SPSS command: SPSS RATIO STATISTICS
Ratio statistics in your browser
Ratio Statistics summarises the ratio of two positive variables, most often assessed value to sale price, with the uniformity and vertical-equity measures assessors report.
Free · No account · Files stay on your device · Updated 18 October 2026
What it tells you
Crosstabs runs the SPSS RATIO STATISTICS procedure on your device: median, mean and weighted mean with confidence intervals, COD, PRD, PRB with its interval, coefficients of concentration and the coefficient of variation, overall and by group.
- The level of the ratio: median, mean and price-weighted mean, each with a confidence interval.
- Uniformity: the coefficient of dispersion (COD) around the median and the share of ratios within a chosen percentage of it.
- Vertical equity: whether high-value items are assessed at lower ratios than low-value ones (PRD and PRB).
- How these compare between groups such as neighbourhoods or property classes.
When to use it
Use it when
- Property tax assessment studies comparing appraised values with sale prices.
- Any audit of an estimate against an observed value: insurance reserves versus paid claims, forecast versus actual spend.
- Comparing uniformity across districts or classes with one column per group.
Use something else when
- Either variable can be zero or negative: those cases are excluded, so a ratio is not meaningful for your data.
- You want to model the ratio on several predictors: use linear regression on the log ratio.
- You need general descriptives of one variable: use Descriptives or Explore.
How to run it in Crosstabs
- 01
Open your data
Open a file with one row per sale or item and switch to Statistics mode.
- 02
Choose Ratio Statistics
In the Agreement and diagnostics group, pick Ratio Statistics (RATIO STATISTICS).
- 03
Set numerator and denominator
Choose the Numerator (e.g. appraised value) and Denominator (e.g. sale price); optionally a Group variable (optional) for one column per group plus Overall.
- 04
Choose interval options
Set Median confidence interval to Distribution-free or Normal distribution, the Confidence level (%), and Concentration within % of median (default 10, 20).
- 05
Run
Declare any weight as a frequency weight (truncated to whole numbers) and press Run.
Worked example
Computed by the Crosstabs engine from the synthetic data below when this page was built — not typed in.
Data
50 synthetic home sales, 25 in each of two districts. Sale prices are log-normal; the appraisal-to-sale ratio is built to fall slightly as price rises, with random scatter on top. Fixed seed.
| Item | North | South | Overall |
|---|---|---|---|
| Count | 25 | 25 | 50 |
| Median | 0.949 | 0.940 | 0.947 |
| 95% CI for Median | 0.880 – 0.992 | 0.925 – 1.000 | 0.925 – 0.985 |
| Actual coverage | 95.7% | 95.7% | 96.7% |
| Mean | 0.947 | 0.968 | 0.957 |
| Weighted Mean | 0.936 | 0.964 | 0.949 |
| Coefficient of Dispersion | 7.3 | 7.1 | 7.2 |
| Coefficient of Concentration — within 10% of median | 68.0% | 72.0% | 70.0% |
| Price Related Differential | 1.012 | 1.004 | 1.009 |
| Price Related Bias | −0.060 | 0.013 | −0.036 |
| 95% CI for PRB | −0.143 – 0.024 | −0.099 – 0.125 | −0.097 – 0.025 |
| Coefficient of Variation — Mean Centered | 8.8% | 8.9% | 8.9% |
Selected rows. The median interval uses order statistics; its actual coverage is at least the nominal level.
How to read it
The overall median ratio is 0.947 (95% CI 0.925 – 0.985), so a typical home is appraised at about 95% of its sale price. The coefficient of dispersion is 7.2, and the PRD of 1.009 is within the usual 0.98–1.03 range; the PRB of −0.036 means ratios change by about −3.6% when value doubles, and its 95% CI (−0.097 – 0.025) includes 0, so the drift is not distinguishable from noise in 50 sales.
Output tables explained
- Ratio Statistics (level rows)
- The single Ratio Statistics table has one column per group plus Overall. Its first rows give the level of the ratio: count, mean with CI, median with CI and the interval's actual coverage, and the price-weighted mean with its delta-method CI. Minimum, maximum and range follow.
- Ratio Statistics (uniformity and equity rows)
- The remaining rows measure spread and vertical equity: standard deviation, average absolute deviation, PRD, PRB with its CI, COD, one coefficient of concentration per percentage you entered, and the mean-centred coefficient of variation.
Assumptions and notes
- Both variables are strictly positive; non-positive cases are excluded and counted in a footnote.
- The sales are a representative sample of the population being assessed, without outlier trimming unless you do it first.
- The normal-theory median interval assumes roughly normal ratios; the distribution-free interval does not.
How the results are validated
On a 60-case weighted reference file, every statistic (median and mean with intervals, weighted mean and its delta-method interval, AAD, COD, COV, PRD, PRB with its interval, COC at 10% and 20%, minimum and maximum) matches an independent NumPy implementation of the SPSS RATIO STATISTICS algorithm on replicated data, with statsmodels OLS for PRB, to 1e-9. Validation evidence
Questions
What COD is acceptable?
Assessment standards commonly cite COD of 5–15 for single-family homes, with higher values tolerated for older or heterogeneous property. Check the standard your jurisdiction uses.
How do PRD and PRB differ?
PRD is the mean ratio divided by the price-weighted mean; values above about 1.03 suggest regressivity. PRB is a regression slope: the percentage change in the ratio when value doubles, with a confidence interval, so it is easier to test.
Which median interval should I use?
Distribution-free uses order statistics and needs no normality; its actual coverage, shown in the table, is at least the nominal level. The normal-theory option is narrower but only valid when ratios are roughly normal.
What is the coefficient of concentration?
The percentage of ratios within a given percentage of the median, for example within 10%. Enter several percentages separated by commas to get one row each.
Related procedures
- DescriptivesDESCRIPTIVES
- ExploreEXAMINE
- Complex Samples DescriptivesCSDESCRIPTIVES
- Linear RegressionREGRESSION
- Free SPSS alternative: full coverage list
Run Ratio Statistics on your own data
Open a .sav, CSV or Excel file. Everything runs in your browser; the file never leaves your device.
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