Minitab Icc Calculation How To Use This

I am looking at 3 raters, who are rating how long it took for a patient to fall asleep.

Example 1: Four judges assess 8 types of wine for quality by assigning a score from 0 to 9 with the ratings given in Figure 1.

We would like to determine whether the wines can be judged reliably by different judges.

Figure 1 Data for Example 1 We can see from the data that there is a fair amount of consistency between the ratings of the different judges with a few noticeable differences.

We will assume that the four judges are taken from a random sample of judges and use Excels Anova: Two Factor without Replication data analysis (i.e.

Figure 2 Calculation of Intraclass Correlation Here the rows relate to the Between Subjects (Wines) and the columns relate to the Judges (who are the raters).

From Definition 1 in Two Factor ANOVA without Replication we have the model The intraclass correlation is then Thus there are three types of variability: var( ): variability due to differences in the subjects (i.e.

B really likes wine 3, while judge C finds it to be very bad) var( ): variability due to differences in the rating levelsscale used by the judges (e.g.

B and C both find wine 1 to be the worst, but while judge C assigns wine 1 a Likert rating of 0, judge B gives it a bit higher rating with a 2).

Real Statistics Function: The Real Statistics Resource Pack contains the following function: ICC (R1) intraclass correlation coefficient of R1 where R1 is formatted as in the data range B5:E12 of Figure 1.

For Example 1, ICC(B5:E12).728.

This function is actually an array function that provides additional capabilities, as described in Intraclass Correlation Continued.

Real Statistics Data Analysis Tool: The Interrater Reliability data analysis tool supplied in the Real Statistics Resource Pack can also be used to calculate the ICC.

Minitab Icc Calculation How To Use This

We show how to use this tool in Intraclass Correlation Continued.

Observation: There are a number of other measures of ICC in use.

Click here for information about these other versions of ICC.

Observation: We now show how to calculate an approximate confidence interval for the ICC.

We start by defining the following Note that for newer versions of Excel, the FINV function should be replaced by F.INV.RT.

From these we calculate the lower and upper bounds of the confidence interval as follows: Using these formulas we calculate the 95 confidence interval for ICC for the data in Example 1 to be (.434,.927) as shown in Figure 3.

Figure 3 95 confidence interval for ICC As stated above, for newer versions of Excel, the FINV function in cells L39 and L40 should be replaced by F.INV.RT.

Observation: The ratings by the judges indicate the difficulty or leniency of the judge.

In this case, the rating corresponds to the difficulty or leniency of the question.

Observation: The measure of ICC is dependent on the homogeneity of the population of subjects being measured.

For example, if the raters are measuring the level of violence in the general population, the value of var( ) may be high compared to var( ) and var( ), thus making ICC high.

If instead, the raters are measuring levels of violence in a population of inmates from maximum-security prisons, the value of var( ) may be low compared to var( ) and var( ), thus making ICC low.

Observation: There isnt universal agreement as to what constitutes an acceptable ICC value.

This can also depend on the field in which it is used.

E.g. in the medical field, an ICC less than.40 is considered to be poor, between.40 and.50 fairmoderate, between.60 and.75 good and ICC.75 and above excellent.

Others will change these boundaries to.50,.75 and.90.

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