Agreement of Continuous Measurements

 

Menu location: Analysis_Agreement_Continuous (Intra-class).

 

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 ζw 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
220 200 240 230
260 260 240 280
210 300 280 265
270 265 280 270
280 280 270 275
260 280 280 300
275 275 275 305
280 290 300 290
320 290 300 290
300 300 310 300
270 250 330 370
320 330 330 330
335 320 335 375
350 320 340 365
360 320 350 345
330 340 380 390
335 385 360 370
400 420 425 420
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 Continuous from the Agreement 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

 

 

 

 

 

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