Menu location: Analysis_Analysis of Variance_Agreement.
The function calculates one way random effects intra-class correlation coefficient, estimated within-subjects standard deviation and a repeatability coefficient (Bland and Altman 1996a and 1996b, McGraw and Wong, 1996).
Intra-class correlation coefficient is calculated as:
- where m is the number of observations per subject, SSB is the sum of squared between subjects and SST is the total sum of squares (as per one way ANOVA above).
Within-subjects standard deviation is estimated as the square root of the residual mean square from one way ANOVA.
The repeatability coefficient is calculated as:
- where m is the number of observations per subject, z is a quantile from the standard normal distribution (usually taken as the 5% two tailed quantile of 1.96) and xw is the estimated within-subjects standard deviation (calculated as above).
Intra-subject standard deviation is plotted against intra-subject means and Kendall's rank correlation is used to assess the interdependence of these two variables.
An agreement plot is constructed by plotting the maximum differences from each possible intra-subject contrast against intra-subject means and the overall mean is marked as a line on this plot.
A Q-Q plot is given; here the sum of the difference between intra-subject observations and their means are ordered and plotted against an equal order of chi-square quantiles.
Agreement analysis is best carried out under expert statistical guidance.
Example
From Bland and Altman (1996a).
Test workbook (Agreement worksheet: 1st, 2nd, 3rd, 4th).
Five peak flow measurements were repeated for twenty children:
|
1st |
2nd |
3rd |
4th |
|
190 |
220 |
200 |
200 |
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220 |
200 |
240 |
230 |
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260 |
260 |
240 |
280 |
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210 |
300 |
280 |
265 |
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270 |
265 |
280 |
270 |
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280 |
280 |
270 |
275 |
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260 |
280 |
280 |
300 |
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275 |
275 |
275 |
305 |
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280 |
290 |
300 |
290 |
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320 |
290 |
300 |
290 |
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300 |
300 |
310 |
300 |
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270 |
250 |
330 |
370 |
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320 |
330 |
330 |
330 |
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335 |
320 |
335 |
375 |
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350 |
320 |
340 |
365 |
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360 |
320 |
350 |
345 |
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330 |
340 |
380 |
390 |
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335 |
385 |
360 |
370 |
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400 |
420 |
425 |
420 |
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430 |
460 |
480 |
470 |
To analyse these data using StatsDirect you must first enter them into a workbook or open the test workbook. Then select Agreement from the Analysis of Variance section of the Analysis menu.
Agreement
Variables: 1st, 2nd, 3rd, 4th
Intra-class correlation coefficient (one way random effects) = 0.882276
Estimated within-subjects standard deviation = 21.459749
For within-subjects sd vs. mean, Kendall's tau b = 0.164457 two sided P = .3296
Repeatability (for alpha = 0.05) = 59.482297
