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I covered a number of statistical tests using Excel LAMBDA. The reason for using Excel LAMBDA was its ubiquity and undemanding learning curve . While there are more statistical inferences test, I only covered those that I commonly used. If however you think other common ones, please let me know. I would be interested as well. Data Mining or Machine Learning When I started data analysis, the term data mining made sense. The techniques used within Data Mining is with the intention of identifying patterns within a data set. The problem came when I started searching more of a topic from data mining, they keep popping up in  machine learning . Machine Learning  is the process of computers learning in a way that mimics human learning or through algorithms. To accomplish this machine learning use data mining techniques as the process requires identification of patterns. While there is a difference between data mining and machine learning, do not be surprise of the overlap or if you start wond

Recently I wanted to find the correlation coefficient between multiple groups of data. A correlation coefficient shows the relationship between two groups of data . A positive correlation means as one variable increase the other increases, while a negative correlation means as one variable increases the other variable decreases. The correlation of variable with itself is always 1. A zero correlation indicates no relationship. Correlation coefficient is always between -1 and 1. Positive, Zero and Negative Correlation Excel provides the CORREL  function for this. It is fairly easy to use as shown by its syntax: CORREL(array1, array2) A correlation matrix is a table showing the correlation between pairs of variables . You could put the coefficients in a table like the one shown below. Implementing a Correlation Matrix function I thought of using LAMBDA instead. Such correlation matrix would be n x n table, where n is the number of data groups; number of columns from the d

Camel Case   Snake Case There are a few syntax styles among programmers. I mentioned snake and camel case previously. Here are a few of the different notations: snake_case_notation cameCaseNotation PascalCaseNotation nocasenotation kebab-case-notation Excel LAMBDA is not case sensitive. So while you don't have to use these notations, without them code reading becomes difficult. I also recommend keeping Excel native functions in upper case. e.g. SUM, AVERAGE, COUNT . This to distinguish Excel functions from your own functions and variables.  Snake Case Notation I used snake case notation in Excel LAMBDA because LAMBDA didn't have an IDE (yet!) and I was writing the functions in a plain text editor. Snake case notation is easy to read as the individual words are spaced out. grp_sum, BYCOL(array, LAMBDA(p_column, SUM(p_column))), my_var, long_function_name(array), Camel Case Notation I switched to camel case notation when I started implementing data m

You conducted your survey and collected your data. You plotted your charts and suspect a certain conclusion. Which test should you use to validate your hypothesis? Having learnt different statistical tools and showing their implementation in Excel LAMBDA, we want a reference to guide us. Qualitative and Quantitative Data The first is to distinguish the type of data. Data can be qualitative or quantitative . Qualitative data can be nominal or ordinal. Nominal data are named categorised data, for example gender:{male, female} and direction:{north, south, east, west}. Ordinal data are categories with implied order, for example size:{small, medium, large}, school grades:{A, B, C, D, E} and service rating:{very poor, poor, average, good, great}. The order however are not equally spaced, i.e. you cannot equate the difference between poor and average, with the difference between average and good. Quantitative data can be interval or ratio. Unlike qualitative data, quantitative data are equal

Previously I showed one-way  ANOVA  for comparing samples means. It assumes the samples are normally distributed. For non-parametric samples, we have Kruskal-Wallis test. Kruskal-Wallis the alternative to one-way ANOVA when your samples do not follow the normal distribution. Distribution 2 samples > 2 samples Normal Two Sample Mean Test ANOVA Non-parametric Mann-Whitney Kruskal-Wallis How does Kruskal-Wallis test work? Kruskal-Wallis test is used to test if there is any statistically significant differences between the medians of three or more independent (unrelated) groups. It is similar to Mann-Whitney test in that it sorts the data altogether, ranks them and then calculates the test statistics. But where Mann-Whitney uses NORM.S.DIST to calculate the test statistics, Kruskal-Wallis uses CHISQ.DIST instead. Implementing Kruskal Wallis in LAMBDA Step 1 : Group data together We can group the data together using

In an earlier post, we used the Two Sample Mean Test to compare the mean of two samples (duh). If you have 3 samples you could use the same test, and compare between pairs of samples, i.e. sample 1 & sample 2, sample 2 & sample 3, and sample 1 & sample 3. The problem arises when you have many more sample sets. Running this test means keeping track of the permutations. This approach is wastefully repetitive and you are likely to make mistakes. Also, sometimes, you only want to know if there is at least one sample that is different from the rest. Scientific or medical break throughs are rare. In most experiments and trials, there will be no change/difference. A single test that tells you that there is no difference between the samples allows you to move on.  Is there a better method to compare the mean of multiple samples? Enter ANOVA Analysis Of Variance (ANOVA) is a statistical method used to compare the means between samples. It tells you if there's any significant d

If you have not heard, Microsoft announced that it will be releasing Python in Excel . Python commands and libraries will be accessible from within Excel. No installation or add-ons required. The various Python libraries including charting capabilities will be available for you. Python commands will be executed in Microsoft Cloud. Security will be ensured. The screenshot below shows Python commands entered from within an Excel cell, with Python referencing data from the worksheet, almost as if Python is native in Excel. Advance visualisation will be available. Machine learning capabilities will at your finger tips. Will it benefit you? Short answer : No. The majority of Excel usage would not need these Python libraries and charts. It will not entice  non-Python users over to Python. Any workbook created with Python scripts would still require a Python user to maintain changes. So in a company, an employee who introduces Python in Excel, would not enjoy the reception. Any workbook creat