| Course | PHLT 8032 SPSS Revealed |
|---|---|
| Week | Week 8 |
| Paper type | Association write-up |
| Length | About 1,010 words, 6 pages |
| Format | APA 7 student paper |
| School | Walden University |
| Program | PhD in Public Health |
| Updated | October 2026 |
Free sample paper for PHLT 8032 Week 8
Association Run: Household Income Bracket and Self-Rated General Health in a Composite County Survey, Read Through a Row-Percentage Crosstab and Kendall's Tau-b, With the Sign Explained and the Choice of Measure Argued
Student Name
Walden University
PHLT 8032: SPSS Revealed
Instructor Name
Month Day, Year
Association Run: Household Income Bracket and Self-Rated General Health in a Composite County Survey, Read Through a Row-Percentage Crosstab and Kendall's Tau-b, With the Sign Explained and the Choice of Measure Argued
The Question and the Variables
Is household income related to how respondents rate their general health? Both variables are ordinal, as the definition week established. Income has five brackets from under $25,000 to $100,000 or more, coded 1 to 5 from lowest to highest. The health scale puts excellent at code 1 and poor at code 5, so a higher health code means worse reported health. The run draws on 1,675 people who answered both questions; 164 refused income and 6 did not rate their health. All figures are unweighted and describe respondents.
The Crosstab
Crosstabs was run with income in the rows and self-rated health in the columns, requesting row percentages so that each row sums to 100% and shows how respondents within one income bracket rated their health.
Reading down any column shows the pattern. The share rating their health excellent triples, from 8.2% in the lowest bracket to 24.9% in the highest. The share rating it poor falls from 9.3% to 1.5%. Combining fair and poor, the figure charted in Week 5, the share falls from 31.7% to 7.1%, and it falls at every step. The middle category behaves differently: good health is the most common rating in the three lowest brackets and is overtaken by very good in the two highest. Row percentages are the right choice because the question is how health differs across income levels; column percentages would describe the income makeup of each health category, which depends on how many respondents fall in each bracket.
Table 1
Self-Rated Health by Household Income Bracket, Row Percentages
| Income bracket | n | Excellent | Very good | Good | Fair | Poor | |
|---|---|---|---|---|---|---|
| Under $25,000 | 268 | 8.2 | 19.0 | 41.0 | 22.4 | 9.3 | |
| $25,000 to $49,999 | 354 | 10.7 | 26.0 | 41.0 | 16.4 | 5.9 | |
| $50,000 to $74,999 | 362 | 14.4 | 32.6 | 37.8 | 11.6 | 3.6 | |
| $75,000 to $99,999 | 297 | 18.5 | 37.7 | 33.3 | 8.1 | 2.4 | |
| $100,000 or more | 394 | 24.9 | 40.6 | 27.4 | 5.6 | 1.5 | |
Note. Unweighted row percentages; rows may not sum to exactly 100 because of rounding. N = 1,675.
The Ordinal Measure
The Statistics button in Crosstabs offers several measures for ordinal variables. Kendall's tau-b was requested along with gamma and Spearman's correlation for comparison, and the Pearson chi-square was kept as a general test of association.
The result is reported as follows: income bracket and self-rated health were associated, tau-b = -.24, p < .001, N = 1,675.
Table 2
Symmetric Measures and Chi-Square Test
| Measure | Value | Approximate significance | |
|---|---|---|
| Kendall's tau-b | -.24 | Below .001 | |
| Gamma | -.32 | Below .001 | |
| Spearman correlation | -.29 | Below .001 | |
| Pearson chi-square, 16 df | 155.6 | Below .001 | |
Note. N = 1,675. Tau-b is the measure reported; the others are shown for comparison.
Why the Coefficient Is Negative
A negative coefficient here does not mean that higher income goes with worse health. It means that higher income codes go with lower health codes, and lower health codes mean better health, because excellent sits at the bottom of the health scale and poor at the top. Read in words, respondents in higher income brackets tended to rate their health more favorably. A reader who sees a negative tau-b without this paragraph could easily draw the opposite conclusion, which is why the coding paragraph sits directly under the result. Had the health variable been coded the other way, with 5 for excellent, the same data would have produced a positive tau-b of the same size.
What the Size Means
A tau-b of -.24 describes a modest tendency, not a rule. In plain terms, when two respondents with different income brackets and different health ratings are compared, the one with the higher income more often has the better rating, but many pairs run the other way. The crosstab shows this directly: even in the highest bracket, 34.5% rate their health only good, fair or poor, and in the lowest bracket 27.2% rate it excellent or very good. Agresti (2010) recommends interpreting ordinal measures through the table they summarize rather than through general labels, and the cells above make the modest size concrete. The very small p-value reflects the sample size more than the strength of the association.
Why Tau-b Rather Than Spearman's Rho or Gamma
Two short ordinal scales produce a great many ties. With five income brackets and five health ratings, thousands of respondent pairs share the same income bracket, the same health rating, or both. The three measures handle those ties differently. Gamma ignores tied pairs entirely and uses only pairs that differ on both variables, which is why its value, -.32, is the largest; it describes the untied pairs well but overstates the association for the sample as a whole. Spearman's rho correlates ranks and assigns tied cases the average of their ranks, and it is easy to interpret as a correlation, but its value is harder to translate into statements about pairs. Kendall's tau-b counts concordant and discordant pairs and adjusts for ties on each variable separately, which makes it suited to square tables with many ties (Agresti, 2010). Schober et al. (2018) note that the choice of coefficient should follow the measurement level and the data's structure, and here both point to tau-b. Pearson's correlation was not used because the income codes are ranks of unequal brackets, not amounts.
What the Association Does Not Show
The run shows that income and self-rated health move together among respondents. It does not establish that income affects health. Poor health can reduce income through lost work, and age, employment, education and chronic illness can shape both. A survey collected at one point in time cannot separate these paths. The association is also unadjusted and unweighted. Self-rated health is a meaningful outcome nonetheless; a meta-analysis found that a single general rating predicts mortality even after adjustment for other risk factors (DeSalvo et al., 2006), which is why a county health department would care about a gradient in it.
References
Agresti, A. (2010). Analysis of ordinal categorical data (2nd ed.). Wiley.
DeSalvo, K. B., Bloser, N., Reynolds, K., He, J., & Muntner, P. (2006). Mortality prediction with a single general self-rated health question: A meta-analysis. Journal of General Internal Medicine, 21(3), 267-275. https://doi.org/10.1111/j.1525-1497.2005.00291.x
Schober, P., Boer, C., & Schwarte, L. A. (2018). Correlation coefficients: Appropriate use and interpretation. Anesthesia & Analgesia, 126(5), 1763-1768. https://doi.org/10.1213/ANE.0000000000002864
PHLT 8032 Week 8 instructions, in plain terms
The eighth assignment usually asks for an association between two variables from the course data, presented with a crosstab and an appropriate measure, then explained in plain language. Faculty expect the variables' levels and coding direction stated before the output, row or column percentages chosen to match the question, and the measure justified from the data's structure. A plain-language sentence describing the relationship is often required, and graders read it for accuracy about direction and size. Many prompts also ask why the chosen measure suits the data better than alternatives, and what the association does not establish. Ordinal variables with few categories create many ties, and a strong submission explains how the chosen coefficient handles them. A cross-sectional survey cannot establish cause, and saying so plainly earns credit.
How this PHLT 8032 Week 8 example is built
An opening section states the question, both variables' levels and their coding directions, and the respondents used. The crosstab section presents a five by five table of row percentages and reads it by column, noting that good health is the most common rating in the lower brackets and is overtaken by very good at the top, before explaining why row percentages fit the question. A second table lists tau-b, gamma, Spearman's correlation and the chi-square. Separate sections explain the negative sign in words, translate the coefficient's size into what happens when pairs of respondents are compared, and argue for tau-b by explaining how each measure treats ties. A final section sets out what the association cannot show and why self-rated health still matters to a health department.
PHLT 8032 Week 8 rubric: what earns full marks
Graders give much of the credit to correct interpretation of direction and size. A negative coefficient reported without a coding explanation invites the reader to conclude the opposite of what the data show, and that omission loses marks. The choice of measure is read closely: Pearson's r on bracket codes, or gamma presented without noting that it ignores ties, weakens the paper. Credit goes to describing strength with reference to the table rather than borrowed labels, and to noting that a very small p-value reflects sample size. The crosstab should use row percentages for a question about how health differs by income. A limits section separating association from cause is expected. Tables need APA titles and notes, and sources on ordinal measures support the argued choice.
Common PHLT 8032 Week 8 mistakes, and how to avoid them
Association runs often stumble on the sign. Before reporting any coefficient, say which way each variable is coded and what a negative value would therefore mean, then write the relationship in words a county reader would understand. Choose percentages that match the question; for health by income, that means percentages within each income bracket. When both variables have only a few ordered categories, explain how your measure handles ties and why that makes it more suitable than the alternatives. Describe size through the table, for example the share at the top that still reports only good health, rather than through a generic label. Close by stating what the association does not show. An association write-up with variables from your section's file can be built on this model.
Get a PHLT 8032 Week 8 example written to your instructions
Tell the desk the two variables your run relates and how each is coded, along with the Week 8 prompt and rubric. Within 24-48h, first request free, an association run arrives whose plain sentence is checked against the coding. Its crosstab is invented for the purpose.
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PHLT 8032 Week 8 questions, answered
Why not use Pearson's correlation for income and health?
Pearson's r assumes both variables are measured on interval scales and related linearly. Income brackets of unequal width and a five-category health rating meet neither condition well, and the bracket codes are ranks rather than quantities. An ordinal measure such as tau-b uses only the ordering, which is what the data support. Reporting Pearson's r alongside, labeled as a rough check, is acceptable in some sections.
How should the strength of tau-b be described?
In words tied to the table rather than generic labels. The run can say the association is modest and point to the crosstab, where the fair-or-poor share falls across brackets but remains substantial at the top. Conventional labels exist, but they vary by source and field. Describing what the coefficient means for these respondents is more defensible than borrowing a word from a chart.
Does a significant association mean income affects health?
No. The run establishes that the two variables move together among respondents. Income could shape health, poor health could reduce income, and age, employment or chronic illness could shape both. Survey data collected at a single point in time cannot separate those paths. The run says so plainly, and that sentence earns credit of its own this week.
Where can I find a free PHLT 8032 Week 8 sample paper?
The complete Week 8 association run is on this page, with a crosstab of self-rated health by income bracket, a table of ordinal measures and paragraphs on the sign, the size and the choice of tau-b.
Why is gamma larger than tau-b for the same table?
Gamma uses only pairs of respondents who differ on both variables and ignores tied pairs. With many ties, that inflates its value, while tau-b adjusts for ties and describes the whole sample more fairly.