## How to do Data Presentation, analysis and Discussion

**Introduction**

This comes up, usually, in *Chapter Four* of the research project. This is where the researcher presents the data collected from respondents though not in the raw form. In their raw forms, it is quite difficult to present and analyse data, which is why there is a need for the raw data to be organized and presented in more compact forms. Subjecting the data to tabulation, grouping or even graphic forms, so as to allow for easy handling and analysis, could do this.

In doing this, the chapter sets out on an introductory note often referred to as *“Preamble”* where the researcher provides useful background information on the respondents’ group (s), their characteristics with respect to their bio-data and the rate of returns of the data gathering instruments.

After this, he moves on to the main theme of his research by presenting necessary data in the form (s) considered most appropriate for the purpose of analysis. If, as an instance, the tabular mode of data presentation was used, the tables should be well titled; each followed by detailed explanation on the data presented. This pattern should be used for each of the tables presented. Also important under data analysis is the *Discussion of Results* segment.

This comes up, normally, after the entire presentation exercise had been concluded. It is the segment where the researcher gives a more detailed insight into the issues directly relating to the data presentation and analysis. The segment helps to articulate the issues emanating from the data analysis with respect to whatever implications they have on the subject of investigation.

If the study is concerned with hypotheses testing, it is in this segment that the implications of the outcomes of the tests as they relate to the subject of research would be explained. Here also, conclusions on the relationship of the outcomes of the present study with previous ones are drawn; with a view to establishing a link between the outcomes of the present study and those of previous studies as already established under the literature review. Further more, the researcher dedicates a part of this segment to interpretation of the outcomes of his findings, thereby giving more meaning and sense to the data analysis exercise.

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**The Use of Statistics in Data Analysis**

Sulaiman {1997} defined the term statistics as “a branch of applied mathematics, which is employed in analysis of data to facilitate meaningful decision making.” It is also described as the theory and methods of analysis obtained from samples of observation in order to compare data from different empirical observations using hypothesized relationships in order to make meaningful decisions.

Even then, the methods of data analysis depend on the aims and objectives of the study and the nature of the data gathered. It becomes clear from the above, that statistical analysis could be useful for: –

(i) Reducing quantities of data to manageable and understandable

form.

(ii) Aiding decision making

(iii) Summarizing samples from which they are calculated (iv) Aiding reliable references and decisions from hypothesis

Statistics thus serves as a tool used in collecting organizing, analysing and interpreting data. Generally speaking, statistical methods are categorized into broad classes of *Descriptive and Inferential Statistics. Descriptive Statistics* are often used to summarise the data collected, while *Inferential Statistics* are used to determine the generalizability of findings arrived at, through the analysis of a sample, to the larger population.

Note that *Descriptive Statistics* can be used for both sample and population data but cannot be used to perform inferential tests on population data. This is because the results obtained from descriptive analysis are definitive enough for the population of interest. The application of either *Descriptive* or *Inferential* statistics to a set of data largely depends on the levels or scales of measurement of underlying variables. In all, there are four (4) levels of measurement otherwise known as scale.

*Nominal Scale*

This is considered as the simplest and the least refined scale of measurement; one whose primary use is to provide a labelling function. A good example of this is the individual’s sex, which can be either male or female. There cannot be any other thing between these two. The *Yes* or *No* kinds of questions are also good examples of this. However, it lacks the property of order and magnitude.

*Ordinal Scale*

This kind of measurement also performs the labelling function apart from its ordering function. This is because it possesses the property of order and magnitude such that two things could be compared in terms of their relative magnitude. A good example of the *Ordinal Scale* relates to the degree of agreement with a statement such as *Strongly Agree, Agree, Disagree,* and *Strongly Disagree.* Using this scale to measure two units, one will be able to determine which is higher or lower and not just that they are not the same.

*Interval Scale*

This also has the property of order, magnitude and additivity since equal intervals on the scale represent that there is a difference with a magnitude. The scale does not posses absolute zero because the zero is arbitrarily set. In addition to its ordering function, this scale can be used to determine the difference between two units. Measuring the temperature of a room in *Celsius and Fahrenheit* is a good example of this scale.

*Ratio Scale*

This scale is the highest level of measurement because it has an absolute zero. As a general rule, whatever statistical methods are applicable to variable measured in the nominal scale can be applied to those measured in ordinal and interval/ratio scales. Similarly, those statistical methods applicable to variables measured in ordinal scale can also be applied to those measured in interval/ratio.

There are, however, statistical methods that are applicable to variables measured in interval/ratio that could not be applied to variables measured in the nominal scale. Some examples of the ratio scale include *weight, time* and *speed;* thus possessing all the properties of the other scales.

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Procedure and Tools for Data Analysis

In data analysis, there are procedures and tools to be employed depending on the type of research as well as the nature of the data to be analysed. Regardless of the instruments/methods used in data collection, and whether the data is from sample or population, the first step in data analysis is to describe the collected data. To do this, however, the data should be summarized either using a frequency table or chart. These two are veritable tools for presenting and communicating data in such writings as technical reports and journal articles.

*The Frequency Table*

There is no doubt that with the *Frequency Table,* the researcher can display the number of cases, which have each of the attributes of a given variable. It also serves to display both qualitative and quantitative data. When confronted with the number of attributes or categories of a variable that is too large, the *Frequency Table* adopts the grouped data approach by combining the attributes into classes.

E.g. with *Age* as a variable, the *Frequency Table* may present data

as: –

20-24 25-29 30-34 35-39 40-44

*The Charts*

Just like the *Frequency Tables,* there are also *Charts,* which serve similar purposes. The two most commonly used *Charts* are the *Pie* and *Bar Charts.* That is, both could be used to present data summaries and also used to interpret and convey the message more quickly, concisely and clearly than frequency tables. Their great limitation however lies in the fact that they hardly cope in situations where the attributes of a variable to display are too many, especially when these are more than nine.

This is particularly so for *Pie Charts* which are quite useful in providing vivid picture of data but only in showing the distribution of variables with single responses. Thus, they are inappropriate tools for variables associated with multiple responses from the units of the study. Also, while they are most applicable for qualitative data, *Pie Charts* also serve to display quantitative data particularly those whose number of attributes or categories is not more than five.

As for the *Bar Charts,* they serve for qualitative data in particular, irrespective of the nature of the responses to the variables, either single or multiple. Since *Bar Charts* make it easier to compare the categories of a variable, they are more suitable for displaying data with more than five categories. They also serve to display quantitative data, particularly, the variable presented in a discrete fashion. However, *Histogram* remains the more appropriate tool for displaying continuous variables.

*Measures of Central Tendency*

This is another approach to describing a set of data, considered useful in determining a typical attribute/value of a variable. The measure is also useful in comparing the performances of two or more groups or the performance of a group over two or more periods of time. The *Mean, Mode and Median* are the three most common *Measures of Central Tendency.*

*The Mean*

The *Mean* is the arithmetic average of a set of data usually applicable to quantitative data. To obtain the *Mean,* sum up all the scores in a set of data to be divided by the number of scores. With the distribution of the variable that is skewed, however, the *Median* will better represent the distribution, as extreme values tend to increase or decrease the *Mean.*

*The Median*

The *Median* is considered as the middle value in a set of data when all the values are arranged in order of magnitude. In other words, the *Median* tends to show the grouping together of scores around a central point, dividing a set of data into two main parts. In short, the middle scores between the upper half and the lower half is the *Median.* Although the *Median* is most appropriate for *Ordinal Data,* it is also applicable to *Ordinal, Interval and Ratio Data.*

*The Mode*

Meanwhile, the score, which has the largest frequency in a set of data, is referred to as the *Mode.* It refers to the most common attributes or value of a variable in which case it is possible for a set of data to have more than one *Mode.* Although most appropriate for *Nominal Data,* the *Mode* is also applicable to all types of data.

*Measures of Variability*

This is also known as the *Measures of Dispersion* in which a measure of variation or dispersion is calculated primarily to determine the homogeneity of a set of data. There are separate measures of variation for qualitative and quantitative data. For quantitative data, measures of variation include: –

(i) The Range

(ii) Standard Deviation

(iii) Variance or the Square of the Standard Deviation (iv) Coefficient of Variation

*The Range*

This refers to the difference between the highest and lowest attribute or value. Its primary objective is to give the researcher an idea of the data spread to determine the range for a grouped data, minus the highest limit from the lowest limit. Thus, the range is solely based on the two extreme values and fails to recognise how the data are actually distributed between these two values. Hence, the desirability of *Standard Deviation* to offset this inadequacy.

*Standard Deviation*

This is defined as the distance or the average deviation of all values from the *Mean.* The difference between each *Score* and the *Mean* is the *Deviation Scores* from the *Mean.* The bigger the *Deviation,* the more variable the set of *Scores.* The *Standard Deviation* is obtained by taking the square of the average of these deviations and divided by the number of *Scores.* Thus, it is an indication of the typical deviation of the values from the *Mean.* If the *Standard Deviation* is small, the group is considered homogeneous whereas a large *Standard Deviation* is an indication of a heterogeneous group.

*Variance*

This refers simply to the square of the *Standard Deviation,* obtained by subtracting each observation from the *Mean (x),* squaring the resulting difference *(Xi* -X) to eliminate negative signs of *Deviation.* They are added up to give the *Sum of Squares (Xi-X)* and finally dividing it by the number of observation *‘n’.*

*Coefficient of Variation*

This is the *Ratio* of a distribution’s *Standard Deviation* expressed to its *Mean,* multiplied by 100, and is independent of the unit of measurement. *Coefficient* of *Variation* is employed when comparing the *Variability* of two sets of data particularly when they are expressed in different units of measurement.

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**Statistical Hypothesis Testing**

Unlike the general discussion on hypotheses as earlier on presented, the topic is being re-visited here (under data analysis), with particular reference to *Inferential Statistics.* By *Inferential Statistics,* we refer to drawing conclusions regarding the *Population of the Study* based on the information obtained from the *Sample.* It means that this kind of *Statistics* will not be relevant in situations such as when one is working with *Population Data* and when one is not interested in making a general statement about the *Population.* At the centre of *Inferential Statistics* is the concept of *Hypothesis Testing.* This refers to the process whereby the research infers from a sample whether or not to accept a statement about the *Population;* where the statement itself is the *Hypothesis.*

*Hypotheses* are stated either in the *Null* or *Alternative* forms for the researcher to validate; even though that the *Null Hypothesis* remains the more commonly used of the two. As a matter of fact, it is always the *Null Hypothesis* that gets tested and it is mainly on the condition that it is rejected that one can accept the *Alternative Hypotheses.*

When testing *Hypotheses,* the maximum probability with which one may be willing to reject the *Null Hypothesis* is referred to as the *Level of Significance.* It is common practice to use an alpha level of *0.05* or *0.01;* meaning that there are 5 or 1 of 100 chances of committing *Type* 1 *Error.* When the *Reject Decision* has been made at *0.05 level,* it means that the outcome of the experiment is statistically significant at the *0.05% level.*

The procedure, which enables one to decide whether to *Reject* or *Accept Hypotheses* or to determine whether observed *Samples* differ significantly from expected results is differently referred to as *Test of Significance, Rules of Decision, or Test of Hypothesis.* Thus, if against the assumption that a particular hypothesis is true, we find results observed in a random sample differ markedly from those under the hypothesis, we then conclude that the difference is *Significant.* On this basis, we can *Reject* the *Null Hypothesis. Errors* are sometimes made in *Hypothesis* testing and these have been categorized into: –

C a) Type 1 Error Cb) Type 11 Error

In a situation where we *Reject* the *Null Hypothesis* when, in fact, we should *Accept* it, it is said that we have committed a *Type* 1 *Error* of decision or judgement. On the other hand, if we *Accept* the *Null Hypothesis* when we should, indeed, reject it, we are said to have committed *Type* 11 *Error.* Such errors usually lead to wrong decisions.

To have a good *Test of Hypothesis,* there must a design to minimise these errors of decision. A sure way of doing this is to increase our sample size, since the larger the *Sample Size,* the less the possible errors. Some of the several kinds of *Inferential Tests* often employed in the analyses of data include: –

(a) T-Test

(b) Analysis of Variance Cc) Chi-Square

(d) Correlation and Regression Analyses

*T-Test*

This is normally used to compare the *Means* of two groups of data; which means that the data being compared should be quantitative. These two groups of data may be for two independent samples or may be for the same sample with the data collected at two different periods {i.e. paired samples}. If, based on the observed p-value, it is decided that the two groups are different, then, one should be able to state which group has the larger *Mean.*

*Analysis of Variance*

This *Test,* commonly referred to as *ANOVA,* is normally used to examine the effects of qualitative independent variables on a quantitative dependent variable. The *One-way ANOVA* is its simplest form and is used for comparing the *Means* for several groups. If, in the end, the *Null Hypothesis* is *Accepted,* it indicates that the *Means* for all the groups are the same. On the other hand, a *Rejected Null Hypothesis* indicates that not all the *Means* are the same even as it does not mean that they are all different. To ascertain which pairs of means are different, it becomes necessary to conduct a multiple comparison test.

*Chi-Square*

This kind of *Test* is often used to determine the existence of a relationship between two qualitative variables. Before applying the *Test* at all, a *Contingency Table* {Cross-tabulation} is usually formed to study the patterns of frequencies in the *Table.* If, at the end, the *Null Hypothesis* is *Rejected,* it means that there is a relationship between the two variables. It is after this that measures are used to determine the strength of the relationship

*Correlation and Regression Analyses*

These are used to study existing relationship among quantitative variables; and especially that between two quantitative variables. In particular, *Correlation Analysis* measures the strength of the relationship between the two variables, while the *Repression Analysis* develops an equation that enables one to predict the value of the *Dependent Variable* for different values of the *Independent Variable.*

These two methods are commonly used either as *Descriptive* or *Inferential* procedures. As a *Descriptive* procedure, a *Correlation Coefficient* is calculated to determine the strength of relationship between two variables. As an *Inferential* procedure, *Correlation Analysis* determines whether the observed correlation between the variables as determined from the sample can be generalized on the population.

The procedure requires that the *p- value* is calculated and used to *Accept* or *Reject* the *Null Hypothesis.* If the *Null Hypothesis* is accepted {i.e. there is no correlation between the two variables in the population}, there is no need to obtain a *Regression Equation,* as it cannot be used to predict the value of the dependent variable.

**REFERENCE**

Sulaiman, S. N. {1997} Statistics & Analytical Methods for Researchers. Kaduna. NDA Computer Centre.

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