Definition of Quartile A quartile is a statistic describing how a set of data points are divided into 4 groups. Quartiles split a set of data by using 3 points: the lower quartile (Q1), the median (Q2), and the upper quartile (Q3). Together with the minimum and maximum values, 3 quartiles split the data set … Read more
Descriptive statistics aim to summarize the characteristics of a given data set. In contrast, inferential statistics aim to use a sample of data to draw inferences about the whole population (i.e., hypothesis testing). Types of Descriptive Statistics 1. Measures of Central Tendency Central tendency is used to describe where the center of a dataset is located. Mean, … Read more
A population is the entire group of individuals about whom you want to draw conclusions. In contrast, a sample is the subset of the same entire group. Example 1 of sample and population You would like to study if students like online courses at your university. Suppose your university has 10K students; thus, these 10K students … Read more
This tutorial shows the formula for population variance and the steps for calculating population variance by hand. Formula Population variance is the measure of the variability of a population. The following is the formula for population variance. where, Population vs. Sample Data The following is the population of a set of data. It has 11 … Read more
Sample variance is the measure of the variability in a given sample. A sample is a set of observations that are a subset of a population. Sample Variance Formula The following is the formula for sample variance. where, Data Example The following is a sample of 6 students with math scores. Calculating sample variance by … Read more
ANOVA Two-Factor without Replication is used for a design of two factors (e.g., Factor A and Factor B) and only 1 observation in each cell. For instance, both Factor A and Factor B have two levels, leading to 4 cells in total. Each cell only has 1 observations (see below). Variance Partitioning Two-Factor ANOVA without … Read more
You use ANOVA: Two-Factor without Replication when each cell only has 1 observation, but use Two-Factor with Replication when each cell has more than 1 observation. For instance, there are two factors, City and Chain Brand. Each has 2 levels, leading to 4 cells (see the figure below). Each cell in the left-hand data table … Read more
This tutorial explains the difference between logit and probit in statistics with formulas and examples. Formula and Example for Logit We can start with the following formula. Thus, \( \beta_0+\beta_1x_1+…+\beta_nx_n \) can be from \( -\infty \) to \(+\infty \), and \( p(y=1) \) will be always within the range of \( (0,1) \). We … Read more
This tutorial will first show the formulas for Two-way ANOVA and then use an example to show how you can calculate two-way ANOVA by hand. The following depicts the conceptual framework of the variance breaking down for two-way ANOVA. Typically, Two-way is used for experiment data analyses. Data example for two-way ANOVA This is the … Read more
This tutorial includes the formula and examples for Sum of Squares (SS). Sum of Squares (SS) is a measure of deviation from the mean and the following is its formula. It is to square the distance between each data point and the mean then add them together. Formula of Sum of Squares (SS) The following is … Read more