Descriptive Statistics

Purpose:

Describe the characteristics of a data set, and only make statements about the sample. Descriptive statistics are divided into two main categories: describing the central tendency and describing the spread of the data.

Note: Inferential statistics, on the other hand, draw inferences about the population from the sample. Examples of inferential statistics include hypothesis testing and regression.

Context Used:

• To provide basic information about variables in a data set.

• Highlight potential relationships between variables. 

Jamovi Walkthrough:

1. Click "Exploration"

2. Click "Descriptives"

3. Enter variables of interest into the "Variables" box

4. Drop down on the descriptions box and select "Variables across rows"

5. Under the "Statistics" drop-down, select desired tests (Most common: Mean and Std. deviation) 

Output Interpretation:

Central Tendency Measures: (General interpretation: shows the center value of the data)

Mean: The average value in the dataset, calculated by summing all values and dividing by the number of values.

Median: The middle value in the dataset if the values were arranged in ascending or descending order. If the dataset has an even number of observations, the median is the average of the two middle values. 

Mode: The most frequently occurring value in the dataset. A dataset may have one more, more than one mode, or no mode at all.

Spread Measures: (General interpretation: the bigger the number, the more spread/variability in the data)

Standard Deviation (σ): How dispersed or variable the data is in relation to the mean.

If SD is small, the data clusters tightly around the mean.

If SD is large, the data is more spread out from the mean.

Range: The difference between the highest (maximum) and lowest (minimum) value.

If range is small, there is greater dispersion in the data.

If range is large, there is less dispersion in the data.

IQR: The distance between the first quartile (Q1) and the third quartile (Q3). It represents the range within the central 50% of the data falls.

If IQR is small, the central portion of the data is close together and more consistent.

If IQR is large, the central portion of the data is spread out further and more variable. 

Variance: The average squared distance between the data points and the mean. 

If variance is 0, all the data points are the same.

If variance is small, the data points tend to be close to the mean.

If variance is large, the data points are very spread out from the mean and from one another. 

APA Format:

Appropriate data visualization: histograms (Distribution/frequency of discrete or continuous data on an interval scale), box plots (Distribution/skew/variance of numeric data compared between groups), scatter plots (Relationship between two numeric variables), bar graphs (Frequencies of Categorical IV, Numerical DV), pie graphs (Percentage, 2-5 nominal variables), and maps (geographical quantitative & qualitative data).

Sample table: https://apastyle.apa.org/style-grammar-guidelines/tables-figures/sample-tables#demographic

Sample write-up:

The sample as a whole was relatively young (M = 19.22, SD = 3.45). 

OR

The average age of students was 19.22 years (SD = 3.45). 

Note: plugin the mean and standard deviations