Title: Click here to view
Course: PEBL 101: RESEARCH METHODOLOGY & DESIGN FOR BUSINESS > Section: UNIT 7a: DATA PROCESSING, ANALYSIS AND PRESENTATION

Unit 7a Learning Outcomes

Indicative Content

Editing, Coding, Data entry and cleaning, Quantitative data analysis

Intended Learning Outcomes for Unit 7:

By the end of Unit 7, you will be able to;

1. prepare data for analysis
2. apply statistical techniques to analyse quantitative data
3. apply appropriate procedures and techniques to analyse qualitative
4. apply computer software packages to analyse data
5. present and interpret data

Unit 7a E-tivities

Learning Outcome(s) addressed: Unit 7a supports Module Learning Outcomes 2, 3, 4, 5 & 6.

Purpose: When date is collected, the next step is to organize it so that meaningful information is derived from it. This unit will enable you organize both quantitative and qualitative data so as to get meaning out of both types.

Over to you: Many times we encounter situations where we collect data to be used for various purposes. The data can be overwhelming that on can fear to begin. But as a researcher, you need to do analyse it before writing a report. In this unit, you will describe data gathering process and how to clean the data. The unit introduces you concepts vital for completing Units 7b and 8. No facilitation of Basic Statistics will be taught here because you covered Statistics and a separate course unit. You are expected to refer to and apply the knowledge you acquired in statistics regarding descriptive statistics, inferential statistics and data presentation. In this unit, you will learn the practical applicability of that knowledge in business research.

Preparatory research: In order to learn about data analysis;

1. Read minilecture about introduction to data analysis here.
2. Read minilecture about quantitative data analysis here.
3. Read minilecture about statistical methods/approaches to data analysis here.
4. Read about descriptive statistics here.
5. Read about inferential statistics here.
6. Read article about descriptive and inferential statistics here;

E-tivity 7.1: Having read about the statistical methods/approaches to data analysis, make a summary of six statistical tools and what they measures (three for descriptive and three for inferential statistics). You can tabulate the solution and post it to your portfolio by 14^th April 2019.

Link to other Units:  Unit 7a links to Units 1, 2, 5, 6 & 8.

Anticipated time required for Unit 7a activities: 8 hours

Deadline for Unit 7a activity:

E-tivity 7.1: Tabulating statistical tools and what they measure: 14^th April 2019.

Introduction to Data Analysis

Data analysis is a practice in which raw data is ordered and organized so that useful information can be extracted from it. It involves inspecting, cleaning, transforming, and modeling data with the goal of highlighting useful information, suggesting conclusions, and supporting decision making. Data analysis has multiple facets and approaches, encompassing diverse techniques under a variety of names, in different business, science, and social science domains.

The process of organizing and thinking about data is key to understanding what the data does and does not contain. There are a variety of ways in which people can approach dataanalysis, and it is notoriously easy to manipulate data during the analysis phase to push certain conclusions or agendas. For this reason, it is important to pay attention when dataanalysis is presented, and to think critically about the data and the conclusions which were drawn.

Raw data can come from measurements, survey responses, and observations. In its raw form, this information can be incredibly useful, but also overwhelming. Over the course of the dataanalysisprocess, the raw data is ordered in a way which will be useful. For example, survey results may be tallied, so that people can see at a glance how many people answered the survey, and how people responded to specific questions.

In the course of organizing the data, trends often emerge, and these trends can be highlighted in the write-up of the data to ensure that readers take note. In a casual survey of ice cream preferences, for example, more women than men might express a fondness for chocolate, and this could be a point of interest for the researcher. Modeling the data with the use of mathematics and other tools can sometimes exaggerate such points of interest in the data, making them easier for the researcher to see.

Charts, graphs, and textual write-ups of data are all forms of dataanalysis. These methods are designed to refine and distill the data so that readers can glean interesting information without needing to sort through all of the data on their own. Summarizing data is often critical to supporting arguments made with that data, as is presenting the data in a clear and understandable way. The raw data may also be included in the form of an appendix so that people can look up specifics for themselves.

Data cleaning or data scrubbing

Data cleaning is an important procedure during which the data are inspected, and erroneous data are -if necessary, preferable, and possible- corrected. It is the act of detecting and correcting (or removing) corrupt or inaccurate records from a record set, table, or database. Used mainly in databases, the term refers to identifying incomplete, incorrect, inaccurate, irrelevant etc. parts of the data and then replacing, modifying or deleting this dirty data.

Data cleaning can be done during the stage of data entry. If this is done, it is important that no subjective decisions are made. Therefore, it is important not to throw information away at any stage in the data cleaning phase. All information should be saved (i.e., when altering variables, both the original values and the new values should be kept, either in a duplicate dataset or under a different variable name), and all alterations to the data set should carefully and clearly documented. The actual process of data cleansing may involve removing typographical errors or validating and correcting values against a known list of entities. The validation may be strict (such as rejecting any address that does not have a valid postal code) or fuzzy (such as correcting records that partially match existing, known records).

This involves going through interview notes, questions and/or listening to tapes to ensure all information needs is collected.It ensures completeness and consistency. As you prepare for analysis, a key issue is to distinguish methods or techniques that are appropriate for the kind of data that have collected.

Data cleaning has 3 stages: Screening phase, Diagnosis phase and Treatment phase

a) Screening Phase

Examine data for five different kinds of possible errors:

1. Lack of data – Do some questions have far fewer answers than surrounding questions?
2. Excess of data – Are there duplicate responses?
3. Outliers/inconsistencies – Are there values that are so far beyond the typical that they seem potentially erroneous?
4. Strange patterns – Are there patterns that imply cheating rather than honest answers? For instance, does a respondent alternate between ratings of 4 and 5 on every other topic in a matrix question?
5. Suspect analysis results – Do the answers to some questions seem counterintuitive or extremely unlikely?

b) Diagnosis Phase

From the Screening Phase you have highlighted data that needs investigation. To clarify suspect data, you often must review all of a respondent’s answers to determine if the data makes sense taken in context. Sometimes you must review a cross-section of different respondents’ answers, to identify issues such as a skip pattern that was specified incorrectly.

With this research complete, what is the true nature of the data that you’ve highlighted? The five possible values the authors give:

1. Missing data – Answers omitted by the respondent or questions skipped over
2. Errors –Answers that indicate the question was misunderstood
3. True extreme – An answer that seems high but can be justified by other answers (e.g., the respondent working 100 hours a week because they work a full-time job and two part-time jobs)
4. True normal – A valid answer
5. No diagnosis, still suspect – The verdict is out on this “idiopathic” data. When it comes time for the Treatment Phase, you may need to make a judgment call on how to treat this data.

c) Treatment Phase

You’ve screened the data and tried to come to a verdict on whether suspect data is guilty or innocent. You have three choices for what to do with suspect data:

1. Leave it unchanged – The most conservative course of action is to accept this data as a valid response and make no change to it. The larger your sample size, the less that one suspect response will affect the analysis; the smaller your sample size, the more difficult the decision.
2. Correct the data – If the respondent’s original intent can be determined, then fix their answer. For instance, perhaps it is clear from the respondent’s explanation for their ratings that they reversed the scale in their minds; you can invert each of their answers to this question to correct the issue.
3. Delete the data – The data seems illogical and the value is so far from the norm that it will affect descriptive or inferential statistics. What to do? Delete just this response or delete the entire record?

ANALYSIS OF QUANTITATIVE DATA

This is the process of presenting and interpreting numerical data.

The ‘Results’ section of papers including quantitative data analysis often contain descriptive statistics and inferential statistics.

Descriptive statistics include measures of central tendency (averages - mean, median and mode) and measures of variability from the average (range and standard deviation). These give the reader a 'picture' of the data collected and used in the research project.

Inferential statistics are the outcomes of statistical tests, helping deductions to be made from the data collected, to test hypotheses set and relating findings from the sample to the population.

Research that follows the positivistic paradigm (way of thinking) will usually be quantitative, requiring some form of statistical analysis.

Pre- analysis considerations

The researcher should note the following;

a.Ensure that the data was collected with quantitative analysis in mind.

b.Ensure that you (the researcher) have knowledge of statistical techniques and that you appreciate when to use them.

Post data collection consideration

a.Data type.

The level of numerical measurement determines the range of statistical tools available for analysis.

b.The level of precision (accuracy)

The more precise the data collected the greater the range of statistical tools available for analysis.

c.Number of variables

E.g. you can’t do regression analysis using one variable.

d)Whether your variables are related or not

ANALYSIS OF QUATITATIVE DATA (ctd...)

Data layout

The researcher or analyst must be clear about the data layout that he /she requires. In the same way, the researcher or analyst must be conversant with the use of different layout approaches.

Data coding

A code is an abbreviation (a number or alphabet or a combination of the two) which is assigned by the researcher to every questionnaire, item and response category. With a few exceptions, data should be coded using numerical codes and when coding, remember to create a code for missing data.

For example, if one is getting information from Kampala district and Jinja district, questionnaires from Kampala can be coded K and the first questionnaire from Kampala can be coded K1. The first questionnaire from Jinja can be coded J1. Further, each response can have a code. For example on the question of Gender, Male can be coded ‘1’ while Female can be coded ‘2’. If the question requiring gender was question one in Section A of the Questionnaire, then a response of Male can be coded as A11. The missing data can have a code say MD.

When allocating codes, the researcher should have a code sheet or code book where all codes are written together with their meanings. These will then be entered into the computer.

Once entered in a computer, the researcher can then use analytical software such as Statistical Package for Social Sciences (SPSS) to group or combine data to create new variables with less detailed categories.

Coding may be done at data collection level particularly when there are only two categories into which observations can be placed.

After coding, it important to check for errors. Errors may usually originate from:-

i)Use of incorrect codes

ii)Meaningless relationships

iii)Where filter questions have been used, some responses ought to be coded as missing.

Approaches Data analysis

There are two ways in which we can analyse data:-

1.Descriptive / Exploratory data analysis- here we use descriptive data.

2.Inferential / confirmatory data analysis- This uses inferential data.

1. Descriptive Data Analysis

This describes or displays data through tables, charts, graphs, pictograms and it also summarises data using different types of analyses like frequency counts, descriptive statistics (mean, standard deviation, median), normality (skewness, kurtosis, frequency diagrams, histograms, normal probability plots)and associations.

.

The quality of the data should be checked as early as possible. Data quality can be assessed in several ways, using different types of analyses: frequency counts, descriptive statistics (mean, standard deviation, median), normality (skewness, kurtosis, frequency diagrams, histograms, normal probability plots), associations (correlations, scatter plots).

Descriptive Data Analysis Techniques.

1. Frequency Distribution

This includes the following:

a)Frequency tables

b)Calculated percentages

c)Cumulative frequencies.

For example if we are investigating the how frequently different media are used in advertising a companies' products, the following frequency table can be used;

Media | f | % | Cumulative frequencies | Cumulative Percentage
New papers | 75 | 44.9 | 75 | 44.9
Bull boards | 60 | 35.9 | 135 | 80.8
T.V | 32 | 19.2 | 167 | 100
Total | 167 | 100 |  |

Where samples are large, it may be convenient to group observations and present frequencies of groups. It is common but not mandatory to list the highest frequency first.

The above table is an example of a simple table. However, a complex frequency table may be presented as follows;

The students selected were of varying age and gender as shown in the table below;

Table 1: Age and gender of respondents

 | Gender
 | Male | Female
Age Bracket | Frequency | Percentage | Frequency | Percentage
20 - 29 | 17 | 41.5 | 12 | 70.6
30 - 39 | 23 | 56.1 | 4 | 23.5
40 - 49 | 1 | 2.4 | 1 | 5.9
50 and above | 0 | 0.0 | 0 | 0.0
Total | 41 | 100.0 | 17 | 100.0

Source: Primary data

2

Cross tabulation

This is used to present bivariate and multi- variate data in tabular form. The researcher here is interested in establishing the inter-correlation of the various variables.

Example:

 | Age | Gender |  |  |
B. com option |  |  |  |  |
Workexperience 0-5

6-10
Income |  |  |  |  |

The data represents more than one variable.

c) Figures (charts, graphs and pictures)

They are a means of communicating data visually. Each chart or graph should be accompanied by a short paragraph that describes the information in it and its implication to the objectives of the study..

Graphs and Charts include;

·Bar charts eg simple, composite, multiple or percentage

These represent discrete data

·Pie charts

These represent continuous data as opposed to discrete data which the bar chart represents

·Histograms

These represent continuous data as opposed to discrete data which the bar chart represents.

·Frequency polygons

These also represent continuous data.

DIAGRAMS.

These include scatter diagrams which are used to represent relationship is bi-variate data.

Guidelines For Using Charts, Graphs And Diagrams

1.They should be neat and bounded.

2.They should always be titled.

3.They should be numbered in an orderly and chronological manner.

4.They should be source even if the source is primary data.

5.They should be shaded i.e. legend

6.They should be explained.

USING INFERENTIAL OR CONFIRMATING ANALYSIS.

This uses data collected from a sample to make conclusions about a population from which the sample is drawn.

For more on data analysis, watch the video here.

STATISTICAL METHODS/APPROACHES TO DATA ANALYSIS

DESCRIPTIVE AND INFERENTIAL STATISTICS SUMMARY AND TABLE

Descriptive Statistics

A set of techniques for summarizing and displaying the data from your sample. Descriptive statistics consists of the collection, organization, summation and presentation of data.

1)    When the researcher needs to summarize or describe the distribution of a single variable

2)    When the researcher wishes to understand the relationship between two or more variables

It describes or displays data through tables, charts, graphs, pictograms and it also summarises data using different types of analyses like frequency counts, descriptive statistics (mean, standard deviation, median), normality (skewness, kurtosis, frequency diagrams, histograms, normal probability plots) and associations.

 | Statistical tool | What it measures
A | Measures of Central Tendency | Measures of Central Tendency provide you With information about How your results are grouped. The central tendency of a distribution is its middle—the point around which the scores in the distribution tend to cluster.
1 | Mean (represented by M or μ) M=ΣX/N | It is the average measure,
2 | Median (represented by Mdn) | The median is the halfway point of the data. To calculate simply order arrange your values from lowest to highest and see at what value half the data is below, and half is above.
3 | Mode | It is simply the most frequently occurring value in a dataset.
B | Measures of Variability or Spread | The variability of a distribution is the extent to which the scores vary around their central tendency. Measures of spread will tell us whether the values are clustered around the mean or more spread out.
1 | Range | It is calculated simply by subtracting the lowest score from the highest score. However, this is not the most accurate method as the range can be skewed by outlier values (a very high or very low score).
2 | Interquartile range | Is less likely to be distorted by outliers, as it is calculated by ordering the sample from highest to lowest, then dividing the sample into four equal quarters. The median is then calculated for each quartile. Subtracting the median of the first quartile from the third quartile obtains the interquartile range.
3 | Standard deviation (represented by SD or σ) | A standard deviation is the average distance between the scores and the mean. The higher the standard deviation, the larger the spread. A standard deviation score of 0 indicates that there is no variation of values.
3 | Percentile Ranks | The percentile rank of a score is the percentage of scores in the distribution that are lower than that score.
4 | z Scores z = (X−M)/SD | The z score for a particular individual is the difference between that individual’s score and the mean of the distribution, divided by the standard deviation of the distribution. It indicates how far above or below the mean a raw score is, but it expresses this in terms of the standard deviation. For example, in a distribution of intelligence quotient (IQ) scores with a mean of 100 and a standard deviation of 15, an IQ score of 110 would have a z score of (110 − 100) / 15 = +0.67.
D | Normality | Data is normal if it is equally distributed both below and above the mean of that data. "Normal" data are data that are drawn (come from) a population that has a normal distribution.
1 | Skewness | Skewness is a measure of symmetry or the lack of symmetry. A distribution, or data set, is symmetric if it looks the same to the left and right of the center point.
2 | Kurtosis | Kurtosis is a measure of whether the data are heavy-tailed or light-tailed relative to a normal distribution. That is, data sets with high kurtosis tend to have heavy tails, or outliers. Data sets with low kurtosis tend to have light tails, or lack of outliers.
3 | Frequency distribution (grouped frequency distribution, ungrouped frequency distribution, cumulative frequency distribution, relative frequency distribution, relative cumulative frequency distribution) tables and graphs/ diagrams | A frequency distribution is defined as an orderly arrangement of data classified according to the magnitude of the observations. It can be tabulated and also graphed using histograms.
6 | Normal probability plots | These are scatter diagrams and graphs displaying normality of data

Inferential statistics

Inferential statistics

This is where sample statistics are you used to conclude about population parameters.  Involves using information from samples (carefully chosen subsets of the defined populations) to make inferences about populations. Inferential statistics consists of generalizing from samples to populations, performing hypothesis testing, determining relationships among variables, and making predictions.

We use inferential statistics for;

1. Estimation.
2. Measuring relationships (association )
3. Measuring differences. (comparative )
4. Testing significance of findings.
5. Forecasting.

Parametric and Non-parametric tests

In the literal meaning of the terms, a parametric statistical test is one that makes assumptions about the parameters (defining properties) of the population distribution(s) from which one's data are drawn, while a non-parametric test is one that makes no such assumptions (Frost, 2017).

Nonparametric tests don't require that your data follow the normal distribution. They are also known as distribution-free tests and can provide benefits in certain situations. Typically, people who perform statistical hypothesis tests are more comfortable with parametric tests than non-parametric tests (Frost, 2017).

Difference between parametric and non-parametric tests adopted from Frost, J (2017). Nonparametric Tests vs. Parametric Tests. Accessed on 03/10/2018 at http://statisticsbyjim.com/hypothesis-testing/nonparametric-parametric-tests/

The table below gives the various parametric and non-parametric tests used in inferential statistics

Function | Techniques | Data type | Classification
Estimation
Confidence intervals
- Uni-variate data.
- Normal distribution
Parametric test
Measuring relation ships
- Correlation (r) coefficient
- Regression ( R )
- Pearson moment coefficient
- Bi-variate data multiple.
- Bi- variate data ordinal
Parametric

Non -parametric
Comparison of sampling
- AVOVA ( analysis of variance)
- t- test
- Bi-variate data
- Multi-variate data
- Interval
Parametric
Independence of variable | Chi- square (X^2) | Bi-variate data, ordinal | Non - parametric
Good ness of fit | Chi- square ( X^2 ) test | Uni-variate data | Non –parametric.
Forecasting trends future values
- Time series analysis
- Regression
- Uni- variate
- Simple regression
- Multiple regression
Parametric

Bi-variate data.

1
Correlations Analysis (Correlation Coefficients)
Correlation coefficients measure the strength of association between two variables, and reveal whether the correlation is negative or positive. A negative relationship means that when one variable increases the other decreases (e.g., drinking alcohol and reaction time). A positive relationship means that when one variable increases so does the other (e.g. study time and test scores). Correlation scores range from ‐1 (strong negative correlation) to 1 (strong positive correlation). The closer the figure is to zero, the weaker the association, regardless whether it is a negative or positive integer.

When should you use correlation coefficients?

Correlation coefficients should be used whenever you want to test the strength of a relationship. There are many tests to measure correlation; which one to use depends on what variables you are examining. A few are listed below:

- Nominal variables: Phi, Cramer’s V, Lambda, Goodman and Kruskal’s Tau
- Ordinal variables: Gamma, Sommers D, Spearman’s Rho
- Ratio variables: Pearson’s r
2 | Bivariate Analysis | Determining relationships between two variables
3 | Multivariate Analysis | Looks at the relationship between more than two variables. Using bivariate statistical methods, it is not possible to see the relationship between two independent variables as well as their effect on the dependent variable. There are several multivariate statistical methods.
4 | Cross Tabulation | Essentially a cross tabulation (cross tab) is a table in which each cell represents a unique combination of values. This allows you to visually analyze whether one variable’s distribution is contingent on another’s. Cross tabulations can be used to show relationships between two nominal variables. This is used to present bivariate and multi- variate data in tabular form. The researcher here is interested in establishing the inter-correlation of the various variables.
5 | Multiple linear regression | Examines “the relationship between one ‘effect’ variable, called the dependent or outcome variable, and one or more predictors, also called independent variables” (Muijs 168). It is designed to work with continuous variables, although there are different techniques available for analyzing other variable types. While performing and analyzing regressions are complicated, they are valuable tools for examining the relationship between many variables. It is important to note that, like other inferential statistical techniques, values are created that provide the statistical significance of the relationships.

6 | Chi‐Square (x^2 ) | It is a test which looks at each cell in a cross tabulation and measures the difference between what was observed and what would be expected in the general population. It is used to evaluate whether there is a relationship between the values in the rows and columns of a cross tab, and the likeliness that any differences can be put down to chance. How do I know if the relationship is statistically significant? The chi‐square test provides a significance value called a p‐value. The p‐value is compared to α, which can be set at different levels. If α = .05, then a p score less than .05 indicates statistical significant differences, a p score greater than .05 means that there is no statistical difference.
7
T‐test
A t‐test compares the means between two values. It tests whether any differences in the means are statistically significant or can be explained by chance. The difference between two means.

When do you use a t‐test?

T‐tests are normally used when comparing differences between two groups (i.e., undergraduates versus graduates) or in a before and after situation. A t‐test involves means, therefore the dependent variable (the variable you are attempting to measure) must be a ratio variable. The independent variable is nominal or ordinal.

Limitations of the t‐test

A t‐test can only be used to analyze the means of two groups. For more than two groups, use ANOVA.

Like the chi‐square test, the t‐test provides a significance value called a p‐value, and is presented the same way.

Limitations of correlation coefficients Correlation does not indicate causality.

Simply because there is a relationship between two variables does not mean that one causes the other. Keep in mind correlation only looks at the relationship between two variables; there are many be others affecting the relationship (remember the confounding variable!).
8
Analysis of Variance (ANOVA)
Like the t‐test, ANOVA compares means, but can be used to compare more than two groups. ANOVA looks at the differences between categories to see if they are larger or smaller than those within categories.

When should you use ANOVA?

The dependent variable in ANOVA must be ratio. The independent variable can be nominal or ordinal, but most be composed of mutually exclusive groups

Limitations of ANOVA

ANOVA measures whether there are significant differences between three or more groups, but it does not illustrate where the significance lies – there could be differences between all groups or only two.

There are tests called post hoc comparisons which can be performed to determine where significance lies, however.

How do I know if the relationship is statistically significant?

An ANOVA uses an f‐test to determine if there is a difference between the means of groups. The f‐test can be used to calculate a p‐score, which is analyzed in the same way as chi‐squares and t‐tests.
9 | Multivariate analysis of variance (MANOVA) | It is an ANOVA which analyses several dependent variables. It can be interpreted in much the same way as ANOVA tests. MANOVA has advantages over doing multiple ANOVA tests, including reducing the potential for Type I errors (concluding that there is a relationship when there is not). Conversely, MANOVA tests can also reveal relationships not apparent in ANOVA tests.

Statistical Significance

For something to be statistically significant, it is unlikely to have occurred by chance (remember that every time you are dealing with a sample you are taking the chance that your results will not reflect the population). Another way of putting it is that significance tests denote how large the possibility is that you are committing a Type I error. Significance tests are affected by the strength of relationship between variables and the size of the sample. Common levels of significance (represented by alpha, or α) are 5%, 1% and 0.1%; if α =.01, you are stating that there is a one in one thousand chance this happened by coincidence.

Cross Tabulation

Essentially a cross tabulation (cross tab) is a table in which each cell represents a unique combination of values. This allows you to visually analyze whether one variable’s distribution is contingent on another’s. Cross tabulations can be used to show relationships between two nominal variables. This is used to present bivariate and multi- variate data in tabular form. The researcher here is interested in establishing the inter-correlation of the various variables.

An example of a cross tab is below;

The table below summarizes the result of data analysis on the research conducted on entrepreneurship students at Makerere University. 811 students were sampled.

 | I want to start my own business | A tertiary education is not necessary to be an entrepreneur | Academic institutions should encourage students to consider entrepreneurship
 | Sig. (2-tailed) | .069 | .113 | .764
N | 770 | 754 | 767
I want to start my own business | Pearson Correlation | 1 | .054 | .348^**
Sig. (2-tailed) |  | .132 | .000
N | 800 | 771 | 786
Sig. (2-tailed) | .000 | .956 | .000
N | 771 | 755 | 773
A tertiary education is not necessary to be an entrepreneur | Pearson Correlation | .054 | 1 | .098^**
Sig. (2-tailed) | .132 |  | .007
N | 771 | 782 | 768
Sig. (2-tailed) | .572 | .003 | .204
N | 757 | 759 | 754
Academic institutions should encourage students to consider entrepreneurship | Pearson Correlation | .348^** | .098^** | 1