Course Project Worksheet – Measures of Variability

Independent Variable 1

Justification:

The ordinal scale “Education Level” is measured on a scale ranging from 0 (Less than high school) through 4 (Graduate degree). Because there are categories that are not equidistant, the IQR is the appropriate measure of variability for an ordinal variable with no equal intervals between categories. (Gravetter & Wallnau, 2017). The IQR is especially well-fit for ordinal data because it orients itself to the middle 50% of responses and does not support the assumption of equal distances, an assumption which would be inappropriate when educational levels can vary considerably in both effort and length. Most importantly, the IQR gives a dispersion measure that resists outliers or extremes, hence providing representative measures of central tendencies (Field, 2018). The use of IQR avoids overstating variability due to unequal intervals between education levels while focusing on the spread around the median, which becomes key in drawing patterns within educational attainment.

Level of Measurement:

Ordinal

Measure of Variation Table:

Statistic	Value
Minimum	0
First Quartile (Q1)	1
Median	1
Third Quartile (Q3)	3
Interquartile Range (IQR)	2

Summary of Table Results:

The interquartile range for Education Level from the above table is 2; this would indicate that there is a medium spread between respondents. This range indicates that the middle 50% of responses are spread between the high school level and the bachelor’s degree level. Clustering around these levels forms a pattern that the majority of respondents either hold a high school diploma or undergraduate degree, which composes a foundational trend for the level of education in this sample. In support, Gravetter and Wallnau cite that IQR stands useful in ordinal data to reflect actual trends without distorting from extreme values. Consequently, with this response population having a central concentration, a classic educational distribution is somewhat typical of greater trends in comparable populations. In this way, the distribution would suggest that there is limited sample variation at both the lowest and highest levels of education, which can be a specific factor in determining perceptions about various sociocultural phenomena of interest, including political views and attitudes toward national policies.

Independent Variable 2

Justification:

Political Views is an ordinal variable as well. Responses range from a 1 (Extremely liberal) to 7 (Extremely conservative). Again, similar to Education Level, there are no equal intervals between each category, so the best measure of variability would be IQR. It is a better representation of the middle 50% of the responses, not like when the spacing between categories is unequal. The IQR gives an accurate reflection of ideological diversity in the sample (Field, 2018). Here, IQR is selected because it can summarize the spread of the middle part of the data that measures respecting the natural properties of ordinal data measurement are created this way (Trochim et al., 2016). Considering the fact that some data on political views might be skewed, IQR will allow observation of variation without much affection by extreme liberal or conservative answers and thus hold the integrity of the analysis in trying to obtain a balanced overview of politics.

Level of Measurement:

Ordinal

Measure of Variation Table:

Statistic	Value
Minimum	1
First Quartile (Q1)	3
Median	4
Third Quartile (Q3)	5

Summary of Table Results:

The interquartile range for the variable Political Views is 2, indicating that most respondents identify closer to the middle of the ideological spectrum, with scores clustering between “Slightly liberal” and “Slightly conservative.” This finding is supported by the median score of 4 that reflects centrist or moderate orientation. The distribution of political views is bellshaped, peaking in moderate viewpoints that reflect the tendency of respondents to shy away from extreme positions. According to Gravetter and Wallnau (2017), by focusing on the middle 50%, the IQR will give insight into the core spread of responses by providing a look at variability that respects symmetry in the distribution around the median. This moderate spread across middle categories gives grounds for diversity, yet epidemiological balance in ideological perspectives within the sample, with subconscious emergence of a single common element of respondents such as average political leanings.

Dependent Variable

Justification:

The “Healthcare Spending” variable is ordinal because the values are coded from 1 (Too little) to 3 (Too much). As with the other variables, IQR is chosen because the nature of the variable is ordinal. IQR is preferred for an ordinal variable because it allows for a focus on the variation in the central responses, and it does not impose any assumptions about the distribution of distances between “Too little,” “About right,” and “Too much” variables. IQR serves well to communicate the public’s opinion on spending about healthcare and, more specifically, whether there is a significant dispersion around the preferred response, “Too little,” without giving too much weight to the outliers. It depicts, in this manner, a real sense of variation by focusing on responses that reflect the opinion of the majority without being skewed.

Level of Measurement:

Ordinal

Measure of Variation Table:

Statistic	Value
Minimum	1
First Quartile (Q1)	1
Median	1
Third Quartile (Q3)	2
Interquartile Range (IQR)	1

Summary of Table Results:

Health Care Spending-Interquartile range is 1. This would suggest there is strong clustering around the belief that current spending is “Too little.” The median is 1, and the mode is also 1; this would suggest there is uniform agreement among respondents with a belief that more money needs to be spent on healthcare, supporting low variability of opinion. Field, 2018 adds that such a small spread in an ordinal variable may mean a similar view among the people, which only goes to reiterate that in issues such as healthcare funding, interpretation shall be stretched to the level of public opinion. The IQR does not spread out much; this means most of these responses fall in the ‘More Spending’ category, hence critical in bringing out societal values and policy preferences. This is in tandem with the social trend that citizens would wish to have more investment in health, as described by Trochim et al. (2016), which might have a strong influence on public policy and the issue of politics.

References

Field, A. (2018). Discovering statistics using IBM SPSS statistics (5th ed.). Sage Publications.

Gravetter, F. J., & Wallnau, L. B. (2017). Statistics for the behavioral sciences (10th ed.). Cengage Learning.

Trochim, W. M. K., Donnelly, J. P., & Arora, K. (2016). Research methods: The essential knowledge base. Cengage Learning.

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Using Figure 4.7, How to Choose a Measure of Variation, on p. 164 of Social Statistics for a Diverse Society, determine the correct measure of variability based on the levels of measurement for your variables from Week 1 and complete the following worksheet.

Independent Variable 1

Justification: (State the measure of variation chosen and why.)

[Enter your response here.]

Level of Measurement: (List the level of measurement: nominal, ordinal, interval, or ratio.)

[Enter your response here.]

Measure of Variation Table:

[Paste the Measure of Variation Table here.]

Summary of Table Results: (Summarize the table results.)

[Enter your response here.]

Independent Variable 2

Justification: (State the measure of variation chosen and why.)

[Enter your response here.]

Level of Measurement: (List the level of measurement: nominal, ordinal, interval, or ratio.)

[Enter your response here.]

Measure of Variation Table:

[Paste the Measure of Variation Table here.]

Summary of Table Results: (Summarize the table results.)

[Enter your response here.]

Dependent Variable

Justification: (State the measure of variation chosen and why.)

[Enter your response here.]

Level of Measurement: (List the level of measurement: nominal, ordinal, interval, or ratio.)

[Enter your response here.]

Measure of Variation Table:

[Paste the Measure of Variation Table here.]

Summary of Table Results: (Summarize the table results.)

[Enter your response here.]

References

[List references according to APA guidelines.]