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# Quantitative Analysis: Descriptive Statistics

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QUANTITATIVE ANALYSIS: DESCRIPTIVE STATISTICS
Introduction
Suppose that we have carried out a survey on the effect of carrying out a management audit with three groups of nine participant institutions each i.e. small medium and large. Each group was given the same survey questions in questionnaire format and the answers from the scores were tagged between 0 and 20. What is to be done with the raw scores? There are two key types of measures that can be taken whenever we have a set of scores from participants in a given condition.
First, there are measures of central tendency, which provide some indication of the size of average or typical scores. Second, there are measures of dispersion, which indicate the extent to which the scores cluster around the average or are spread out. Various measures of central tendency and of dispersion are considered next. For this assignment, a survey is the type of data collection method in consideration and how the results of that survey would be analysed.

SURVEYS
Surveys are a very popular form of data collection, especially when gathering information from large groups, where standardization is important. Surveys can be constructed in many ways, but they always consist of two components: questions and responses. While sometimes evaluators choose to keep responses “open ended,” i.e., allow respondents to answer in a free flowing narrative form, most often the “close-ended” approach in which respondents are asked to select from a range of predetermined answers is adopted. Open-ended responses may be difficult to code and require more time and resources to handle than close-ended choices. Responses may take the form of a rating on some scale (e.g., rate a given statement from 1 to 4 on a scale from “agree” to “disagree”), may give categories from which to choose (e.g., select from potential categories of partner institutions with which a program could be involved), or may require estimates of numbers or percentages of time in which participants might engage in an activity (e.g., the percentage of time spent on teacher-led instruction or cooperative learning).
Although surveys are popularly referred to as paper-and-pencil instruments, this too is changing. Evaluators are increasingly exploring the utility of survey methods that take advantage of the emerging technologies such as the internet. Thus, surveys may be administered via computer-assisted calling, as e-mail attachments, and as web-based online data collection systems. Even the traditional approach of mailing surveys and questionnaire format can be used.
Selecting the best method for collecting surveys requires weighing a number of factors. These include the complexity of questions, resources available, the project schedule, etc. For example, web-based surveys are attractive for a number of reasons. First, because the data collected can be put directly into a database, the time and steps between data collection and analysis can be shortened. Second, it is possible to build in checks that keep out-of-range responses from being entered. However, at this time, unless the survey is fairly simple (no skip patterns, limited use of matrices), the technology needed to develop such surveys can require a significant resource investment. The type of survey to be used here will be in questionnaire format.

Analysing Quantitative Data Results
Measures of Central Tendency
Measures of central tendency describe how the data cluster together around a central point.
There are three main measures of central tendency: the mean; the median; and the mode.

Mean
The mean in each group is calculated by adding up all the scores for a given question, and then dividing by the number of participants in the group which in this case is 9. Suppose that the scores of the nine participants in the small scale businesses condition are as follows: 1, 2, 4, 5, 7, 9, 9, 9, 17. The mean is given by the total, which is 63, divided by the number of participants, which is 9. Thus, the mean is 7. The main advantage of the mean is the fact that it takes all the scores into account. This generally makes it a sensitive measure of central tendency, especially if the scores resemble the normal distribution, which is a bell-shaped distribution in which most scores cluster fairly close to the mean. However, the mean can be misleading if the distribution differs markedly from the normal and there are one or two extreme scores in one direction.

Median
Another way of describing the general level of performance in each condition is known as the median. If there is an odd number of scores, then the median is simply the middle score, having an equal number of scores higher and lower than it. In the example with nine scores in the no-noise condition (1, 2, 4, 5, 7, 9, 9, 9, 17), the median is 7. Matters are slightly more complex if there is an even number of scores. In that case, we work out the mean of the two central values. For example, suppose that we have the following scores in size order: 2, 5, 5, 7, 8, 9. The two central values are 5 and 7, and so the median is
The main advantage of the median is that it is unaffected by a few extreme scores, because it focuses only on scores in the middle of the distribution. It also has the advantage that it tends to be easier than the mean to work out. The main limitation of the median is that it ignores most of the scores, and so it is often less sensitive than the mean.
In addition, it is not always representative of the scores obtained, especially if there are only a few scores.

Mode
The final measure of central tendency is the mode. This is simply the most frequently occurring score. In the example of the nine scores in the no-noise condition, this is 9. The main advantages of the mode are that it is unaffected by one or two extreme scores, and that it is the easiest measure of central tendency to work out. In addition, it can still be worked out even when some of the extreme scores are not known. However, its limitations generally outweigh these advantages. The greatest limitation is that the mode tends to be unreliable. For example, suppose we have the following scores: 4, 4, 6, 7, 8, 8, 12, 12, 12. The mode of these scores is 12. If just one score changed (a 12 becoming a 4), the mode would change to 4! Another limitation is that information about the exact values of the scores obtained is ignored in working out the mode. This makes it a less sensitive measure than the mean. A final limitation is that it is possible for there to be more than one mode.

Levels of Measurement
From what has been said so far, we have seen that the mean is the most generally useful measure of central tendency, whereas the mode is the least useful. Thus the mean will be used in this project.

Justification
Quantitative methods of data analysis are a good way of attempting to draw meaningful results from a large body of data. Though this project is more or less qualitative in nature, it has been approached in a quantitative manner as quantitative methods of analysis provide the means to separate out the large number of confounding factors that often obscure the main qualitative findings. Take for example, a study whose main objective is to analyse why certain firms are more inclined to financial audits rather than management audits. Participatory discussions with a number of focus groups could give rise to a wealth of qualitative information which would however still require to be interpreted in numerical terms. But the complex nature of inter-relationships between factors such as the ease of financial audits compared to management audits, financial cost of the same, etc., requires some degree of quantification of the data and a subsequent analysis by quantitative methods. Once such quantifiable components of the data are separated, attention can be focused on characteristics that are of a more individualistic qualitative nature which can be translated into quantitative results for ease of interpretation.
Quantitative analytical approaches such as the mean to be used here also allow the reporting of summary results in numerical terms to be given with a specified degree of confidence. So for example, a statement such as 45% of households use an unprotected water source for drinking is more definite than saying the majority of people in a particular locality use unprotected water for drinking. The mean method of analysis gives an average of the actual scores making it more accurate and meaningful especially for odd numbers such as those chosen in this project i.e. 9.
Quantitative analysis approaches such as the mean are meaningful when there is a need for data summary across many repetitions of a participatory process, e.g. focus group discussions leading to seasonal calendars, venn diagrams, etc. Data summarisation in turn implies that some common features do emerge across such repetitions. Thus the value of a quantitative analysis arises when it is possible to identify features that occur frequently across the many participatory discussions aimed at studying a particular research theme. For example, suppose it is of interest to learn about peoples. Perceptions of what poverty means for them. It is likely that the narratives that result from discussions across several communities will show some frequently occurring answers like experiencing periods of food shortage, being unable to provide children with a reasonable level of education, not owning a radio, etc. Such information can be extracted from the narratives and coded. The mean approach provides an opportunity to study this coded information first and then to turn to interpret the meaning of the data thereafter.
These can then be discussed more easily, unhindered by the quantitative components.
Quantitative analysis approaches are particularly helpful when the qualitative information has been collected in some structured way, even if the actual information has been elicited through participatory discussions and approaches or surveys in this case. An illustration is provided by a daily activity diary study (Abeyasekera and Lawson-McDowall, 2000) conducted as part of the activities of a Farming Systems Integrated Pest Management Project in Malawi. This study was aimed at determining how household members spend their time throughout the year. The information was collected in exercise books in text format by a literate member of a household cluster and was subsequently coded by two research assistants by reading through many of the diaries and identifying the range of different activities involved. Codes 1, 2, 3, 4, were then allocated to each activity. In this study, the information was collected in quite a structured way since the authors of the diaries were asked to record daily activities of every household member by dividing the day into four quarters, i.e. morning, mid-morning, afternoon and late evening, and recording the information separately within each quarter. In such a case, using the mean method of analysis gave the most accurate picture as statistics are meant to record “the majority” or “most likely” situation which gives clearer statistics of the trend in reality.

Conclusion
For the mean method, it is easy to draw meaningful conclusions based on the key provided for the summary of results provided. Thus using this method would give a clear and more accurate picture of the effect of carrying out a management audit compared to a financial audit in a given institution hence the reason for using it in this research.

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