Kurtosis is a measure of the tailedness of a distribution. Tailedness is how often outliers occur. Excess kurtosis is the tailedness of a distribution relative to a normal distribution.
Distributions with medium kurtosis (medium tails) are mesokurtic.
Distributions with low kurtosis (thin tails) are platykurtic.
Distributions with high kurtosis (fat tails) are leptokurtic.
Tails are the tapering ends on either side of a distribution. They represent the probability or frequency of values that are extremely high or low compared to the mean. In other words, tails represent how often outliers occur.
Published on
June 15, 2022
by
Shaun Turney.
Revised on
July 1, 2022.
A systematic review is a type of review that uses repeatable methods to find, select, and synthesize all available evidence. It answers a clearly formulated research question and explicitly states the methods used to arrive at the answer.
Example: Systematic reviewIn 2008, Dr. Robert Boyle and his colleagues published a systematic review in the Cochrane Database of Systematic Reviews.
They answered the question “What is the effectiveness of probiotics in reducing eczema symptoms and improving quality of life in patients with eczema?”
In this context, a probiotic is a health product that contains live microorganisms and is taken by mouth. Eczema is a common skin condition that causes red, itchy skin.
They used systematic methods to find, select, and synthesize all available evidence, and they described these methods in detail in their article. Based on the evidence, Boyle and colleagues concluded that probiotics cannot be recommended for reducing eczema symptoms or improving quality of life in patients with eczema.
A probability distribution is a mathematical function that describes the probability of different possible values of a variable. Probability distributions are often depicted using graphs or probability tables.
Example: Probability distributionWe can describe the probability distribution of one coin flip using a probability table:
A frequency distribution describes the number of observations for each possible value of a variable. Frequency distributions are depicted using graphs and frequency tables.
Example: Frequency distributionIn the 2022 Winter Olympics, Team USA won 25 medals. This frequency table gives the medals’ values (gold, silver, and bronze) and frequencies:
Published on
May 31, 2022
by
Shaun Turney.
Revised on
June 17, 2022.
The chi-square (Χ2) distribution table is a reference table that lists chi-square critical values. A chi-square critical value is a threshold for statistical significance for certain hypothesis tests and defines confidence intervals for certain parameters.
Chi-square critical values are calculated from chi-square distributions. They’re difficult to calculate by hand, which is why most people use a reference table or statistical software instead.
Example: Chi-square test of independenceImagine a city wants to encourage more of its residents to recycle their household waste.
The city decides to test two interventions: an educational pamphlet or a phone call. They randomly select 300 households and randomly assign them to the pamphlet, phone call, or control (no intervention) group. They’ll use the results of their experiment to decide which intervention to use for the whole city.
The city plans to use a chi-square test of independence to test whether the proportion of households who recycle differs between the interventions.
Published on
May 24, 2022
by
Shaun Turney.
Revised on
June 17, 2022.
A chi-square (Χ2) goodness of fit test is a type of Pearson’s chi-square test. You can use it to test whether the observed distribution of a categorical variable differs from your expectations.
Example: Chi-square goodness of fit testYou’re hired by a dog food company to help them test three new dog food flavors.
You recruit a random sample of 75 dogs and offer each dog a choice between the three flavors by placing bowls in front of them. You expect that the flavors will be equally popular among the dogs, with about 25 dogs choosing each flavor.
Once you have your experimental results, you plan to use a chi-square goodness of fit test to figure out whether the distribution of the dogs’ flavor choices is significantly different from your expectations.
The chi-square goodness of fit test tells you how well a statistical model fits a set of observations. It’s often used to analyze genetic crosses.
Published on
May 23, 2022
by
Shaun Turney.
Revised on
June 21, 2022.
A Pearson’s chi-square test is a statistical test for categorical data. It is used to determine whether your data are significantly different from what you expected. There are two types of Pearson’s chi-square tests:
The chi-square goodness of fit test is used to test whether the frequency distribution of a categorical variable is different from your expectations.
The shape of a chi-square distribution is determined by the parameter k. The graph below shows examples of chi-square distributions with different values of k.
