Tables, Charts and Graphs

Methods of Displaying Data in Statistics

Data analysed in research is often displayed in three ways:

1. Tables.
2. Charts.
3. Graphs.

Different Types of Tables and Graphs in Research

Various forms of tables, charts and graphs in research are used to display results. The type of table, chart or graph used is determined by what the researcher wants to illustrate and the type of test used to obtain the results. Let's discuss this in more detail.

Frequency Tables and Diagrams

The purpose of frequency tables and diagrams is to visually show how often a variable is observed and occurs in research. For instance, frequency tables and diagrams may be used to show the frequency of colour preferences. To do this, researchers need to list each variable on a table and tally how often reports the colour.

An example of how a frequency table may look is shown below.

From the frequency table shown, it is apparent that most participants reported blue (four) as their favourite colour, and the least amount of people said green (one) as their favourite colour.

Graphs in Psychology

Bar charts and histograms are often confused. Although they may look similar, i.e. they both have bars, there are many differences between them. For instance, they display different information, and there are gaps between the bars in bar charts but not in histograms.

Bar Charts

Bar charts are a form of frequency diagrams, and they can be used to display frequency tables in graph form. Bar charts show the frequency of nominal or categorical data.

When plotting the data on graphs, the frequency should be plotted along the y-axis, and the variables should be listed on the x-axis.

Histograms

Histograms, similar to bar charts, are used to display data visually. In addition, to bars being of differing heights, each bar can vary in width, and the area of each bar represents the frequency of each grouped data. Before data is plotted on a histogram, a calculation must be done to group data.

Histograms are used to show how data for each variable is distributed, whereas bar charts are used to show how frequently a variable occurs. Whether data is normally distributed or not determines later statistical tests that could be used. Histograms are often used to analyse numerical data that is non-discrete.

When the bars in a histogram take the shape of a bell curve, the mean and median of the data can be considered approximately the same. The data can be deemed to have a normal distribution.

When the tallest bars, which get shorter across the x-axis, are shifted to the histogram's left, the data is positively skewed. Typically the mean is thought to be larger than the median. The data is negatively skewed when the bars go from short to taller across the x-axis. Typically this suggests that the median is greater than the mean.

How to complete a histogram?

We will learn about how to complete a histogram through the use of an example. Let's start by taking a look at the table below.

To plot a histogram, the next step is calculating each bar's height. To do this, you need to divide the frequency by the class interval; this value is known as frequency density.

Once the frequency density is known, the data can be plotted onto a histogram. On the x-axis, each age (25-50) would be listed, and frequency density would be labelled along the y-axis.

Charts in Psychology: Pie Charts

Pie charts are used when researchers want to highlight the proportions of data. Pie charts allow readers to easily identify the differences between the proportions of variables via the visual diagram.

Let's take the following tables as an example to help understand how pie charts are constructed:

• The first step is to calculate the total frequency; this is done by adding all of the colour preferences frequency together (5 + 3 + 6 + 4). Therefore the total frequency is 18.

• The next step is to figure out the angles of each colour. To calculate this, you need to calculate each colour's frequency divided by the total frequency and times this by 360 (shown in the table).

• After completing these sections, the pie chart can be constructed. To do this, draw a circle (this should be 360^o) and find the centre point. From the centre point, draw the radius (a line from the centre point to the edge of the circle). From here, use a protractor to measure each segment's angle, which should be drawn onto the circle.

Fig. 2. Pie charts are used in research to show the proportions of variables.

The pie chart shows that most participants consider pink their favourite colour, and blue is the least popular preference.

Scatter Diagrams in Psychology

To finish up discussing the different types of tables and graphs in research, let's talk about scatter diagrams. Scatter diagrams are used to illustrate the results of correlational tests. Correlations aim to identify if there is a relationship/ association between two variables.

From scatter diagrams, we can identify the strength of the association and the direction of the relationship between the two variables.

• If the data points are close together and tend to go in the same/similar direction, the strength can be considered strong. The strength is weak if the points are spread out and moderate if they are relatively close.

• When the data points appear to be moving upward, the association is thought of as positive; this indicates that if one variable increases, the other will too. When the data shows a downward pattern, the correlation can be assumed to be negative, meaning that as one variable increases, the other will decrease. Finally, if there appears to be no pattern in the direction of the data points, then it can be assumed that there is no relationship between the variables.

• We can also identify outliers (extreme data points that are random) by looking if there are data points that do not match the trend of the majority of data.

Fig. 3. The scatterplot shows a strong positive correlation between studying time and exam grades.

Benefits of Charts, Tables and Graphs in Research

• It helps researchers to identify patterns and trends in the data that may be difficult to identify from statistical findings.

• It can make it easier for researchers to understand what statistical tests should follow. Histograms are commonly used to identify what type of statistical test can be used.

• Tables, charts and graphs in research are data-driven. Therefore, they are objective and are often considered a straightforward method to deliver results.

The Importance of Tables and Graphs in Research

• It makes it easier for readers to visualise and understand the research findings when displayed in pictorial form.

• Tables, charts and graphs in research papers can be helpful to organise and deliver results in a manner that is easier for lay audiences to understand.