DC-Den

  Shapiro-Wilk and Anderson Darling Tests The Shapiro-Wilk test is another statistical test to assess the normality of a dataset. Just as Anderson-Darling test , both are goodness-of-fit test. Why would we need another normality test? Let me put some points forward: The Shapiro-Wilk SW test is specifically a test for normality. The Anderson-Darling AD test can be applied to other distributions, not just normal distribution. That said, my AD implementation  was specific for normal distribution. AD test is more sensitive to deviations in the tails of the distribution, while SW test is sensitive to deviations across the entire distribution. Both AD and SW can be used to calculate p-values, but the p-value will not be comparable. This means there can be instances where AD and SW disagree . From implementation perspective, I find AD test easier to write than the SW test (a lot more steps), but AD test was much more difficult to understand compared to SW test. So, which test should you use:

Have a look at the Excel Histogram chart above based on a given set of data. Does it look normally distributed? How could you find out? Well, you could calculate the kurtosis and skewness, e.g. using  Descriptive Statistics , or generate a BoxPlot. But still, how can you know with certainty? Descriptive Statistics showing Kurtosis and Skewness BoxPlot of Sample Data Why is Checking for Normality Important? In previous blogs on One Sample Mean Test and Two Sample Mean Test , I assumed the given data is normally distributed. If the sample is normally distributed then choosing a parametric test like t-test is applicable since we are using the mean (central tendency) and standard deviation (spread) to calculate the t-statistics . Assuming normal distribution is a simplification. It is therefore only to justify using parametric tests. However, mean and standard deviation should not be used to describe a sample that is not normally distr

In the previous blog, I implemented a Two Sample Mean hypothesis test with Excel LAMBDA. In this blog, I will create a new function that takes in two sample data arrays directly, calculate the necessary statistics, and then reuse the Two Sample Mean function to perform the hypothesis test. This approach will ensure the same result. Parameter Changes In the earlier implementation, the dcrMean.Two.TTest input parameters are: dcrMean.Two.TTest =LAMBDA(sample_mean_1, sample_stdev_1, sample_size_1, sample_mean_2, sample_stdev_2, sample_size_2, [tail], [show_details], To take in two arrays, I will create a new function dcrMean.Two.TTest.Array with input parameters as follows: dcrMean.Two.TTest.Array =LAMBDA(array_1, array_2, [tail], [show_details], Within this new function, the mean and standard deviation of the two input arrays will be pre-calculated before passing the values into the hypothesis test. The implementation will be like this: =LAMBDA(array_1, array_2, [tail], [show_