Statistical Analysis

SMALL & MICRO ENTREPRENEURS IN BANGLADESH

CATEGORY: VEGETABLE VENDORS

Course: Business Statistics

Submitted to:

Mohammad Jahangir Alam Chowdhury

Professor

Department of Finance

University of Dhaka

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January 7, 2016

Mohammad Jahangir Alam Chowdhury Professor Department of Finance

University of Dhaka

Subject: Letter of transmittal

Dear Sir,

With great pleasure I submit my report on “Statistical Analysis: Small & Micro Entrepreneurs in

Bangladesh(Category :Vegetable Vendors) assigned to us as a topic of the term paper which is

prepared as a partial requirement of the course named Business Statistics (F-503) of EMBA

program under Department of Finance, University of Dhaka. In preparing the report, sincere

efforts have been made to present the relevant information pertinent to this report and organize

them accordingly.

I hope my work will meet the level of your expectation and my sincere efforts reflected in this report will be blessed with your kind approval. If you have any further enquiry concerning any additional information I would be very pleased to clarify that.

Thanking You.

Yours sincerely,

Asifa Ishrat Noor

Acknowledgement

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On the completion of the term paper I thank the Almighty for bestowing me with His blessings and enabling me to complete the assigned task. I owe my profound gratitude to our honorable teacher Prof. Mohammad Jahangir Alam Chowdhury, Dept. of Finance, University of Dhaka for his guidance in completing this project to us. Surveying the vegetable vendors, learning the application of statistical software and writing this report-all have been a unique experience for me. It was one kind of research work. I have learnt a lot. It is my conviction that this learning experience will be very helpful in my career. Finally, yet importantly, I would like to express my heartfelt thanks to my beloved parents, for cooperation, kindness and blessings, family and friends for their support and wishes for the successful completion of the work.

Executive Summary

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For a developing country like Bangladesh, the economic growth is dependent on the funding & expansion of the small & micro enterprises to some extent. Vegetable vendors are an important part in this sector. This report provides application of both descriptive and inferential statistics in the context of data collected from survey on the vegetable vendors. The statistical procedures of descriptive statistics have been used to organize, summarize and describe pertinent data of our sample. Frequency distributions, measures of location and dispersion with graphs according to the level of data (nominal, ordinal, interval, and ratio) have been explored. Inferential statistics, by definition is the branch of statistics that generalizes the larger population that the sample represents. It has been used in this report to make predictions about the population from observations and analysis of the sample. Under this category, probability concepts, one sample tests hypothesis, different features of regression and correlation analysis etc. have been discussed.

ContentsAcknowledgement………………………………………………………………………………………………………2

Executive Summary……………………………………………………………………………………………………3

Chapter 1: Introduction……………………………………………………………………………………………….5

Chapter 2

Objective of the Study…………………………………………………………………………………………………5

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Methodology…………………………………………………………………………………………………………..…5

Limitations………………………………………………………………………………………………………………....5

Chapter 3: Descriptive Statistics

Frequency Distribution ……………………………………………………………………………………………...6

Histogram………………………………………………………………………………………………………………….7

% Cumulative Frequency Polygon & Frequency Polygon……………………………………………..8

Bar Chart…………………………………………………………………………………………………………………..9

Pie Chart……………………………………………………………………………………………………………………10

Chapter 4: Inferential Statistics

Contingency Table……………………………………………………………………………………………………12

Bayes’ Theorem………………………………………………………………………………………………..………13

One Sample Tests Hypothesis………………………..…………………………………………………..………14

Correlation Analysis…………………………………………………………………………………………………15

Multiple Regressions……………………………………………………………………………………..…………16

Evaluating Individual Regression Co-efficient & Dropping Insignificant Variable………..17

Confidence & Prediction Interval……………………………………………………………………..……….19

Correlation Matrix……………………………………………………………………………………………………20

Dummy Variable………………………………………………………………………………………………………21

Conclusion ………………………………………………………………………………………………………………21

Chapter 1: IntroductionThe development of small and micro enterprises in developing countries is contributing in decentralized job creation. There is no universal definition of micro enterprises, but there are some agreements regarding their general characteristics. These are: very small scale of operation, low level of technology, low access to finance and managerial capacity. Most microenterprise owners are primarily interested in earning a living to support themselves and their families. They only grow the business when something in their lives changes and they need to generate a larger income. The varieties of different services that micro enterprises provide in Bangladesh

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underline its integral role in the economy. These include amongst others: bicycle repair, baking, blacksmithing, brick making, carpentry, carving, computer services, dry cleaning, electronics, furniture making, knitting, motor repairs, photography, pottery, retailing, shoe making, tailoring, transport and welding. Vegetable vendors are one of the representatives of Small & Micro Enterprises in Bangladesh. This study can help to uncover many queries related to the origin, academic qualification, professional experience, type of business, sales and profit dynamics, level of financial inclusion, household status etc. Using this study, this area can be further explored in future with large sample size taking other cities in consideration for comparative analysis with the other Small & Micro Enterprises in Bangladesh.

Chapter 2

Objectives of the Study To provide a bridge between theoretical and practical knowledge.

To analyze the effect of different variables on the average monthly profit of the enterprise.

To develop a mathematical model for interpreting the critical variables.

Methodology Primary data has been used in this study. Survey has been conducted among 140 vegetable vendors in Dhaka. Data has been collected using questionnaires through face to face interview & data sharing with other persons. Majority of the questions are pre-coded to facilitate the analysis of data. Interviews were conducted using the questionnaire as a guide. Then statistical concepts have been explained in the context of this collected information. Both Microsoft Excel and Stata software have been used to analyze the survey data.

Limitations In spite of having the wholehearted effort, there were some limitations, which acted as a barrier to conduct the program and for doing an exploratory research work. Some of them are:

Insufficiencies of raw data as most of the owners were not willing to provide confidential data.

Some variables were time series based. That’s why we faced some autocorrelation problem in data set.

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Chapter 3: Descriptive StatisticsThis kind of statistics deals with the methods of organizing, summarizing and presenting data in an informative way.  Together with simple graphics analysis, they form the basis of virtually every quantitative analysis of data. It explores three major characteristics of a variable:

1. The distribution2. The central tendency3. The dispersion

The application of descriptive statistics to organize different aspects of our collected data is discussed below:

Frequency DistributionA frequency distribution is a grouping of data into mutually exclusive classes showing the number of observations in each.

The monthly profit of 140 vegetable vendors is organized into the following frequency distribution:

profit range Frequency

5000-14999 6615000-24999 63

25000-34999 835000-44999 245000-54999 1

It shows the monthly profit ranges from about 5000tk up to 54999 tk. The monthly profits are concentrated between 5000 tk and 24999 tk. The largest concentration or highest frequency is in the 5000 up to 14999 tk class. The midpoint of this class is 10000 tk. So it can be estimated that a typical monthly profit is 10000 tk.

Graphical Presentation of a frequency distribution

One of the most common ways to portray a frequency distribution is a histogram. It shows the classes on the horizontal axis and class frequencies on the vertical axis. A histogram showing the above frequency distribution is given below:

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5000-14999 15000-24999

25000-34999

35000-44999

45000-54999

010203040506070 66 63

82 1

Histogram of Monthly Profit

Profit Range

Num

ber

of V

eg. V

endo

rs

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The histogram appears to show highly skewed distribution. As it is nonsymmetrical, the median and mode of this distribution are more representative than the arithmetic mean.

We can compute these measures of location using Microsoft Excel Software. The purpose of these measures of location is to pinpoint the center of a set of values.

The arithmetic mean = 14882.14286 tk

Median = 15000 tk

Mode = 20000 tk

A measure of dispersion describes the variation or spread of the data. Software can be used to compute these measures as well.

Range = largest value-smallest value= 45000-5000 =40000 tk

Standard deviation= 6746.598 tk

Skewness= 1.064135

This large value of standard deviation indicates that the observations are widely scattered around the mean. So the mean is not a reliable measure of location in this case.

% Cumulative Frequency PolygonIt shows the upper limit of each class along the X axis and the % of the corresponding cumulative frequencies along the Y axis.

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14999 24999 34999 44999 549990.00%5.00%

10.00%15.00%20.00%25.00%30.00%35.00%40.00%45.00%50.00% 47.14% 45.00%

5.71%1.43% 0.71%

% Cumulative Frequency for Monthly Profit

Profit

Perc

ent o

f Veg

etab

le v

endo

rs

From this chart, it can be easily estimated that the monthly profit of 25% vendors is about 30000 tk.

Frequency PolygonHere frequency polygon is used to compare the monthly profit of the vegetable vendors who own van and who are hawkers. In our sample we have 62 vegetable vendors who have van and 10 hawkers. As the difference between the total numbers of frequencies is quite large, the frequencies have been converted to relative frequencies so that plotting the two distributions allows a clearer comparison.

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2000 8000 14000 20000 26000 32000 380000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0

0.2581

0.3065

0.338700000000001

0.0806000000000001 0.0161

00

0.600000000000001

0.4

0

Count of van Count of hawker

Midpoint

Rel

ativ

e Fr

eque

ncy

From this chart, it can be estimated that 60% vegetable vendors who are hawkers have monthly profit of 8000 tk.It seems van owners enjoy more profit per month than the vegetable hawkers.

Bar ChartWe had information of the home districts of the 140 vegetable vendors. As this is nominal level of measurement, bar chart has been used to get a clear picture of the administrative divisions they belong.

Chittagong

Khulna

Dhaka

Rajshahi

Rangpur

Barisal

Sylhet

Mymensingh

0 5 10 15 20 25 30 35 40 45 50

31

3

43

3

1

16

3

40

No. of veg. vendors

Adm

inis

rtat

ive

divi

sion

s

10

This chart shows that 114 out of 140 vegetable vendors in our sample hail from Dhaka, Mymensingh and Chittagong. Only 1veg. vendor is from Rangpur.

Bar chart has been used to estimate the literacy rate of female family members of the vegetable vendors. By literacy, we have considered the ability to read and write, not the years completed in school. It is interesting to observe that the rate of literacy is the highest in younger generation (6-15 age group).

6 up to 15 16 up to 25 26 up to 35 36 up to 4505

101520253035404550

Literacy of female family members

Age group

Freq

uenc

y

Pie ChartThe quality of house is a good indicator of the overall standard of a person’s lifestyle and economic condition. A pie chart has been used to understand this aspect of the vegetable vendors in our sample.

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5%1%

28%

55%

10%

2%

Quality of sidewalls of the main house

BambooWoodEarthen WallTinBrickMixed

This pie chart shows that 55% vegetable vendors have sidewalls of the main house made by tin. The second highest group has live in house of earthen wall.

Pie chart has also been used to show the % of vegetable vendors who have bank account for themselves.

15%

85%

yes no

Interestingly, no vegetable vendor in our sample of 140 respondents has a bank account for business. While talking on this issue, they showed disinterest, in some cases aversion to banking service. None of them are interested about taking any loan from bank even if they were given freedom. When needed, they prefer to borrow money from family, friends or financially privileged acquaintances as they get money from these sources without interest.

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Chapter 4: Inferential StatisticsInferential statistics is the method used to determine something about a population on the basis of a sample. We use inferential statistics to try to infer from the sample data about the population-to make judgments of the probability that an observed difference between groups is a dependable one or one that might have happened by chance in this study. Thus, it is used to reach conclusions that extend beyond the immediate data.

Following is the application of different examples of inferential statistics in the context of our collected data:

Contingency TableA contingency table is a cross tabulation that simultaneously summarizes two variables of interest and their relationship.

Table 4-1: Contingency table showing the number of vegetable vendors whose home district is in Mymensingh or Chittagong division and whether their families live in or outside Dhaka.

Family lives in DhakaEvent,Ai

MymensinghB1

ChittagongB2

Total

Yes,A1 20 13 33No,A2 20 18 38Total 40 31 71

We can determine the probability of randomly selecting a vegetable vendor whose family lives in Dhaka and has home district belonging to Chittagong division from this contingency table using the rules of addition and multiplication.Here two events occur at the same time-the vendor is from Chittagong and has family living in Dhaka.The probability that event A1 will happen is,

P(A1 ) =3371

The conditional probability that event B2 will happen is,

P(B2|A1) =1333

Using the general rule of multiplication,

P(A1 and B2) = P(A1 ) P(B2|A1)= 3371 .

1333 = 0.183

So, the probability of selecting a vegetable vendor whose family lives in Dhaka and has home district belonging to Chittagong division is 0.183We use the general rule of addition to find the probability of selecting a vegetable vendor whose family lives in Dhaka or has home district belonging to Chittagong division.The probability that event B2 will happen is,

P(B2 ) =3171

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The joint probability that both event A1 and B2 will happen is,

P(A1 and B2) =1371

P(A1 or B2) = P(A1 ) + P(B2)- P(A1 and B2) = 3371+

3171 -

1371 = 0.718

So, the probability of selecting a vegetable vendor whose family lives in Dhaka or has home district belonging to Chittagong division is 0.718

Bayes’ TheoremBy using Bayes’ Theorem, we can determine the probability of a vegetable vendor’s family living in Dhaka given his/her home district is in Chittagong division.

A1 and A 2 are 2 mutually exclusive and collectively exhaustive events.

The prior probabilities are:

P(A1 ) =3371 , The probability that family lives in Dhaka

P(A2 ) =3871 , The probability that family lives outside Dhaka

The conditional probabilities are:

P(B2|A1) =1333 , The probability that the veg. vendor whose family lives in Dhaka is from

Chittagong division.

P(B2|A2) =1838 , The probability that the veg. vendor whose family lives in Dhaka is from

Chittagong division.Using Bayes’ theorem,

P(A1|B2) =P( A 1) P(B 2∨A 1)

P ( A 1 ) P ( B 2|A 1 )+P (A 2) P(B 2∨A 2) =

1331

It means if a vegetable vendor is selected at random from the above sample of 71 people, the

probability that his/her family lives in Dhaka is 3371 or 0.465.If the person’s home district is under

Chittagong division, the probability that his/her family actually lives in Dhaka becomes 1331 or

0.419The conditional probability table showing the data is given below:

Table 4-2:The conditional probability table

Family in DhakaEvent,Ai

Prior Probability,P(Ai)

Conditional Probability,P(B2|Ai)

Joint Probability, P(Ai and B2)

Posterior Probability, P(Ai |B2)

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Yes,A1 3371

1333

1371

1331

No,A2 3871

1838

1871

1831

Total 3171

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One-Sample Tests of HypothesisUsing the software stata, first we draw a histogram of monthly profit.

Looking from this graph, it seems the mean of the data is somewhere near 15000.We can test the null hypothesis that the population mean is 15000.The alternate hypothesis is ‘The mean is not 15000’.These two hypotheses are written:

H0 : µ = 15000

H1 : µ ≠ 15000

We get the following output from Stata:

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It can be seen that my test statistic = -0.2067

My degrees of freedom =139

So this t statistic under the null hypothesis follows the t distribution with 139 degrees of freedom.

Since p value (0.8365) ¿ confidence interval (0.05), we have failed to disprove H0.

We conclude that we do not have evidence in our dataset to disprove the null hypothesis.

Correlation AnalysisCorrelation analysis is the study of the relationship between variables. The chart that is used to show the relationship between two variables graphically is called a scatter diagram.

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This scatter diagram shows that there appears to be a positive relationship between monthly profit and yesterday’s total sales. The strength and direction of this relationship is measured by determining the coefficient of correlation (r).

Using Microsoft Excel in this case, we get r = 0.436

As it is positive, there is a direct relationship between monthly profit and the number of yesterday’s total sales. The value of 0.436 is fairly close to 0.5, so the association is moderate.

The coefficient of determination= r2 = (0.436)2 = 0.190096

It means 19% of the variation in monthly profit is accounted for by the variation in the number of yesterday’s total sales.

Multiple Regression

The multiple regression calculations can be performed using software systems. In this report, Stata 9.2 has been used. A screenshot of a portion of the output is given below:

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From this ANOVA table, we can see the number of observations, n= 140.The total number of degrees of freedom= n-1= 140-1 = 139The dependent variable is monthly profit.The number of degrees of freedom in the regression row = total number of independent variables, k =3 The number of degrees of freedom in the error row = n-(k+1) =140-(3+1)= 136Total variation=SS total= 6.3268× 109

Error variation= SSE= 4.8865× 109

Regression variation= SSR= 1.4403×109

The estimated multiple regression equation is Y/= 10512.22+3.326X1-2.787X2+0.021X3

Here X 1 = yesterday’s total sales X 2 = total daily expenseX 3 = working capital required for running the businessThe intercept value is 10512.22.This is the point where the regression equation crosses the Y axis.The regression co-efficients for yesterday’s total sales and working capital required for running the business show direct relationship with monthly profit. Specifically, for each additional 1 tk sale, all else held constant, the monthly profit is expected to increase 3.326 tk. Similarly, for each additional 1tk working capital, all else held constant, the profit increases 0.021 tk per month.

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The regression co-efficient for the total daily expense is negative. As the expense increases, the profit decreases.For 1 tk the daily expense increases, all else held constant, the monthly profit decreases 2.787 tk.The estimated monthly profit in a hypothetical situation where sales in a day is 4000,total daily expense is 2500 tk, and working capital is 4500 can be solved by using the equation:Y= 10512.22+3.326×4000-2.787×2500+0.021×4500 =16943.22 tkThe co-efficient of multiple determination, R2= 0.2277It means a total of 22.77% of the variation in monthly profit is explained by the 3 independent variables.The multiple standard error of estimate, sy.123 = Root MSE =5994.2It means it is the typical error we make when we use this equation to predict the monthly profit. The units are the same as the dependent variable (in taka).If the errors are normally distributed, about 68% of the residuals should be less than ±5994.2 and about 95% should be less than ±2(5994.2) or ±11988.4

Evaluating Individual Regression Coefficients and Dropping Insignificant VariableUsing t test critical value calculator, we get the critical value for t for a two- tailed test with 136 degrees of freedom and 0.05 significance level is 1.9776.So the independent variable will not be considered a significant predictor of monthly profit if the value of t for each independent variable is 1.9776¿t¿-1.9776.

From the ANOVA table, we can see the computed t ratio for yesterday’s total sales = 3.08

The computed t ratio is for daily total expense = -2.44

The computed t ratio is for working capital required for business = 0.13

So the working capital required for business is not a significant predictor of average monthly profit. It can be dropped from the analysis. Deleting this variable, we rerun the regression equation and find the following output:

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The new regression equation:

Y/ =10554.99+3.377X1 -2.824X2

Here X 1 = yesterday’s total sales X 2 = total daily expenseP-value Interpretation:

As we can see, the p-value of total daily expense is 0.011.It means the probability of a t value less than -2.56 or greater than 2.56,with 137 degrees of freedom is 0.011

Confidence and Prediction IntervalIf we have to determine confidence interval for all vegetable vendors whose total daily sales=4000 tk and total daily expense is 1200 tk and for Md Harun ur Rashid, a vegetable vendor from New Baily Road with similar condition, we have to perform following calculations:

y= 10554.99 +(3.377×4000)-(2.824×1200) =20674.19 tk

Using Microsoft Excel software, we get t statistics =1.977431

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Standard error= 5972.622

√n=√140

So, confidence interval=20674.19±(1.977431×5972.622

√ 140 ) =20674.19±998.165

Thus the 95% confidence interval for all vegetable vendors whose total daily sales is 4000 tk and total daily expense is 1200 tk is from 19676.03 up to 21672.36

And prediction interval=20674.19±(1.977431×5972.622) = 20674.19±11810.448

Thus the prediction interval for Md Harun ur Rashid is from 8863.74 up to 32484.64

Correlation MatrixCorrelation matrix is a matrix showing the coefficients of correlation between all pairs of variables.It can also be used to check for multicollinearity or the correlation among the independent variables. Correlations among the independent variables between -0.7 and 0.7 do not cause difficulties. Following output is derived by using Microsoft Excel for correlation analysis:

It can be observed that the correlation between yesterday’s total sales and working capital required is the strongest (0.687316 or 0.7). So the earlier decision to drop working capital required for business variable and recomputed the regression equation is justified.

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Dummy VariableDummy variable is a qualitative variable in which there are only two possible outcomes.

If we want to determine the significance of including such variable in regression analysis,first we run the regression analysis with it.

Using t test critical value calculator, we get the critical value for t for a two- tailed test with 135 degrees of freedom and 0.05 significance level is 1.9776.So the independent variable will not be considered a significant predictor of monthly profit if the value of t for each independent variable is 1.9776¿t¿-1.9776.

From the ANOVA table, we can see the computed t ratio is for ‘do you have a house of your own in the village’= 1.43

So this newly added independent variable is not a significant predictor of average monthly profit. It should be dropped from the analysis.

Chapter 5: ConclusionIn this report, it is evident that descriptive statistics can only be used to describe the group that is being studied. The results cannot be generalized to any larger group. On the other hand, inferential statistics does start with a sample and then generalizes to a population. This information about a population is not stated as a number. Instead these parameters are expressed

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as a range of potential numbers, along with a degree of confidence. In order to do this; however, it is imperative that the sample is representative of the group to which it is being generalized. To address this issue of generalization, we have tests of significance which can tell us the probability that the results of our analysis on the sample are representative of the population that the sample represents. In other words, these tests of significance tell us the probability that the results of the analysis could have occurred by chance when there is no relationship at all between the variables we studied in the population. In the light of this knowledge, it can be said that the issues discussed in Chapter 3 like average monthly profit, distribution of vendors according to administrative divisions, literacy of female family members, having bank account for themselves etc. show the picture of our sample only. It does not generalize the situation of vegetable vendors of Bangladesh. In contrast, Issues discussed in Chapter 4 like variables on which monthly profit depends can be used for generalization.

ReferenceLind DA,Marchal WG,Wathen SA,2005,Statistical Techniques in Business & Economics,12th

edition,McGraw Hill Irwin, New York.

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