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Previously we saw the One Sample Mean test implemented using LAMBDA  by calculating the test statistics. Excel provides something similar using the  Z.TEST  function. The Z.TEST function compares the average of a sample if it is statistically less than or equal to a test value. The formula is stated as: Z.TEST(array, x, [sigma]) where array is the range of data to be tested against x x is the value of test. sigma is optional. If the population standard deviation is known, put it here. Otherwise leave it empty, and Excel will use the sample standard deviation instead. In effect you are testing to see if the average of the array is less than or equal to x `bar(array) < x` Comparing for Less Than or Equal To Observe the box plot of 5 sample distributions above. We want to check if the distributions averages are less than or equal to the value of 50 . We see samples A and B less than 50, sample C around 50, and samples D and E more than 50. NOTE: Where possible do box plots of the

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_

You received glass window samples from two different vendors. You wish to check if the thickness of the samples are the same. Based on the samples, you obtain the following data: Vendor Sample Sample 1 Sample 2 Mean (cm) 2.0 2.3 Standard Deviation (cm) 0.2 0.3 Number of Samples 15 20 At first glance sample 2 is 0.3cm thicker than sample 1. But are their thickness significantly different? To make a comparison you would need a perform a Two Sample Mean test . Two Sample Mean Test A two sample mean test compares two sample distribution means against each other. It differs from the one sample mean test that compares against a target value. We write the Null Hypothesis as the means of sample 1 and of sample 2 are equal. `H_0: mu_1 = mu_2` And the Alternative Hypothesis as the mean of sample 1 and of sample 2 are not equal. `H_1: mu_1 != mu_2` We could also test

In the previous blog, I implemented a One Sample Mean hypothesis test in Excel LAMBDA. When given an array of sample data, we firstly calculate the sample mean, standard deviation and size, before passing these into the function. The function compares a sample mean against an expected population mean. In this blog, we will create a new function to take the sample data array directly, calculate the necessary statistics, and then reuse the One Sample Mean function to perform the hypothesis test. This extension ensures the same result regardless of the approach used. Parameter Changes In the earlier One Sample Mean dcrMean.One.TTest the input parameters were defined as: dcrMean.One.TTest =LAMBDA(expected_mean, sample_mean, sample_stdev, sample_size, [tail], [show_details], To implement One Sample Mean test for array,  dcrMean.One.TTest.Array  input parameter will take the entire data array: dcrMean.One.TTest.Array =LAMBDA(expected_mean, array, [tail], [show_details], Within this

Suppose you visited a village. The village elders claims to possess a secret elixir that makes their children grower taller! You are aware of the national 12-year old  average height is 150cm. And you could measure the village's 12-year old children's height. Plotting the village's children's height gives you a distribution like in the graph above. At first glance the village's children does seem taller than the national average. Is the village's children really taller? Is the distribution significantly different? One Sample Mean Test A one sample mean test compares a sample distribution's mean against a target value. It is similar to the one proportion test but the sample data is continuous, giving a normal distribution curve instead of a yes/no binary result. We write the Null Hypothesis as the sample mean equal to the population mean. `H_0: mu = mu_0` And the Alternative Hypothesis as the sample mean not equal to the population mean. `H_1: mu != mu_0` We