MCM607 CU-MCOM-SEM-II-RESEARCH METHODOLOGY

b. Itemized rating scaling Raking Q-sort c. scale (b) d. Answers: 1. 3. (c) 4. (b) 5. (b) 2. (d) REFERENCES  Donald, R. Cooper & Pamela S. Schindler (2014).  Business Research Methods. New Delhi: Tata McGraw-Hill Publishing Co. Ltd.  Gupta, S.C. (2010). Fundamentals of Statistics. 6th Ed. Mumbai: HPH.  Gupta, S. P. (2002). Statistical Methods. New Delhi: Sultan Chand & Sons.  Beri, G. C. (2012). Business Statistics. New Delhi: Tata McGraw-Hill Publishing Co. Ltd.  Zikmund. (2015). Business Research Methods. New Delhi: Cengage Learning  Abrams, M.A., Social Surveys and Social Action, London: Heinemann, 1951.  Arthur, Maurice, Philosophy of Scientific Investigation, Baltimore: John Hopkins University Press, 1943.  RS. Bhardwaj, Business Statistics, Excel Books, New Delhi, 2008.  S.N. Murthy and U. Bhojanna, Business Research Methods, Excel Books, 2007. 151 CU IDOL SELF LEARNING MATERIAL (SLM)

UNIT-10 DATA ANALYSIS Structure Learning Objectives Introduction Tabulation of Data Data Preparation –frequency tables, bar charts, pie charts, percentages Summary Keywords Learning Activity Unit End Questions (Mcq And Descriptive) References LEARNING OBJECTIVES After studying this Unit, you will be able to:  Explain data tabulation  State significance of tabulated data  Identify types of data analysis  Discuss the various data preparation methods INTRODUCTION According to LeCompte and Schensul, research data analysis is a process used by researchers for reducing data to a story and interpreting it to derive insights. The data analysis process helps in reducing a large chunk of data into smaller fragments, which makes sense. Three essential things take place during the data analysis process — the first data organization. Summarization and categorization together contribute to becoming the second known method used for data reduction. It helps in finding patterns and themes in the data for easy identification and linking. Third and the last way is data analysis – researchers do it in both top-down or bottom-up fashion. Marshall and Rossman, on the other hand, describe data analysis as a messy, ambiguous, and time- consuming, but a creative and fascinating process through which a mass of collected data is being brought to order, structure and meaning. 152 CU IDOL SELF LEARNING MATERIAL (SLM)

We can say that “the data analysis and interpretation is a process representing the application of deductive and inductive logic to the research and data analysis.” TABULATION OF DATA Tabulation comprises sorting of the data into different categories and counting the number of cases that belong to each category. The simplest way to tabulate is to count the number of responses to one question. This is also called univariate tabulation. The analysis based on just one variable is obviously meagre. Where two or more variables are involved in tabulation, it is called bivariate or multivariate tabulation in marketing research, projects generally both types of tabulation are used. Definition: Prof. Neiswanger has defined a statistical table as “In a systemic organisation of data in columns and rows.” L. K Connor has defined tabulation as the orderly and systematic presentation of numerical data in a form designed to elucidate the problem under consideration. The tabular presentation of data is one of the techniques of presentation of data. The tabular presentation means arranging the collected data in an orderly mariner in rows and in columns. The horizontal arrangement of the data is known as rows, whereas the vertical arrangement is called columns. The classified facts are recorded in rows and columns to give then tabular form. Objects of Tabulation: The following are the main objects of tabulation. a. To make the purpose of enquiry clear tabulation in the general scheme of statistics investigation is to arrange in easily accessible form. b. To make significance clear by arranging in form of table the significance of data, is made very clear. This is because table permits the observation of the whole data in one glance. The total information is clear to the view and the significance of different parts can easily be followed. c. To express the data in the least space table also permits the data to be represented in least possible space, making the whole information clear to the view. If it is expressed in form of a passage it would not only be difficult to follow, but would require more space too. d. To make comparison easy mainly because of the arrangement of figures in it. When two sets of figures are given side by side, it is much easier to form a comparative idea of their significance classification of tabulation: A. Simple Tabulation B. Complex Tabulation. 153 CU IDOL SELF LEARNING MATERIAL (SLM)

A. Simple Tabulation: It gives information about one or more groups of independent questions. This result, in one-way table, provides information of one characteristics of data. B. Complex Tabulation: In this type of tabulation, the data is divided in two or more categories which gives information regarding more sets of interrelated question. Importance of Tabulation a. S ystematic Presentation of Data: Generally the collected data is in fragmented form. The mass of data is presented in a concise and simple manner by means of statistical tables. Thus, tabulation helps in presenting the data in an orderly manner. b. F acilitates Comparison of Data: If the data is in the raw form, it is very difficult to compare. Comparison is possible when the related items of data are presented in simple and concise form. The presentation of complete and unorganized data in the form of tables facilitates the comparison of the various aspects of the data. c.I dentification of the Desired Values: In tabulation, data is presented in an orderly manner by arranging it in rows and columns. Therefore, the desired values can be identified without much difficulty. In the absence of tabulated data, it would be rather difficult to locate the required values. d. P rovides a Basis for Analysis: Presentation of data in tabular form provides a basis for analysis of such data. The statistical methodology suggests that analysis follows presentation of data. A systematic presentation of data in tabular form is a prerequisite for the analysis of data Statistical tables are useful aids in analysis. e. E xhibits Trend of Data: By presenting data in a condensed form at one place, tabular presentation exhibits the trend of data. By looking at a statistical table, we can identify the overall pattern of the data. Data Analysis 154 CU IDOL SELF LEARNING MATERIAL (SLM)

The data collected may or may not in numerical form. Even if data is not in numerical form still, we can carry out qualitative analysis based on the experiences of individual participants. When data is collected in numerical form than through descriptive statistics findings can be summarised. This includes measure of central tendency like mean range etc. Another way to summarised finding is by means of graphs and charts. In any of the research study there is experimental hypothesis or null hypothesis one the basis of data of both hypothesis, various test has been devised to take decision. Where decision is taken on the basis statistical test, it is subject to error, and such correct decision is difficult. But some standard procedures followed to arrive at proper decision. Analysis involves estimating the values of unknown parameters of the population and testing hypothesis for drawing inferences. Types of Analysis:  Q ualitative analysis  C ontent analysis  Q uantitative analysis  D escriptive analysis  B ivariate analysis  S equential analysis  C asual analysis  M ultivariate analysis I nferential analysis  S tatistical analysis. a. Qualitative Analysis: It is less influenced by theoretical assumption. The limitation of this type of 155 CU IDOL SELF LEARNING MATERIAL (SLM)

analysis is that the findings tend to be unrealisable. The information categories and interpreted after, differ considerable from one investigator to another one. In this system researcher to go through, research cycle, to increase reliability, repeating the research cycle is of value in some ways, but it does not ensure that the findings will have high reliability. Qualitative analyses are carried out in several different kinds of study like interview, case studies and observational studies. b. Content Analysis: Content analysis is used where originally qualitative information is reduced to numerical terms. It is a method of analysis media output includes articles published in new papers, speeches made in radio, television and various type of propaganda. This method of analysis is applied to all most all form of communications. c. Quantitative Analysis: The numerical data collected in study through descriptive statistics analysis can be conducted through measure of central tendency. d. Descriptive Analysis: This analysis of one variable is called one dimensional analysis. This analysis measures condition at particular time. e. Bivariate Analysis: The analysis in respect of two variables is called bivariate analysis. In this analysis collected data in placed into tabular form, so that the meaning of the data can be derived. In this method simple dimensional data is developed and put into two or more categories. f. Sequential Analysis: When only factor is revel in the table at one time, this type of analysis is called sequential analysis is called sequential analysis. If we do the further analysis of the same data regard four going showed that person with leave travel concession facilities is more frequently going on tourism than those who are not gating facilities of casual analysis. It is concerned with study of one variable affecting another one. g. Causal Analysis: The purpose of causal analysis is trying to find the root cause of a problem instead of finding the symptoms. This technique helps to uncover the facts that lead to a certain situation. h. Multivariate Analysis: With an advancement of compute application there is fast development of multivariate analysis, in which statistical method simultaneously analysis more than two variables. i. Inferential Analysis: In order to decide the validity of data to indicate conclusion this analysis is concerned with tests for significance of hypothesis. One the basis of inferential analysis the task of interpretation is performed by estimating the population values. j. Statistical data analysis: Statistical data analysis is a procedure of performing various statistical operations. It is a kind of quantitative research, which seeks to quantify the data, and typically, applies some form of statistical analysis. Quantitative data basically involves descriptive data, such 156 CU IDOL SELF LEARNING MATERIAL (SLM)

as survey data and observational data. DATA PREPARATION –FREQUENCY TABLES, BAR CHARTS, PIE CHARTS, PERCENTAGES Research shows that the data preparation process is estimated to take up to 80% of the overall analysis time. For businesses, this continues to be a major barrier to getting quick and accurate analysis. The data preparation process allows anyone to quickly turn any raw data from multiple sources into refined information assets so it can be used for accurate analysis and valuable business insights. The self-service data preparation process is quickly becoming a skill that is required for an increasing number of data analysts, data scientists and business users. These individuals have been learning and adopting this new skill to support their daily business intelligence activities and analytic initiatives. To date, the tools available for data preparation processing have been somewhat limited to Excel or other spreadsheet applications. As a result, it’s not always clear what a data preparation process should be, who’s responsible for it and how it fits with the current analytics practice. Frequency tables, pie charts, and bar charts can be used to display the distribution of a single categorical variable. These displays show all possible values of the variable along with either the frequency (count) or relative frequency (percentage). Relative frequencies are more commonly used because they allow you to compare how often values occur relative to the overall sample size. They are calculated by dividing the number of responses for a specific category by the total number of responses. Pie charts represent relative frequencies by displaying how much of the whole pie each category represents. Frequency tables and bar charts can display either the raw frequencies or relative frequencies. If you wish to perform an inferential test on the distribution of a single categorical variable, see the chi-squared goodness-of-fit test. Example: A researcher asked her class to pick who would win in a battle of superheroes. Below is a frequency table and charts of the results: Out of a total of 128 responses, 41% (or 52/128) of students reported that Batman would win the battle, followed by Iron Man with 27%, Captain America with 19%, and Superman with 13%. A pie chart and bar chart of these results are shown below: 157 CU IDOL SELF LEARNING MATERIAL (SLM)

Percentage Frequency Table 158 Example CU IDOL SELF LEARNING MATERIAL (SLM)

Percentage Cumulative Frequency Table Example SUMMARY R esearchers rely heavily on data as they have a story to tell or problems to solve. It starts with a question, and data is nothing but an answer to that question. But, what if there is no question to ask? Well! It is possible to explore data even without a problem – we call it ‘Data Mining’ which often reveal some interesting patterns within the data that are worth exploring. I 159 CU IDOL SELF LEARNING MATERIAL (SLM)

rrelevant to the type of data, researchers explore, their mission, and audiences’ vision guide them to find the patterns to shape the story they want to tell. One of the essential things expected from researchers while analyzing data is to stay open and remain unbiased towards unexpected patterns, expressions, and results. Remember, sometimes, data analysis tells the most unforeseen yet exciting stories that were not expected at the time of initiating data analysis. Therefore, rely on the data you have at hand and enjoy the journey of exploratory research. Q ualitative data analysis is a process that seeks to reduce and make sense of vast amounts of information, often from different sources, so that impressions that shed light on a research question can emerge. It is a process where you take descriptive information and offer an explanation or interpretation. The information can consist of interview transcripts, documents, blogs, surveys, pictures, videos etc. You may have been in the situation where you have carried out 6 focus group discussions but then are not quite sure what to do with the 30 pages of notes you collected during the process. Do you just highlight what seems most relevant or is there a more systematic way of analyzing it? Q ualitative data analysis ought to pay attention to the ‘spoken word’, context, consistency and contradictions of views, frequency and intensity of comments, their specificity as well as emerging themes and trends. We now explain three key components of qualitative data analysis. S tatistics help us turn quantitative data into useful information to help with decision making. We can use statistics to summarize our data, describing patterns, relationship and connections. Statistics can be descriptive or inferential. Descriptive statistics help us to summarize our data whereas inferential statistics are used to identify statistically significant differences between groups of data (such as intervention and control groups in a randomized control study). KEYWORDS  Hypothesis -- A formal statement made about the predicted relationship between variables in a research study, which is directly tested by the researcher. Generally linked to deductive reasoning. I deographic explanations - Only valid for a specific situation or ‘case’ and not generalizable to 160 CU IDOL SELF LEARNING MATERIAL (SLM)

others. I ndividual fallacy - Taking an exception to a general rule and considering it as cancelling the rule. I nformants - A person who helps a researcher in a field study by helping them gain access to the setting, introduce them to the members of the setting, answer questions the researcher may have and provide clarifications. Often it is a member of the setting. I nteractions - Factors that influence each other within a system. LEARNING ACTIVITY 1. Prepare a Pie Chart & Bar Charts for the following information. Student No. Marks in 1 Physics Chemistry 2 30 40 3 49 48 4 25 30 30 30 UNIT END QUESTIONS (MCQ AND DESCRIPTIVE) Descripti Explain A. What do ve Questions Explain 1. 161 the significance of data tabulation. 2. you mean by data analysis? 3. the type of data analysis. Give examples. CU IDOL SELF LEARNING MATERIAL (SLM)

4. Explain the importance of graphs, diagrams in data analysis. Give examples. B. Multiple Choice Questions (MCQs) 1. Which of the following is not a “Graphic representation”? a. Pie Chart b. Bar Chart c. Table d. Histogra m 2. A pie chart is: a. A chart demonstrating the increasing incidence of obesity in society. b. Any form of pictorial representation of data. c. Only used in catering management research. d. An illustration where the data are divided into proportional segments according to the share each has of the total value of the data. 3. Qualitativ e data analysis is still a relatively new and rapidly developing branch of research methodology. True a. False b. 4. A graph that uses vertical bars to represent data is called a Line a. Bar graph graph Scatterpl b. c. 162 ot CU IDOL SELF LEARNING MATERIAL (SLM)

d. Vertical (c) graph Answers: 1. 2. (d) 3. (a) 4. (b) REFERENCES  Donald, R. Cooper & Pamela S. Schindler (2014).  Business Research Methods. New Delhi: Tata McGraw-Hill Publishing Co. Ltd.  Gupta, S.C. (2010). Fundamentals of Statistics. 6th Ed. Mumbai: HPH.  Gupta, S. P. (2002). Statistical Methods. New Delhi: Sultan Chand & Sons.  Beri, G. C. (2012). Business Statistics. New Delhi: Tata McGraw-Hill Publishing Co. Ltd.  Zikmund. (2015). Business Research Methods. New Delhi: Cengage Learning  Churchill, Gilbert A (1983) Marketing Research: Methodological Foundations, The Dryden Press, New York.  Kothari C.R. (1990) Research Methodology: Methods and Technique. Wishwa Prakashan, New Delhi.  Mahalotra N.K. (2002) Marketing Research: An Applied Orientation. Pearson Education Asia.  Mustafi, C.K. 1981. Statistical Methods in Managerial Decisions, Macmillan: New Delhi.  Raj, D. (1968), “Sampling Theory,” McGraw-Hill Book Company, New York.  Singh, D. and F.S. Chaudhary, 1986. Theory and Analysis of Sample Survey Designs, Wiley Eastern: New Delhi.  Yates, E (1960), “Sampling Methods for Censuses and Surveys,” Charles Griffin & Company, Ltd., London 163 CU IDOL SELF LEARNING MATERIAL (SLM)

UNIT-11 HYPOTHESIS TEST 164 Structure Learning Objectives Introduction Parametric and Non Parametric Tests: Definition and use T Test Z Test Chi Square Test F Test Summary Keywords Learning Activity Unit End Questions (Mcq And Descriptive) References LEARNING OBJECTIVES After studying this Unit, you will be able to:  Explain various parametric tests  Discuss about various non-parametric tests CU IDOL SELF LEARNING MATERIAL (SLM)

INTRODUCTION When you conduct a piece of quantitative research, you are inevitably attempting to answer a research question or hypothesis that you have set. One method of evaluating this research question is via a process called hypothesis testing, which is sometimes also referred to as significance testing. Hypothesis testing or significance testing is a method for testing a claim or hypothesis about a parameter in a population, using data measured in a sample. In this method, we test some hypothesis by determining the likelihood that a sample statistic could have been selected, if the hypothesis regarding the population parameter were true. A hypothesis is an educated guess about something in the world around you. It should be testable, either by experiment or observation. PARAMETRIC AND NON PARAMETRIC TESTS: DEFINITION AND USE Parametric tests assume underlying statistical distributions in the data. Therefore, several conditions of validity must be met so that the result of a parametric test is reliable. For example, Student’s t-test for two independent samples is reliable only if each sample follows a normal distribution and if sample variances are homogeneous. Nonparametric tests do not rely on any distribution. They can thus be applied even if parametric conditions of validity are not met. Parametric tests often have nonparametric equivalents. You will find different parametric tests with their equivalents when they exist in this grid. T Test The t test tells you how significant the differences between groups are; In other words it lets you know if those differences (measured in means) could have happened by chance. A very simple example: Let’s say you have a cold and you try a naturopathic remedy. Your cold lasts a couple of days. The next time you have a cold, you buy an over-the-counter pharmaceutical and the cold lasts a week. You survey your friends and they all tell you that their colds were of a shorter duration (an average of 3 days) when they took the homeopathic remedy. What you really want to know is, are these results repeatable? A t test can tell you by comparing the means of the two groups and letting you know the probability of those results happening by chance. Another example: Student’s T-tests can be used in real life to compare averages. For example, a drug 165 CU IDOL SELF LEARNING MATERIAL (SLM)

company may want to test a new cancer drug to find out if it improves life expectancy. In an experiment, there’s always a control group (a group who are given a placebo, or “sugar pill”). The control group may show an average life expectancy of +5 years, while the group taking the new drug might have a life expectancy of +6 years. It would seem that the drug might work. But it could be due to a fluke. To test this, researchers would use a Student’s t-test to find out if the results are repeatable for an entire population. The T Score The t score is a ratio between the difference between two groups and the difference within the groups. The larger the t score, the more difference there is between groups. The smaller the t score, the more similarity there is between groups. A t score of 3 means that the groups are three times as different from each other as they are within each other. When you run a t test, the bigger the t-value, the more likely it is that the results are repeatable.  A large t-score tells you that the groups are different.  A small t-score tells you that the groups are similar. T-Values and P-values How big is “big enough”? Every t-value has a p-value to go with it. A p-value is the probability that the results from your sample data occurred by chance. P-values are from 0% to 100%. They are usually written as a decimal. For example, a p value of 5% is 0.05. Low p-values are good; They indicate your data did not occur by chance. For example, a p-value of .01 means there is only a 1% probability that the results from an experiment happened by chance. In most cases, a p-value of 0.05 (5%) is accepted to mean the data is valid. Calculating the Statistic / Test Types There are three main types of t-test:  A n Independent Samples t-test compares the means for two groups.  A Paired sample t-test compares means from the same group at different times (say, one year apart).  A 166 CU IDOL SELF LEARNING MATERIAL (SLM)

One sample t-test tests the mean of a single group against a known mean. You probably don’t want to calculate the test by hand (the math can get very messy, but if you insist you can find the steps for an independent samples t test here. Use the following tools to calculate the t test:  H ow to do a T test in Excel.  T test in SPSS.  T distribution on the TI 89.  T distribution on the TI 83. What is a Paired T Test (Paired Samples T Test / Dependent Samples T Test)? A paired t test (also called a correlated pairs t-test, a paired samples t test or dependent samples t test) is where you run a t test on dependent samples. Dependent samples are essentially connected — they are tests on the same person or thing. For example:  K nee MRI costs at two different hospitals,  T wo tests on the same person before and after training,  T wo blood pressure measurements on the same person using different equipment. When to Choose a Paired T Test / Paired Samples T Test / Dependent Samples T Test Choose the paired t-test if you have two measurements on the same item, person or thing. You should also choose this test if you have two items that are being measured with a unique condition. For example, you might be measuring car safety performance in Vehicle Research and Testing and subject the cars to a series of crash tests. Although the manufacturers are different, you might be subjecting them to the same conditions. With a “regular” two sample t test, you’re comparing the means for two different samples. For 167 CU IDOL SELF LEARNING MATERIAL (SLM)

example, you might test two different groups of customer service associates on a business-related test or testing students from two universities on their English skills. If you take a random sample each group separately and they have different conditions, your samples are independent and you should run an independent samples t test (also called between-samples and unpaired-samples). The null hypothesis for the for the independent samples t-test is μ1 = μ2. In other words, it assumes the means are equal. With the paired t test, the null hypothesis is that the pairwise difference between the two tests is equal (H0: µd = 0). The difference between the two tests is very subtle; which one you choose is based on your data collection method. Benefits of T-Test and Hypothesis Testing T-test and hypothesis testing presents a lot of benefits, both statistically and in business. In statistics, this method is particularly important for post-testing analysis to validate data findings between two different groups and demonstrate the extent of the compared differences. For businesses, it estimates the potential that these differences are purely chance.  P ractical for business users: In many cases, a typical business user without statistical training can perform a simple t-test using the general formula.  M inimal data required: The t-test requires limited data for accurate testing; only the subject values regarding the variables from each individual group are needed.  A dapt marketing strategies: Create better marketing strategies based on the statistical difference between purchase quantities for two separate demographics.  C ost efficiency: Rather than performing expensive stress or quality testing, t-tests can accurately calculate the population variables from small test samples. Z Test A z-test is a statistical test used to determine whether two population means are different when the variances are known and the sample size is large. The test statistic is assumed to have a normal distribution, and nuisance parameters such as standard deviation should be known in order for an accurate z-test to be performed. A z-statistic, or z-score, is a number representing how many standard deviations above or below the mean population a score derived from a z-test is. 168 CU IDOL SELF LEARNING MATERIAL (SLM)

How Z-Tests Work Examples of tests that can be conducted as z-tests include a one-sample location test, a two-sample location test, a paired difference test, and a maximum likelihood estimate. Z-tests are closely related to t-tests, but t-tests are best performed when an experiment has a small sample size. Also, t-tests assume the standard deviation is unknown, while z-tests assume it is known. If the standard deviation of the population is unknown, the assumption of the sample variance equaling the population variance is made. Hypothesis Test The z-test is also a hypothesis test in which the z-statistic follows a normal distribution. The z-test is best used for greater-than-30 samples because, under the central limit theorem, as the number of samples gets larger, the samples are considered to be approximately normally distributed. When conducting a z-test, the null and alternative hypotheses, alpha and z-score should be stated. Next, the test statistic should be calculated, and the results and conclusion stated. One-Sample Z-Test Example Assume an investor wishes to test whether the average daily return of a stock is greater than 1%. A simple random sample of 50 returns is calculated and has an average of 2%. Assume the standard deviation of the returns is 2.5%. Therefore, the null hypothesis is when the average, or mean, is equal to 3%. Conversely, the alternative hypothesis is whether the mean return is greater or less than 3%. Assume an alpha of 0.05% is selected with a two-tailed test. Consequently, there is 0.025% of the samples in each tail, and the alpha has a critical value of 1.96 or -1.96. If the value of z is greater than 1.96 or less than -1.96, the null hypothesis is rejected. The value for z is calculated by subtracting the value of the average daily return selected for the test, or 1% in this case, from the observed average of the samples. Next, divide the resulting value by the standard deviation divided by the square root of the number of observed values. Therefore, the test statistic is calculated to be 2.83, or (0.02 - 0.01) / (0.025 / (50) ^ (1/2)). The investor rejects the null hypothesis since z is greater than 1.96 and concludes that the average daily return is greater than 1%. Chi Square Test The Chi-Square test is a statistical procedure used by researchers to examine the differences between categorical variables in the same population. For example, imagine that a research group is interested in whether or not education level and marital status are related for all people in the U.S. 169 CU IDOL SELF LEARNING MATERIAL (SLM)

After collecting a simple random sample of 500 U.S. citizens, and administering a survey to this sample, the researchers could first manually observe the frequency distribution of marital status and education category within their sample. The researchers could then perform a Chi-Square test to validate or provide additional context for these observed frequencies. Chi-Square calculation formula is as follows: When is the Chi-Square Test Used in Market Research? Market researchers use the Chi-Square test when they find themselves in one of the following situations:  T hey need to estimate how closely an observed distribution matches an expected distribution. This is referred to as a “goodness-of-fit” test.  T hey need to estimate whether two random variables are independent.  W hen to Use the Chi-Square Test on Survey Results  T he Chi-Square test is most useful when analyzing cross tabulations of survey response data. Because cross tabulations reveal the frequency and percentage of responses to questions by various segments or categories of respondents (gender, profession, education level, etc.), the Chi-Square test informs researchers about whether or not there is a statistically significant difference between how the various segments or categories answered a given question. Important things to note when considering using the Chi-Square test First, Chi-Square only tests whether two individual variables are independent in a binary, “yes” or 170 CU IDOL SELF LEARNING MATERIAL (SLM)