There are a number of ways to calculate inter rater reliability but one of the most common is the Krippendorff’s alpha statistic. This statistic can be used to calculate the agreement between two or more raters when there are more than two categories of ratings.
To calculate Krippendorff’s alpha you first need to calculate the agreement between each pair of raters. This can be done by calculating the percentage of ratings that are in agreement for each category. For example if there are three raters and two categories you would calculate the agreement between each pair of raters for each category (e.g. the agreement between Rater 1 and Rater 2 for Category 1 the agreement between Rater 1 and Rater 3 for Category 1 the agreement between Rater 2 and Rater 3 for Category 1 etc.).
Once you have calculated the agreement for each pair of raters you can then calculate the Krippendorff’s alpha statistic using the following formula:
α = 1 – (Σw(d – m)^2)/(N * Σw * S^2)
where:
α = Krippendorff’s alpha
w = the number of ratings in each category
d = the disagreement between each pair of raters
m = the mean of the agreements
N = the total number of ratings
S = the standard deviation of the agreements
If you are using a software program to calculate Krippendorff’s alpha you will likely need to input the following information: the number of categories the number of ratings in each category the agreement between each pair of raters and the mean of the agreements.
Once you have inputted this information the software will calculate the Krippendorff’s alpha statistic for you.
How do you calculate inter-rater reliability?
There are a few different ways to measure inter-rater reliability but the most common is to use Cohen’s Kappa.
Cohen’s Kappa is a statistic that measures the agreement between two raters on a scale from 0 (no agreement) to 1 (complete agreement).
To calculate Cohen’s Kappa you first need to calculate the observed agreement and the expected agreement.
The observed agreement is simply the number of times the two raters agree divided by the total number of ratings.
The expected agreement is the probability that the two raters would agree by chance and is calculated using a formula that takes into account the number of ratings and the number of ratings for each level of agreement.
The Kappa statistic is then calculated by subtracting the expected agreement from the observed agreement and dividing by 1- the expected agreement.
What are the benefits of using Cohen’s Kappa to measure inter-rater reliability?
There are a few benefits to using Cohen’s Kappa to measure inter-rater reliability.
First Kappa is a more accurate measure of agreement than simple percent agreement.
Second Kappa takes into account the possibility of chance agreement which is important when you are trying to determine whether two raters are actually in agreement or if they are just agreeing by chance.
Finally Kappa is a relatively easy statistic to calculate and it can be used to compare the agreement of multiple raters.
