Quantitative Methods

Foreword

Although qualitative analysis of data can provide some idea about the nature of the variables involved and to a certain degree their relative importance, the study of the precise relationship between the different factors involved requires quantitative methods. These methods enable the researcher to measure the exact relationship between different variables.

In the past quantitative methods were mainly used by scientists and mathematicians. Social scientists were rather hesitant about using these methods, mainly due to their lack of familiarity with the mathematics involved. However, nowadays as there is greater need for certainty and accuracy, more and more social scientists use quantitative methods instead or in conjunction with their traditional qualitative methods.

Quantitative data analysis

In order to use quantitative methods effectively it is important to have a clear idea about the data required. Having done that, the second step is to decide how the data should be collected. Then the collected data should be collated and displayed in suitable graphs. If the relationship between two variables is linear a formula to show the relationship between the variables can be derived by drawing the line of best fit. It might also be desirable to find out about the degree of dispersion of the data. This can be done by calculating standard deviation.

Questionnaires

The following gives a list of what should be borne in mind before designing a questionnaire for either a survey or other research methods suitable for quantitative analysis:

* The questionnaire should gather all the information required.

* Questions should not be too long and cumbersome to answer.

* Each question should have one clear answer.

* Tick boxes, yes and no answers or circling the answers are usually best methods for collecting data for quantitative methods.

* Clear choices for answers should be provided to stop people writing answers which could not be used later on.

* All possible answers need to be covered.

* Efforts should be made to stop people making value judgments i.e. questions with answers such as: seldom, rarely, often should be avoided.

* Finally the number of people answering the questions should be as large as possible and certainly no less than 50 people randomly chosen out of the population. This would make the survey have meaningful statistical value.

Once the data is collected it should be collated (put together) so that it can be used more easily. Depending on the nature of the questions and the aim of the research the following methods for displaying the results can be chosen.

1. Scatter Graph and Correlations

This method is chosen when the aim of the research is to find the existence and nature of the relationships between two variables. The following example explains how this method can be used.

Example 1:

The question is to establish whether there is a relationship between the environmental temperature and the rate of the growth of the crops. In a controlled laboratory condition where the other variables such as humidity, light and texture of the soil were kept identical, temperatures were kept at different levels for 25 seeds of the same crop and the heights of the plants were measured after a month. The following table shows the results.

Fig. I

Correlations

One look at this scatter graph shows that there is a correlation between the temperature and the rate of the growth of the plants. Furthermore this correlation is a positive correlation since as one variable increases the other one also increases.

Example 2.

Under the same conditions as in example one the effect of salinity of soil on the growth of the plants was studied. The effect of salt content of the soil had an adverse effect on the growth of the plants as the scatter graph shows.

Fig. ii

In this case the correlation is negative and the graph clearly shows that as the salt content of the soil increases the level of growth decreases.

Example 3.

Under the same condition the effect of exposing the plant to different hours of playing classical music to the growth of the plants was studied and the results were presented in the following scatter graph.

Fig. IV

This information can be shown in the following bar chart.

Pie Charts

In pie charts a circle which represents the whole population is divided into a number of sectors. The angle of each sector is proportional to the frequency of each category divided by the whole population.

The angle of each sector = (frequency of the category)/(sum of the frequencies)X 360

Example 5:

The data used in example 4 can also be shown in a pie chart. The following table shows the calculation for the angle of each sector:

The following pie chart shows the choice of favourite colours out of seven colours of rainbow:

Fig. V

Pictograms

In pictograms data are represented by symbols. Every symbol represents a number of units.

Example 6:

In this example the data used in examples 4 and 5 are shown in a pictograms. In this pictogram every represents 5 units.

Fig VI

Histograms

Histograms are used for continuous data such as most physical data like time, temperature, weight, length, volume.... and also when group frequencies are used. In previous examples the data was discrete and not suitable for histograms. The use of histograms enables the user to manipulate and present data more effectively.

The main differences between histograms and bar charts are listed in the following table:

Bar Charts:

1. The bars are the same width

2. The height of the bars represent their frequencies

3. Only one axis is scaled.

Histograms:

1. The width of each bar is proportional to the size of the class or group of data

2. The height represents frequency density (frequency divided by group size).

3. The frequency for a particular group is represented by the area of the column representing it.

4. The horizontal axis should also be scaled

Example 7:

The owner of a coffee shop decided to find out about the amount of money spent by each one of its customers during the course of a day. He produced the following table:

In this table the frequency ranges from 1 to 60. So he regrouped the data using different class intervals to produce a more balanced histogram. The following table shows the new groups and the frequency densities.

The height (frequency density) of the bars in histograms are calculated by dividing the respected frequency by its class interval..

Height = frequency? class interval

The figures shown in this table were used in the next figure to produce a histogram.

Fig. vii