Univariate analysis (frequency tables, bar charts, pie charts, percentages)

 Univariate Analysis Overview

• A basic statistical data analysis technique.
• Data contains only one variable, excluding cause and effect relationships.
• Useful in identifying patterns in data.
• Methods include mean, mode, median, standard deviation, and dispersion.
• Univariate analysis is the simplest form of data analysis.
• It involves summarizing data and identifying patterns.

HOW DO YOU CONDUCT UNIVARIATE ANALYSIS?

Univariate analysis is conducted in many ways and most of these ways are of a descriptive nature. These are the Frequency Distribution Tables, Frequency Polygons, Histograms, Bar Charts and Pie Charts

Types of Univariate Analysis

Let us get into details here of the kind of analysis that is done to analyze univariate data.

1. Frequency distribution table

Frequency means how often something takes place. The observation frequency tells the number of times for the occurrence of an event. The frequency distribution table may show categorical or qualitative and numeric or quantitative variables. The distribution gives a snapshot of the data and lets you find out the patterns.

Table 1

2. Diagrams

Diagrams are among the most frequently used methods of displaying quantitative data. Their chief advantage is that they are relatively easy to interpret and understand.

If you are working with nominal or ordinal variables, the bar chart and the pie chart are two of the easiest methods to use.

 2.1. Bar chart

The bar chart is represented in the form of rectangular bars. The graph will compare various categories. The graph could be plotted vertically or these could be plotted horizontally. In maximum cases, the bar will be plotted vertically. The horizontal or the x-axis will represent the category and the vertical y-axis represents the category’s value. The bar graph looks at the data set and makes comparisons.

 2.2. Pie Chart

The pie chart displays the data in a circular format. The graph is divided into pieces where each piece is proportional to the fraction of the complete category. So each slice of the pie in the pie chart is relative to categories size. The entire pie is 100 percent and when you add up each of the pie slices then it should also add up to 100.

Pie charts are used to understand how a group is broken down into small pieces.

 

 2.3. Histogram

The histogram is the same as a bar chart which analysis the data counts. The bar graph will count against categories and the histogram displays the categories into bins. The bin is capable of showing the number of data positions, the range, or the interval.

 

 Fig:4

 If you are displaying an interval/ratio variable, a histogram is likely to be employed. Figure 4, which was also generated by SPSS, uses the same data and categories as Table 1.

As with the bar chart, the bars represent the relative size of each of the age bands. However, note that, with the histogram, there is no space between the bars, whereas there is a space between the bars of a bar chart.

Histograms are produced in quantitative data analysis, for interval/ratio variables, whereas bar charts are produced for nominal and ordinal variables.

3. Measures of central tendency

Measures of central tendency encapsulate in one figure a value that is typical for a distribution of values three different forms of average are recognized. 

The arithmetic mean, the average of a distribution, is used to represent the average age of a sample. In fig-4, the mean is 33.6, indicating a nearly 34-year-old average age.

The median, the midpoint of a distribution, is less affected by outliers and can be used for both interval/ratio and ordinal variables. In the case of fig-4, the median is 31.

The mode, the value most frequently occurring in a distribution, is 28 and can be used for all types of variables. These measures help in understanding the distribution and its characteristics.

 4. Measures of Dispersion in Sample Analysis

• Measures of dispersion can help draw contrasts between similar distributions of values.
• The range, the difference between the maximum and minimum value in a distribution, is the most common method.
• The range for cardiovascular equipment is 64 minutes, while for weights machines it is 48 minutes.
• Outliers can influence the range, as seen in the fig-5
• Standard deviation, the average variation around the mean, is another measure of dispersion.
• The standard deviation for cardiovascular equipment is 9.9 minutes, while for weights equipment it is 8 minutes.
• Outliers can affect the standard deviation, but their impact is offset by dividing by the number of values in the distribution.

Figure-5

Boxplot Analysis in Data Analysis

• Boxplot is a popular tool for displaying interval/ratio variables.
• It provides indication of central tendency (median) and dispersion (range).
• It also identifies outliers.
• Example: Boxplot for gym usage: Outlier: case 41.
• Box represents middle 50% of users.
• Upper line indicates greatest use within 50%.
• Lower line indicates least use within 50%.
• Median line indicates median.
• Lines upwards and downwards indicate usage levels.
• Boxplots display central tendency and dispersion.
• Box and median are closer to the bottom end of the distribution, suggesting less variation below the median.