# 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, SS_{B} is the sum of squared between subjects and SS_{T} 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 ζ_{w} 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