Multiple logistic regression. Multiple comparisons. Using spreadsheets for statistics. Displaying results in graphs. Displaying results in tables. Choosing the right test. There are three main types of variables: measurement variables, which are expressed as numbers such as 3. You need to identify the types of variables in an experiment in order to choose the correct method of analysis.
One of the first steps in deciding which statistical test to use is determining what kinds of variables you have. When you know what the relevant variables are, what kind of variables they are, and what your null and alternative hypotheses are, it's usually pretty easy to figure out which test you should use.
I classify variables into three types: measurement variables, nominal variables, and ranked variables. You'll see other names for these variable types and other ways of classifying variables in other statistics references, so try not to get confused. You'll analyze similar experiments, with similar null and alternative hypotheses, completely differently depending on which of these three variable types are involved.
For example, let's say you've measured variable X in a sample of 56 male and 67 female isopods Armadillidium vulgare, commonly known as pillbugs or roly-polies , and your null hypothesis is "Male and female A. If variable X is a genotype such as AA, Aa, or aa , it's a nominal variable, and you'd compare the genotype frequencies in males and females with a Fisher's exact test.
If you shake the isopods until they roll up into little balls, then record which is the first isopod to unroll, the second to unroll, etc. Measurement variables are, as the name implies, things you can measure. An individual observation of a measurement variable is always a number. Examples include length, weight, pH, and bone density. Other names for them include "numeric" or "quantitative" variables. Some authors divide measurement variables into two types. One type is continuous variables, such as length of an isopod's antenna, which in theory have an infinite number of possible values.
The other is discrete or meristic variables, which only have whole number values; these are things you count, such as the number of spines on an isopod's antenna. The mathematical theories underlying statistical tests involving measurement variables assume that the variables are continuous.
Luckily, these statistical tests work well on discrete measurement variables, so you usually don't need to worry about the difference between continuous and discrete measurement variables. The only exception would be if you have a very small number of possible values of a discrete variable, in which case you might want to treat it as a nominal variable instead.
When you have a measurement variable with a small number of values, it may not be clear whether it should be considered a measurement or a nominal variable. For example, let's say your isopods have 20 to 55 spines on their left antenna, and you want to know whether the average number of spines on the left antenna is different between males and females.
You should consider spine number to be a measurement variable and analyze the data using a two-sample t —test or a one-way anova. If there are only two different spine numbers—some isopods have 32 spines, and some have 33—you should treat spine number as a nominal variable, with the values "32" and "33," and compare the proportions of isopods with 32 or 33 spines in males and females using a Fisher's exact test of independence or chi-square or G —test of independence, if your sample size is really big.
The same is true for laboratory experiments; if you give your isopods food with 15 different mannose concentrations and then measure their growth rate, mannose concentration would be a measurement variable; if you give some isopods food with 5 mM mannose, and the rest of the isopods get 25 mM mannose, then mannose concentration would be a nominal variable. But what if you design an experiment with three concentrations of mannose, or five, or seven?
There is no rigid rule, and how you treat the variable will depend in part on your null and alternative hypotheses. If your alternative hypothesis is "different values of mannose have different rates of isopod growth," you could treat mannose concentration as a nominal variable. Even if there's some weird pattern of high growth on zero mannose, low growth on small amounts, high growth on intermediate amounts, and low growth on high amounts of mannose, a one-way anova could give a significant result.
If your alternative hypothesis is "isopods grow faster with more mannose," it would be better to treat mannose concentration as a measurement variable, so you can do a regression. In my class, we use the following rule of thumb: —a measurement variable with only two values should be treated as a nominal variable; —a measurement variable with six or more values should be treated as a measurement variable; —a measurement variable with three, four or five values does not exist.
Of course, in the real world there are experiments with three, four or five values of a measurement variable. Simulation studies show that analyzing such dependent variables with the methods used for measurement variables works well Fagerland et al. I am not aware of any research on the effect of treating independent variables with small numbers of values as measurement or nominal. Your decision about how to treat your variable will depend in part on your biological question. You may be able to avoid the ambiguity when you design the experiment—if you want to know whether a dependent variable is related to an independent variable that could be measurement, it's a good idea to have at least six values of the independent variable.
Something that could be measured is a measurement variable, even when you set the values. For example, if you grow isopods with one batch of food containing 10 mM mannose, another batch of food with 20 mM mannose, another batch with 30 mM mannose, etc.
Be careful when you count something, as it is sometimes a nominal variable and sometimes a measurement variable. For example, the number of bacteria colonies on a plate is a measurement variable; you count the number of colonies, and there are 87 colonies on one plate, 92 on another plate, etc. Each plate would have one data point, the number of colonies; that's a number, so it's a measurement variable.
However, if the plate has red and white bacteria colonies and you count the number of each, it is a nominal variable. Now, each colony is a separate data point with one of two values of the variable, "red" or "white"; because that's a word, not a number, it's a nominal variable.
In this case, you might summarize the nominal data with a number the percentage of colonies that are red , but the underlying data are still nominal. But between 0 and 3, the number of possible values is theoretically infinite.
A student may be 1. In practice, the methods used and the accuracy of the measurement instrument will restrict the precision of the variable. The reported height would be rounded to the nearest centimetre, so it would be 1.
The age is another example of a continuous variable that is typically rounded down. As opposed to a continuous variable, a discrete variable can assume only a finite number of real values within a given interval. An example of a discrete variable would be the score given by a judge to a gymnast in competition: the range is 0 to 10 and the score is always given to one decimal e. You can enumerate all possible values 0, 0. Another example of a discrete variable is the number of people in a household for a household of size 20 or less.
Please contact us and let us know how we can help you. The Mean The mean is the average data point value within a data set. To calculate the mean, add all of the individual data points then divide that figure by the total number of data points. The conclusion will be the process is under control. A p chart using the defect and subgroup size will correctly show the mean of It also identifies subgroup 9 as out of control.
Cheers, AlastairDefects Subgroup size48 JimT:You are welcome. This is one of my bailiwicks. I have seen percentage data misused so often that I propose to never permit its use in a project. Darth, are you mellowing in your old age??? Hey Yoda. Hope you are finding peace in your new environment.
Certainly not mellowing just keeping a lower profile out of respect for the more tenuous times we live in. Most of the black Belts take percentage data as continous and do analysis. It is standard practice and also X Xs are the independent inputs to a process that cause or control a problem to occur in the output Y of a process. However you should not be doing it as converting anything into percentage results in losing out on proportion.
It would be better to use P Chart for percentage. And you can visualize it with pie and bar charts. Additionally, you can use percentiles, median, mode and the interquartile range to summarize your data.
In Data Science, you can use one label encoding, to transform ordinal data into a numeric feature. When you are dealing with continuous data, you can use the most methods to describe your data. You can summarize your data using percentiles, median, interquartile range, mean, mode, standard deviation, and range.
To visualize continuous data, you can use a histogram or a box-plot. With a histogram, you can check the central tendency, variability, modality, and kurtosis of a distribution. This is why we also use box-plots. In this post, you discovered the different data types that are used throughout statistics. Furthermore, you now know what statistical measurements you can use at which datatype and which are the right visualization methods.
You also learned, with which methods categorical variables can be transformed into numeric variables. This enables you to create a big part of an exploratory analysis on a given dataset.
Niklas Donges is an entrepreneur, technical writer and AI expert. The Berlin-based company specializes in artificial intelligence, machine learning and deep learning, offering customized AI-powered software solutions and consulting programs to various companies. A Guide to Data Types in Statistics. Niklas Donges. October 8, Updated: July 21, Statistical Methods Summary Introduction to Data Types Having a good understanding of the different data types, also called measurement scales, is a crucial prerequisite for doing Exploratory Data Analysis EDA , since you can use certain statistical measurements only for specific data types.
Categorical Data Categorical data represents characteristics.
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