable competence scale is left skewed. This means that the skewness agrees with the
box plot (Morgan et al., 2019).
D3.4.3.Using Output 4.2b: (a) How many participants have missing data? (b) What percent
of students have a valid (non-missing) motivation scale or competence scale score? (c) Can
you tell from Outputs 4.1 and 4.2b how many are missing both motivation scale and
competence scale scores? Explain.
a) There are four participants that are missing data.
b) The percentage of students that have a valid non-missing motivation scale or competence
scale score is 94.7%.
c) The data in 4.1 b shows that there are 73 competence scale scores and 73 motivation
scale scores. The data in 4.2 b indicates that there are 71 scores competence scale scores,
and 71 motivation scale scores. In this instance, there are no missing competence and
motivation scale scores, as two are missing each of the scores, and four are missing no
less than one of the scores (Morgan et al., 2019).
D3.4.4.Using Output 4.4: (a) Can you interpret the means? Explain. (b) How many
participants are there altogether? (c) How many have complete data (nothing missing)? (d)
What percent are in the fast track? (e) What percent took algebra 1 in h.s.?
a) The descriptives for dichotomous variables in output 4.4 interpret that the mean can
distinguish the number of participants that can be grouped into each category. The mean
within the academic track represents .55 or 55% which represents the participants that
have been rated as 1 for regular track, and 45 % were coded 0 for fast track. As the mean
is greater than .50 more students, there are more students that are on the regular track
than the fast track. If a mean is near 1 or 0 separating the information.
b) There are 75 participants altogether, as the N represents the population.
c) There is no missing data, each variable has a population of 75.
d) Within the first variable which is academic track, the mean is .55 or 55% of the
participants that coded as 1 for regular track, and the remaining 45% coded to 0 for fast
track. In algebra 1 in high school, the mean is .79 or 79% of the participants that coded 1
for regular track, and the remaining 21% is coded as 0 for fast track. In algebra 2 in high
school the mean is .47 or 47% of the participants which were coded as 1 for regular track,
and the remaining 53% are to be coded as 0 for fast track. For geometry in high school
the mean is .48 or 48% which accounts for the ones within regular track to be coded 1,
and the remaining 52% is to be coded as 0 for fast track. For trigonometry in high school
the mean .27 or 27% accounts for the participants that have been coded as 1 for regular
track, and the remaining 73% is to be coded as 0 for fast track. In terms of calculus the
mean is .11 or 11% of participants have been coded as 1 for regular track, and for the
remaining 89% it is to be coded as 0 for fast track. In math grades, the mean is .41 or
41% accounts for participants that have been coded as 1 for regular track, and the
remaining 59% coded as 0 for fast track (Morgan et al., 2019).
e) To obtain the percentage that took algebra 1 in high school., the mean must be multiplied
by the population which is .79 *75, then it must be divided by the amount of variables
which is seven, which is then multiplied by the population (75), that number is then
multiplied by 100% which will provide the percentage. The percentage in this instance
will be 11% (Morgan et al., 2019).
D3.4.5.Using Output 4.5: (a) 9.6% of what group are Asian-Americans? (b) What percent
of students have visualization 2 scores of 6? (c) What percent had such scores of 6 or less?
a) The 9.6 % represents the percentage of participants in the investigation that have
provided sufficient answers to the question, and who identify themselves as Asian-
American. This does not involve individuals who did not answer the question or selected
no less than one or more ethnic group.
b) There is no missing information, the percentage for each and valid percentage are 5.3%.
c) The percentage of individuals that had scores of 6 or less were 70.7% which can be found
in the cumulative percent column (Morgan et al., 2019).
References
Morgan, G.A., Barrett, K.C., Leech, N.L., & Gloeckner, G.W. (2019). IBM SPSS for Introductory
Statistics: Use and Interpretation, Sixth Edition (6th ed.).
