Central tendency: Mean, median and mode

Measures of central tendency help you find the middle, or the average, of a data set. The 3 most common measures of central tendency are the mode, median, and mean.

  • Mode: the most frequent value.
  • Median: the middle number in an ordered data set.
  • Mean: the sum of all values divided by the total number of values.

In addition to central tendency, the variability and distribution of your data set is important to understand when performing descriptive statistics.

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Levels of measurement: Nominal, ordinal, interval, ratio

Levels of measurement, also called scales of measurement, tell you how precisely variables are recorded. In scientific research, a variable is anything that can take on different values across your data set (e.g., height or test scores).

There are 4 levels of measurement:

  • Nominal: the data can only be categorized
  • Ordinal: the data can be categorized and ranked
  • Interval: the data can be categorized, ranked, and evenly spaced
  • Ratio: the data can be categorized, ranked, evenly spaced, and has a natural zero.

Depending on the level of measurement of the variable, what you can do to analyze your data may be limited. There is a hierarchy in the complexity and precision of the level of measurement, from low (nominal) to high (ratio).

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An introduction to descriptive statistics

Descriptive statistics summarize and organize characteristics of a data set. A data set is a collection of responses or observations from a sample or entire population.

In quantitative research, after collecting data, the first step of data analysis is to describe characteristics of the responses, such as the average of one variable (e.g., age), or the relation between two variables (e.g., age and creativity).

The next step is inferential statistics, which are tools that help you decide whether your data confirms or refutes your hypothesis and whether it is generalizable to a larger population.

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An introduction to the Akaike information criterion

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.

Example
You want to know whether drinking sugar-sweetened beverages influences body weight. You have collected secondary data from a national health survey that contains observations on sugar-sweetened beverage consumption, age, sex, and BMI (body mass index).

To find out which of these variables are important for predicting the relationship between sugar-sweetened beverage consumption and body weight, you create several possible models and compare them using AIC.

Continue reading: An introduction to the Akaike information criterion

An introduction to the two-way ANOVA

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.

Example
You are researching which type of fertilizer and planting density produces the greatest crop yield in a field experiment. You assign different plots in a field to a combination of fertilizer type (1, 2, or 3) and planting density (1=low density, 2=high density), and measure the final crop yield in bushels per acre at harvest time.

You can use a two-way ANOVA to find out if fertilizer type and planting density have an effect on average crop yield.

Continue reading: An introduction to the two-way ANOVA

An introduction to the one-way ANOVA

ANOVA, which stands for Analysis of Variance, is a statistical test used to analyze the difference between the means of more than two groups.

A one-way ANOVA uses one independent variable, while a two-way ANOVA uses two independent variables.

One-way ANOVA example
As a crop researcher, you want to test the effect of three different fertilizer mixtures on crop yield. You can use a one-way ANOVA to find out if there is a difference in crop yields between the three groups.

Continue reading: An introduction to the one-way ANOVA

ANOVA in R: A step-by-step guide

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.

One-way ANOVA example
In the one-way ANOVA, we test the effects of 3 types of fertilizer on crop yield.
Two-way ANOVA example
In the two-way ANOVA, we add an additional independent variable: planting density. We test the effects of 3 types of fertilizer and 2 different planting densities 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.

Sample dataset for ANOVA

Continue reading: ANOVA in R: A step-by-step guide

A step-by-step guide to linear regression in R

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.

There are two main types of linear regression:

In this step-by-step guide, we will walk you through linear regression in R using two sample datasets.

Simple linear regression
The first dataset contains observations about income (in a range of $15k to $75k) and happiness (rated on a scale of 1 to 10) in an imaginary sample of 500 people. The income values are divided by 10,000 to make the income data match the scale of the happiness scores (so a value of $2 represents $20,000, $3 is $30,000, etc.)
Multiple linear regression
The second dataset contains observations on the percentage of people biking to work each day, the percentage of people smoking, and the percentage of people with heart disease in an imaginary sample of 500 towns.

Download the sample datasets to try it yourself.

Simple regression dataset Multiple regression dataset

Continue reading: A step-by-step guide to linear regression in R