Transcript:
Hello, this is dr. Grande, my video. In calculating the critical values for Mahalanobi’s distance using excel in counseling research, we use the Mahalanobi’s distance to detect multivariate outliers. A multivariate outlier, Kurz. When a combination of scores from several variables represent an outlier compared to other combinations so looking at these fictitious data. I have here a variable for depression, a variable for anxiety and a variable for motivation. So it’s these three values taken together. The combination of these three scores is what we’d be examining using Mahalanobi’s distance, One of the most common ways to calculate Malla. Dobi’s distance is to use software such as SPSS. And I have a few videos that cover that topic, but in this video. I want to show you how you can calculate the critical value for each of the levels 1 through 10 for degrees of freedom and then take that critical value and calculate it back to the probability, so in order for a particular Mahalanobi’s distance value to be indicative of a multivariate outlier, The probability of occurring has to be less than point zero zero one or one tenth of one percent, so using that probability and the degrees of freedom, we can calculate the critical value and, of course, the critical value is different for each of the degrees of freedom levels. So let’s take a look here in cell c3 enter it. The function will calculate the critical value for two degrees of freedom, And, of course, the point zero zero One probability the function would start with the equal sign and then it will be. Chi square inverse. So CH is Q inv? Now you can see the first argument that this function looks for is the probability in this case, we won’t take the probability straight from b3 instead, it will be 1 minus b3 and then the degrees of freedom will be cell 8/3 which is 2 the value 2 We hit enter and we can see that. The critical value here is thirteen point eight one and it’s not unusual to round this up to thirteen point. Eight two. Then we can autofill this function all the way down to row eleven, and then we get the critical values for the degrees of freedom from one through ten as I mentioned because these are usually displayed with this two digits to the right of the decimal. I’m gonna highlight this and just reformat this. So only two digits are displayed to the right of decimal, so there is the table of critical values for Mahalanobi’s distance. Now it’s useful, especially when we’re interpreting actual Mahalanobi’s distances from data to convert this back to a probability, so Ill. First show you how to do this using the critical value, so I’ll convert them back to the probability point. Zero zero one so here. I’ll go into cell d3 start this function with equal sign and it’ll be one minus Chi Square distribution. So Ch is QD is T. X here is the actual value of the Mahalanobi’s distance. In this case, I’m using the critical value, so it’ll be C 3 Then the degrees of freedom will be 2 and then for the last argument, we have our choice between true and false true is the cumulative distribution function. And that’s what we want and you can see. It returns it to the probability point 0 0 1 so we’ve moved from the probability over here to the critical value and then back to the probability, and of course we can autofill this down. So in order to use these critical values to evaluate Mahalanobi’s distances I have from these fictitious data generated the Mahalanobis distances for each record now. The outcome variable is not used we’re just using depression, anxiety and motivation here and these Mahalanobi’s distances were generated using SPSS. So we know it because we have three variables here. They’ll be using three degrees of freedom and the critical value associated with three degrees of freedom is sixteen point two seven. So in looking at these Mahalanobis distances, we would note that the first record and the second record both represent multivariate outliers, but the third record and on do not because they are below the critical value of sixteen point two seven And, of course, we can calculate the probability as well using the same function that we used here to turn the critical value back into the probability and that would be equal sign one – chi-square distribution in this case. X is the Mahalanobis distance here. The degrees of freedom will be set at 3 So Ill type in 3 and then, Of course, the last argument is true, and then I’ll automatically critical value table. We’re just looking at the probability and we’re assuming we have a multivariate outlier. If the probability is less than point zero zero one. So again, we get the same result. The probability for the first record in the second record are both below point zero zero one, so those represent multivariate outliers, and the probability for all the remaining records is greater than point zero zero one, so we would assume that these combinations of scores do not represent multivariate outliers. I hope you found this video in calculating critical values for Mahalanobi’s distance to be useful as always. If you have any questions or concerns Feel free to contact me and Ill. Be happy to assist you.