So our two tests on this page are basically methods that we can use to determine if a value within our given data set should be ignored or not. Now, we're gonna look at first Grubbs test, Grubbs test is used to detect a single outlier in a single variable data set that follows some type of normal distribution. Now, here Grubbs tests, we first have to calculate R R G calculated. Here, we have our questionable value. So our potential outlier minus your meaner average in absolute brackets divided by your standard deviation. Now, here we're going to compare our G calculated to our G table. Now, here we have our number of observations and then we have our G table or sometimes called R G critical based on a particular confidence interval, we have 90% 95% and 99% confidence. Now, if our G table value happens to be less than R G calculated, that means that outlier needs to be discarded and we need to recalculate standard deviation and the mean with the remaining data sets next. If you're G table is greater than your G calculated, that means that outlier is fine, it's within the normal level of confidence, so we can retain it, hold onto our mean and standard deviation. Our Q Test is another method that's usually not talked about, but here, this is just another method in finding outliers in very small normal, normally distributed data sets here, the number of measurements is normally between 3-7 values. Now it can exceed that, but the Q Test is usually reserved for very few data measurements. Now here we're gonna say Q calculated equals your gap divided by your range. Now what does that mean? Well your gap is absolute brackets X. One minus X. And plus one X. One is just the suspected outlier that we're looking for. So we're trying to determine if this is the number we need to ignore and then here we're gonna say here this is the next closest data point. So that's the next measurement that's closest to that outlier and then range your range is just your largest value minus the smallest value in your data set for the Q. Test. What you need to do is you need to take all your measurements and need to organize them from smallest to largest value and then your range is just that largest value minus your smallest value. We'll see how to utilize this later on. As we do a question on the Q test. Now, just like the Grubbs test, we compare our Q. Calculated in this case to our queue table. Again we have a number of measurements which you can compare two different levels of confidence here. Again, if your table value is lower than your calculated value in this case Q. We disregard that value, it is an outlier and it cannot be included with our data measurements. If your Q. Q. Table or your cue critical value happens to be greater than your Q. Calculated. Then we can hold onto that suspected outlier and say that it does belong with the other measurements. Again, Grubbs test is the more commonly used test to find. The outlier Q. Test is normally not discussed as much, and it's usually reserved for very small amounts of measurements. So just remember these two different types of tests that are great at finding an outlier within a given data set.
