In statistical research, a variable is defined as an attribute of an object of study. Choosing which variables to measure is central to good experimental design.
If you want to test whether some plant species are more salt-tolerant than others, some key variables you might measure include the amount of salt you add to the water, the species of plants being studied, and variables related to plant health like growth and wilting.
You need to know which types of variables you are working with in order to choose appropriate statistical tests and interpret the results of your study.
You can usually identify the type of variable by asking two questions:
The t-distribution, also known as Student’s t-distribution, is a way of describing data that follow a bell curve when plotted on a graph, with the greatest number of observations close to the mean and fewer observations in the tails.
When you make an estimate in statistics, whether it is a summary statistic or a test statistic, there is always uncertainty around that estimate because the number is based on a sample of the population you are studying.
The confidence interval is the range of values that you expect your estimate to fall between a certain percentage of the time if you run your experiment again or re-sample the population in the same way.
The confidence level is the percentage of times you expect to reproduce an estimate between the upper and lower bounds of the confidence interval, and is set by the alpha value.
The Akaike information criterion (AIC) is a mathematical method for evaluating how well a model fits the data it was generated from. In statistics, AIC is used to compare different possible models and determine which one is the best fit for the data. AIC is calculated from:
the number of independent variables used to build the model.
the maximum likelihood estimate of the model (how well the model reproduces the data).
The best-fit model according to AIC is the one that explains the greatest amount of variation using the fewest possible independent variables.
ANOVA (Analysis of Variance) is a statistical test used to analyze the difference between the means of more than two groups.
A two-way ANOVA is used to estimate how the mean of a quantitative variable changes according to the levels of two categorical variables. Use a two-way ANOVA when you want to know how two independent variables, in combination, affect a dependent variable.
ANOVA is a statistical test for estimating how a quantitative dependent variable changes according to the levels of one or more categorical independent variables. ANOVA tests whether there is a difference in means of the groups at each level of the independent variable.
The null hypothesis (H0) of the ANOVA is no difference in means, and the alternate hypothesis (Ha) is that the means are different from one another.
In this guide, we will walk you through the process of a one-way ANOVA (one independent variable) and a two-way ANOVA (two independent variables).
Our sample dataset contains observations from an imaginary study of the effects of fertilizer type and planting density on crop yield.
We will also include examples of how to perform and interpret a two-way ANOVA with an interaction term, and an ANOVA with a blocking variable.
Linear regression is a regression model that uses a straight line to describe the relationship between variables. It finds the line of best fit through your data by searching for the value of the regression coefficient(s) that minimizes the total error of the model.