1
DESCRIPTIVE STATISTICS, ORDINAL SCALE, AND DICHOTOMOUS VARIABLE
Descriptive Statistics, Ordinal Scale, and Dichotomous Variable
Karli Bryant
BUSI 820 Quantitative Research Methods
November 12th, 2023
Discussion Board 3
2
DESCRIPTIVE STATISTICS, ORDINAL SCALE, AND DICHOTOMOUS VARIABLE
Descriptive Statistics, Ordinal Scale, and Dichotomous Variable
D3.4.1 – Scores and Statistics Using Outputs 4.1a and 4.1b
(a) What is the mean visualization test score?
When reviewing Output 4.1b, the mean visualization test score is listed as 5.2433.
(b) What is the skewness statistic for math achievement test? What does this tell us?
When reviewing Output 4.1b, the skewness statistic for the math achievement test is
listed as 0.44. Skewness represents when one tail of the frequency distribution is longer than the
other indicating if the curve of the chart is skewed to one side or not (Morgan, Leech, Gloeckner,
Barrett, 2020). If the skewness was listed as zero, that would mean the curve is perfectly normal.
Since the skewness is listed as 0.44, this indicates that the variable is not highly skewed as it is
close to zero however, it does have a slightly positive skew.
(c) What is the minimum score for mosaic pattern test? How can that be?
When reviewing Output 4.1b, the minimum score for the mosaic pattern test is listed as
-4.0. It can be determined that this is a valid entry by reviewing the codebook which indicates the
visualization scores range from -4.0 to 16. Since the minimum is listed as -4.0 that indicates that
at least one participant achieved that score.
D3.4.2 – Scale and Skewness 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?
3
DESCRIPTIVE STATISTICS, ORDINAL SCALE, AND DICHOTOMOUS VARIABLE
When reviewing Output 4.1b, it can be seen that the skewness statistic is more than 1.00
or less than -1.00 for the competence scale. The skewness statistic for this variable is listed on
the chart as -1.634.
(b) Why is the answer important?
It is important to recognize that the skewness for the competence scale is less than -1.00
because this indicates the variable is an outlier and the curve is not normally distributed.
(c) Does this agree with the boxplot for Output 4.2? Explain.
When reviewing the boxplot for Output 4.2, it can be seen that this data does agree with
the skewness statistic previously discussed. When the box plot has whiskers that are
approximately the same length and the line in the box is approximately in the middle, then it can
be assumed that the variable is approximately normally distributed (Morgan, Leech, Gloeckner,
Barrett, 2020). However, in this case, the box plot reflects the box being higher making the lower
portion longer meaning the data is skewed to the left or negative just as was seen in the previous
example.
D3.4.3 – Valid vs. Missing Data Using Output 4.2b
(a) How many participants have missing data?
When reviewing Output 4.2b, it can be seen in the processing summary that 4 cases are
missing in both the competence scale and the motivation scale.
(b) What percent of students have a valid (non-missing) motivation scale or competence scale
score?
4
DESCRIPTIVE STATISTICS, ORDINAL SCALE, AND DICHOTOMOUS VARIABLE
When reviewing Output 4.2b, it can be seen that the percentage of students that have a
valid (non-missing) motivation scale or competence scale score is 94.7%.
(c) Can you tell from Outputs 4.1 and 4.2b how many are missing both motivation scale and
competence scale scores? Explain.
When reviewing Output 4.1 and Output 4.2b, you can tell how many are missing both
motivation scale and competence scale scores. In Output 4.1, the competence scale and the
motivation scale have 73 listed as the value for N however, the population is listed as 75
indicating that both are missing two scores. In Output 4.2b, the competence scale and the
motivation scale both have 71 listed as N. Therefore, it can be determined that no participant is
missing both the motivation scale and competence scale scores because two are missing from
each score and four are missing at least one of the scores.
D3.4.4 – Interpreting Data Using Output 4.4
(a) Can you interpret the means? Explain.
In reviewing Output 4.4, the means can be interpreted as percentages. Since the variables
are dichotomous, the percentage represents the number of participants that fall into each group.
When analyzing the first variable listed, it can be seen that the mean for academic track is .55 or
55% meaning 55% of the participants were input with the code “1” for regular track (Morgan,
Leech, Gloeckner, Barrett, 2020). With this in mind, it can be determined that 45% of
participants were input with the code of “0” for fast track since those are the remaining
participants.
(b) How many participants are there altogether?
5
DESCRIPTIVE STATISTICS, ORDINAL SCALE, AND DICHOTOMOUS VARIABLE
In reviewing Output 4.4, it can be seen that there are 75 participants represented by the
population or “N”.
(c) How many have complete data (nothing missing)?
In reviewing Output 4.4, it can be seen that all of the variables listed have a population of
75 which means all of the variables have complete data and nothing is missing.
(d) What percent are in the fast track?
When referencing the code book, it can be determined that 1 represents the regular track
and 0 represents the fast track therefore, the mean represents the percentage of participants on the
regular track. For the academic track, the mean is .55 meaning 55% of participants are on the
regular track and 45% of participants are on the fast track. For algebra 1 in h.s., the mean is .79
meaning 79% of participants are on the regular track and 21% of participants are on the fast
track. For algebra 2 in h.s., the mean is .47 meaning 47% of participants are on the regular track
and 53% of participants are on the fast track. For geometry in h.s., the mean is .48 meaning 48%
of participants are on the regular track and 52% of participants are on the fast track. For
trigonometry in h.s., the mean is .27 meaning 27% of participants are on the regular track and
73% of participants are on the fast track. For calculus in h.s., the mean is .11 meaning 11% of
participants are on the regular track and 89% of participants are on the fast track. Lastly, for math
grade, the mean is .41 meaning 41% of participants are on the regular track and 59% of
participants are on the fast track.
(e) What percent took algebra 1 in h.s.?
6
DESCRIPTIVE STATISTICS, ORDINAL SCALE, AND DICHOTOMOUS VARIABLE
In reviewing Output 4.4, we can determine what percent of participants took algebra 1 in
h.s. as we know that 79% of students were on the regular track meaning they would have taken
algebra 1 in h.s. as they were not on the fast track.
D3.4.5– Percentages and Visualization Scores Using Output 4.5
(a) 9.6% of what group are Asian-Americans?
In reviewing output 4.5, it can be seen that 9.6% of participants who made valid answers
listed themselves as Asian-American.
(b) What percent of students have visualization 2 scores of 6?
In reviewing output 4.5, it can be seen that 8.0% of students have visualization 2 scores
of 6.
(c) What percent had such scores of 6 or less?
In reviewing output 4.5, it can be seen that 66.7% of students have a visualization score
of 6 or less using the cumulative percent column.
