This document provides an overview of key concepts in statistics for management including data collection methods, primary and secondary data, sampling techniques, measures of central tendency, measures of dispersion, probability theory, probability distributions, the normal distribution, and hypothesis testing. It defines primary and secondary data collection methods. It also describes probability sampling techniques like simple random sampling, stratified sampling, and cluster sampling as well as non-probability techniques. Key concepts around measures of central tendency like the mean, median and mode are explained. The document also covers variance, standard deviation, and the normal distribution. It concludes with defining the null and alternative hypotheses.

1. Statistics for management

2. Data Collection Method
It is crucial to understand how the data should be collected in order to make
it reliable
Primary
• It is the data which has been freshly collected and for the first time i.e. the
data is original in nature.
Merits
• The reliability and credibility is high.
• The researcher can control the quality of data
Demerits
• It is time consuming method.
• The cost of collecting data is high.

3. Primary Data Collection Methods
• Interview
Interview is conducted which involves one to one questions and
interrogation
• Observation
Participant
Non Participant
Disguised
• Survey/Questionnaire

4. Secondary data
• This is the data which has been previously acquired by some other
researcher and then published. Thus, it is not an original data.
Merits
• It is easier to collect secondary data.
• • It is quick and consumes less time in collection.
• Sometimes the data can accurate entirely, thus it provides answer to all the
research questions.
Demerits
• The definitions used in the research must be carefully read as it must
reflect that the data was carried for another purpose. Terms may have
entirely different meanings which may not be relevance for research.

5. Factors Affecting Choice of Data Collection
Method
• The method must gather all information required. The choosen
method must be as per the resources available and budget.
• The time constraint should be also considered.
• The researchers must check whether respondents are available and
what is the geographical spread of the sample.
Sources of Secondary data
• Internal Sources of Data: Storage device, financial data
• External Sources of Data: Government data, consultancy,literatures

6. A Classification of Survey Methods
Traditional
Telephone
Computer-Assisted
Telephone
Interviewing
Mail
Interview
Mail
Panel
In-Home Mall
Intercept
Computer-Assisted
Personal
Interviewing
E-mail Internet
Survey
Methods
Telephone Personal Mail Electronic

7. Questionnaire Definition
• A questionnaire is a formalized set of questions
for obtaining information from respondents.

8. Questionnaire Objectives
• It must translate the information needed into a
set of specific questions that the respondents can
and will answer.
• A questionnaire must uplift, motivate, and
encourage the respondent to become involved in
the interview, to cooperate, and to complete the
interview.
• A questionnaire should minimize response error.

9. Specify the Information Needed
Design the Question to Overcome the Respondent’s Inability and Unwillingness to
Answer
Determine the Content of Individual Questions
Decide the Question Structure
Determine the Question Wording
Arrange the Questions in Proper Order
Reproduce the Questionnaire
Specify the Type of Interviewing Method
Identify the Form and Layout
Eliminate Bugs by Pre-testing
Questionnaire Design Process

10. Choosing Question Structure –
Unstructured Questions
• Unstructured questions are open-ended
questions that respondents answer in their own
words.
What is your occupation?
Who is your favorite actor?
What do you think about people who shop at
high-end department stores?

11. Choosing Question Structure –
Structured Questions
• Structured questions specify the set of
response alternatives and the response format.
A structured question may be multiple-choice,
dichotomous, or a scale.

12. Choosing Question Structure –
Multiple-Choice Questions
• In multiple-choice questions, the researcher provides a
choice of answers and respondents are asked to select one
or more of the alternatives given.
Do you intend to buy a new car within the next six
months?
____ Definitely will not buy
____ Probably will not buy
____ Undecided
____ Probably will buy
____ Definitely will buy
____ Other (please specify)

13. Choosing Question Structure –
Dichotomous Questions
• A dichotomous question has only two response
alternatives: yes or no, agree or disagree, and so on.
• Often, the two alternatives of interest are
supplemented by a neutral alternative, such as “no
opinion,” “don't know,” “both,” or “none.”
Do you intend to buy a new car within the next six
months?
_____ Yes
_____ No
_____ Don't know

14. Choosing Question Structure – Scales
• Scales were discussed in detail in Chapters 8 and 9:
Do you intend to buy a new car within the next six months?
DefinitelyProbably Undecided Probably Definitely
will not buy will not buy will buy will buy
1 2 3 4 5

15. Choosing Question Wording –
Define the Issue
• Define the issue in terms of who, what, when, where, why, and way (the six
Ws). Who, what, when, and where are particularly important.
Which brand of shampoo do you use?
(Incorrect)
Which brand or brands of shampoo have you
personally used at home during the last month?
In case of more than one brand, please
list all the brands that apply. (Correct)

16. Determining the Order of Questions
Opening Questions
• The opening questions should be interesting, simple, and
non-threatening.
Type of Information
• As a general guideline, basic information should be
obtained first, followed by classification, and, finally,
identification information.
Difficult Questions
• Difficult questions or questions which are sensitive,
embarrassing, complex, or dull, should be placed late in the
sequence.

17. Determining the Order of Questions
Effect on Subsequent Questions
• General questions should precede the specific
questions (funnel approach).
Q1: “What considerations are important to you in
selecting a department store?”
Q2: “In selecting a department store, how important
is convenience of location?”
(Correct)

18. Determining the Order of
Questions
Logical Order
The following guidelines should be followed for
branching questions:
• The question being branched (the one to which the
respondent is being directed) should be placed as close
as possible to the question causing the branching.
• The branching questions should be ordered so that the
respondents cannot anticipate what additional
information will be required.

19. Form and Layout
• Divide a questionnaire into several parts.
• The questions in each part should be numbered,
particularly when branching questions are used.
• The questionnaires should preferably be precoded.
• The questionnaires themselves should be numbered
serially.

20. Sampling
• Sampling is a statistical tool which helps to know the characteristics of
the universe or population by examining only a small part of it. The
values obtained from the study of sample, such as the average and
variance are known as statistic.

21. Sample vs. Census
Conditions Favoring the Use of
Type of Study Sample Census
1. Budget Small Large
2. Time available Short Long
3. Population size Large Small
4. Variance in the characteristic Small Large
5. Cost of sampling errors Low High
6. Cost of nonsampling errors High Low
7. Nature of measurement Destructive Nondestructive
8. Attention to individual cases Yes No

22. The Sampling Design Process
Define the Target Population
Determine the Sampling Frame
Select Sampling Technique(s)
Determine the Sample Size
Execute the Sampling Process

23. Define the Target Population
The target population is the collection of elements or objects that possess the
information sought by the researcher and about which inferences are to be
made. The target population should be defined in terms of elements, sampling
units, extent, and time.
• An element is the object about which or from which the information is
desired, e.g., the respondent.
• A sampling unit is an element, or a unit containing the element, that is
available for selection at some stage of the sampling process.
• Extent refers to the geographical boundaries.
• Time is the time period under consideration.

24. Define the Target Population
Important qualitative factors in determining the sample size
• the importance of the decision
• the nature of the research
• the number of variables
• the nature of the analysis
• sample sizes used in similar studies
• incidence rates
• completion rates
• resource constraints

25. Classification of Sampling Techniques
Sampling Techniques
Nonprobability
Sampling Techniques
Probability
Sampling Techniques
Convenience
Sampling
Judgmental
Sampling
Quota
Sampling
Snowball
Sampling
Systematic
Sampling
Stratified
Sampling
Cluster
Sampling
Other Sampling
Techniques
Simple Random
Sampling

26. Choosing Nonprobability vs.
Probability Sampling
Conditions Favoring the Use of
Factors Nonprobability
sampling
Probability
sampling
Nature of research Exploratory Conclusive
Relative magnitude of sampling
and nonsampling errors
Nonsampling
errors are
larger
Sampling
errors are
larger
Variability in the population Homogeneous
(low)
Heterogeneous
(high)
Statistical considerations Unfavorable Favorable
Operational considerations Favorable Unfavorable

27. Technique Strengths Weaknesses
Nonprobability Sampling
Convenience sampling
Least expensive, least
time-consuming, most
convenient
Selection bias, sample not
representative, not recommended for
descriptive or causal research
Judgmental sampling Low cost, convenient,
not time-consuming
Does not allow generalization,
subjective
Quota sampling Sample can be controlled
for certain characteristics
Selection bias, no assurance of
representativeness
Snowball sampling Can estimate rare
characteristics
Time-consuming
Probability sampling
Simple random sampling
(SRS)
Easily understood,
results projectable
Difficult to construct sampling
frame, expensive, lower precision,
no assurance of representativeness.
Systematic sampling Can increase
representativeness,
easier to implement than
SRS, sampling frame not
necessary
Can decrease representativeness
Stratified sampling Include all important
subpopulations,
precision
Difficult to select relevant
stratification variables, not feasible to
stratify on many variables, expensive
Cluster sampling Easy to implement, cost
effective
Imprecise, difficult to compute and
interpret results
Strengths and Weaknesses of
Basic Sampling Techniques

28. Measure of Central tendency
• This depicts the middle point of any data distribution. The measures
of central tendency are also known as measures of location
• Mean
• Median
• Mode

29. Definition of the mean
• Given a sample of n data points, x1, x2, x3, … xn, the
formula for the mean or average is given below.
pts
data
number
the
pts
data
the
of
sum
the
n
x
x 



30. Find the mean
• My 5 test scores for Calculus I are 95, 83, 92, 81, 75. What is the
mean?
• ANSWER: sum up all the tests and divide by the total number of tests.
• Test mean = (95+83+92+81+75)/5 = 85.2

31. Find the median.
• Here are a bunch of 10 point quizzes from MAT117:
• 9, 6, 7, 10, 9, 4, 9, 2, 9, 10, 7, 7, 5, 6, 7
• As you can see there are 15 data points.
• Now arrange the data points in order from smallest to largest.
• 2, 4, 5, 6, 6, 7, 7, 7, 7, 9, 9, 9, 9, 10, 10
• Calculate the location of the median: (15+1)/2=8. The eighth piece of
data is the median. Thus the median is 7.
• By the way what is the mean???? It’s 7.13…

32. The mode
• The mode is the most frequent number in a collection of data.
• Example A: 3, 10, 8, 8, 7, 8, 10, 3, 3, 3
• The mode of the above example is 3, because 3 has a frequency of 4.
• Example B: 2, 5, 1, 5, 1, 2
• This example has no mode because 1, 2, and 5 have a frequency of 2.
• Example C: 5, 7, 9, 1, 7, 5, 0, 4
• This example has two modes 5 and 7. This is said to be bimodal.

33. Measure of Dispersion
• The second attribute of a data is to learn how far the data is spread,
i.e. its variability. It is possible that the mean of all the data set is
same, but they may vary in variability. Thus, it is significant to study
how the data is spread or dispersed
• Range: Difference between highest point and lowest point
• Variance
• Standard Deviation

34. Variance
• Each population is characterized by variance which is denoted by (read as sigma squared). The
formulae to calculate variance is derived by dividing the sum of squared distances between the
mean and each observation, finally dividing by the entire population

35. Standard Deviation
• The population standard deviation is the square root of average of
the squared distances of the observations from the mean. Thus, it is
the square root of variance

36. Probability Theory
• Theory of probability states that "If an experiment is performed
repeatedly under essentially homogeneous and similar conditions,
the result of what is commonly termed as an outcome may be unique
or certain indefinite but may be certainly one of the various
possibilities depending on the experiments."

37. Probability approaches
• Classical Approach
• This approach assumes that all possible outcomes of an experiment
are mutually exclusive and equally likely.
• When we draw a card at random from well shuffled, bridge ace has
the same chance of being drawn, i.e. I in 52 or 1/52, the probability of
drawing a red card is 26/52 = 1/2

38. Empirical approach
• All possible outcomes are known you can use Classical but how about
• Will this tree fall within next winter ?
• The likelihood that the tree will fall is much smaller than it will stand.
How much smaller? This is the type of question that requires
references to empirical data.
• The probability of an event is determined objectively by repetitive
empirical observations,

39. Axiomatic Approach
• a type of probability that has a set of axioms (rules) attached to it. For
example, you could have a rule that the probability must be greater
than 0%, that one event must happen, and that one event cannot
happen if another event happens. the entire theory is developed by
logic of deduction

40. Probability Distribution
• Probability distribution is related to frequency distribution ,how the
• outcomes of a said event are expected to vary, there are two types
1. Discrete Probability Distribution
2. Continuous Probability Distribution
• Discrete Probability Distribution
• Distributions where only limited number of values can be Listed
• Eg: Probability of a student getting selected in a class of three section
for the game ?

41. Continuous Probability Distribution
• This comprises of variables which can take any value, within a
specified range.
• All the possible outcomes cannot be listed because there are
numerous variable and outcomes within a range. e.g.
• Measuring the level of ppm in air quality index will vary near sea level
(Mumbai) and cities like Delhi. Thus, the variable can assume any
value here.

42. What is this Normal Distribution?

43. There is nothing to worry about understanding
the concept of normal distribution The bell curve
• Imagine an example (Fuel efficiency of a bike,)
• Collect data and plot the data points, Most probably according to the
theory behind the Normal distribution you shall get a Bell shaped
curve.
• Not clarified yet, Okay lets talk about frequency of some events man
made or natural ( Weight of students, rain fall ,temperature, financial
data ,sales etc)
• For these, datum close to the mean are frequent and the data away
from mean or less and less frequent and they are sometimes called as
outliers.

44. Characteristics
• We say the data is "normally distributed”
• The Normal Distribution has:
• mean = median = mode
• symmetry about the center
• 50% of values less than the mean
and 50% greater than the mean
• A bell curve / normal curve has predictable standard deviations that
follow the 68.26 95.44 99.74 rule .
• The area under the cure is always equal to 1

45. Cont...
• The mean (average) is always in the center of a bell curve or normal
curve.
• A bell curve / normal curve has only one mode, or peak. Mode here
means “peak”; a curve with one peak is unimodal; two peaks is
bimodal, and so on.
• A bell curve / normal curve is symmetric. Exactly half of data points
are to the left of the mean and exactly half are to the right of the mean.
• The two tails never touch the horizontal lines they extend indefinitely
so its –infinity to + infinity at the horizontal sides

46. • There are many different normal
distributions, with each one depending
on two parameters:
1.Population mean, μ(Mu) and
2.Population standard deviation, σ(Sigma).
• These two determine the shape of the
curve
• Can we look how the changes in Mu (L 2
R) and Sigma (Breadth) appears
• What you mean there's low S.D? can we
relay on the data?

48. Hypothesis Testing
Null Hypothesis (H0)
• A statement in which no difference or effect is expected. If the null
hypothesis is not rejected,no changes will be made.
Alternate/Alternative Hypothesis(Ha)
• A statement that some difference or effect is expected. Accepting the
alternative hypothesis will lead to changes in opinions or actions.

49. Types of Hypotheses
- Descriptive Hypotheses
- Relational Hypotheses

50. Descriptive Hypotheses
• Describes the existence, size, form or distribution of some variable.
- 60% of investors favors cash dividend.
- MBA institutes facing problems in placement

51. Relational Hypotheses
• Describes the relationship between two or more variables.
The greater the stress experienced in the job the lower the job-
satisfaction.( directional)
Women are better than men
There is a relationship between age and job-satisfaction. (non-
directional)

52. Relational Hypotheses
• Correlational Hypotheses
Only shows the correlation between two or more variables but no
claims are made that one causes the other.
• Explanatory Hypotheses.
Claims are made that one variable causes other to occur.

53. Importance of Hypotheses
• Guides the direction of study;
• Identifies the facts relevant for the study;
• Helps in the selection of Research Design;
• Helps in providing the framework in which the results have to be
given.

54. Characteristics of a Good Hypothesis
• Adequate for the purpose
i) Should address the original problem
ii) Clearly identifies the variables relevant in the study.
iii) Helps in knowing the research design
iv) Helps in organizing the results of the study.

55. Characteristics of a Good Hypothesis
• Testable
i) Uses acceptable techniques
ii) Simple requiring few conditions
iii) Explanation can be given from the given theoretical framework.

56. Characteristics of a Good Hypothesis
• Better than its rivals
i) Explains more facts than its rivals
ii) Greater variety or scope of facts

57. Steps for Hypothesis Testing
Draw Research Conclusion
Formulate H0 and H1
Select Appropriate Test
Choose Level of Significance
Determine Prob
Assoc with Test Stat
Determine Critical
Value of Test Stat
TSCR
Determine if TSCR
falls into (Non)
Rejection Region
Compare with Level
of Significance, 
Reject/Do not Reject H0
Calculate Test Statistic TSCAL

58. Type I Error
• Occurs if the null hypothesis is rejected when it is in fact true.
• The probability of type I error ( α ) is also called the level of
significance.
Type II Error
• Occurs if the null hypothesis is not rejected when it is in fact false.
• The probability of type II error is denoted by β .
• Unlike α, which is specified by the researcher, the magnitude of β
depends on the actual value of the population parameter
(proportion).
It is necessary to balance the two types of errors.
Choose Level of Significance

59. • Power of a Test
The power of a test is the probability of rejecting the null hypothesis
when it is false and should be rejected. Although is unknown, it is
related to .
• An extremely low value of (e.g., 0.001) will result in intolerably high
errors. So it is necessary to balance the two types of errors.

60. chi-square statistic
• The chi-square statistic is used to test the statistical significance of
the observed association in a cross-tabulation. It assists us in
determining whether a systematic association exists between the two
variables.

61. Correlation
• Chi-square test depict whether there is any relation between two
variables but it does not define what relation exist between
• Correlation means that between two series or group of data there
exist some casual connections." Correlation is an analysis of the co-
variation between two or more variables

62. Types of Correlation
• Positive Correlation
If one variable increases the other also increases and vice versa
• Negative Correlation
If one variable increases the other decreases and vice versa

63. Degrees of Correlation
• Perfect Positive Correlation When two variables change in the same
proportion in same direction. In this case,coefficient of correlation is
(r = + l).
• Perfect Negative Correlation When two variables change in the same
proportion in opposite directions. In this case, coefficient of
correlation is (r = -1).
• If there is no relation between two sets of variaAbsence of
Correlation bles, i.e. change in one has no effect on the change in
other variable, degree of correlation is zero (r = 0).

64. Regression
• It is often more important to find out what the relation actually is, in
order to estimate or predict one variable and the statistical technique
appropriate to such a case is called regression analysis
• Regression is the statistical tool which will help to estimate or predict
the unknown values of one variable from known values of another
variable
• Regression equation of y on x : y = a + bx + e

65. Assumptions of Regression Analysis
• Linearity The relationship between two variables must be linear.
• Normality of Error Distribution The error terms or possible value of
error terms should be normally distributed
• Independence of Error The errors must not be dependent on each
other and there should not be any pattern followed by the errors.
• Homoskedasticity The error terms should not change or vary with the
value of independent (predictor) variables. This property is called
homoskedasticity.

66. Types of Regression
• Simple Regression (One DV)
• Multiple Regression (Multiple DV)
Utility of Regression Analysis
• Determination of rule of change in variables.
• Helps in estimating the event like changes in value sales
or profit.
• Calculation of coefficient of correlation.

67. Probability Distributions
• Binomial Distribution or Bernoulli Distribution
• Poisson Distribution
• Normal Distribution

68. Binomial
• Expresses the probability of one set of dichotomous alternatives, known as
success and failure.
• It is computed by (q + p)^n
q = Failure
p = Success
n = Total number of experiments
Characteristics
• All the trials are independent of each other.
• The probability of success in any trial 'p' is constant for each trial. The
probability of failure, q = I— p is also constant.
• Thus p=0.5 and q =I-P

69. Cont..
• These conditions are satisfied if we toss a coin, say five times and
want to know the probability of two heads resulting from these five
tosses. It be HTHTT,THHTT, THTTH.. (n=5,x=2)

70. • Regardless of the values of n, the distribution is symmetrical, when P
= 0.5
• When P is greater than 0.5, the distribution is negatively skewed
asymmetrical distribution, with the peak occurring to the right of the
centre. Like if P = 0.9
• When P is less than 0.5, the distribution is positively skewed and
asymmetrical with the peak occurring to the left of the centre. For P =
0.1

71. Formula to remember
• Mean of BD
• Variance of Binomial Distribution

72. t-distribution
• A symmetrical bell shaped distribution that is contingent on sample
size ,has a mean of 0 and a standard deviation equal to 1.
• A univariate t-test is used for testing hypotheses involving some
observed mean against some specified value .
• When sample is greater than 30 the results from t-test and z-test are
almost same.So t-test is appropriate for small sample and S.D is
unknown
• The shape of the t-distribution is influenced by degrees of freedom
• The number of observation minus the number of constraints or
assumptions needed to calculate the statistical term.

73. T-Test /student’s t-test-Prof Gosset
• When size of the sample is less than 30, theory of sampling is called
as small sample. If size of sample is small, normality of distribution
cannot be applied. It is also called as one sample t-test
• t-test may be used to test the significance between the difference of
sample mean and population mean

74. Example
• The mean height of Indian adults ages 20 and older is about 66.5
inches (69.3 inches for males, 63.8 inches for females).
• H0: µHeight = 66.5 ("the mean height is equal to 66.5")
H1: µHeight ≠ 66.5 ("the mean height is not equal to 66.5")

75. Independent sample t-test/two sample
• The Independent Samples t Test compares the means of two
independent groups in order to determine whether there is statistical
evidence that the associated population means are significantly
different.
• The Independent Samples t Test can only compare the means for two
(and only two) groups. It cannot make comparisons among more than
two groups

76. Example
• In our sample dataset, students reported their typical time to run a
mile, and whether or not they were an athlete. Suppose we want to
know if the average time to run a mile is different for athletes versus
non-athletes
• The hypotheses for this example can be expressed as:
• H0: µnon-athlete - µathlete = 0 ("the difference of the means is equal to
zero")
• H1: µnon-athlete - µathlete ≠ 0 ("the difference of the means is not equal to
zero")

77. Non-paired t –test
• Two groups-two sample -independent

78. Paired /dependent sample t-test
• The Paired Samples t Test compares the means of two measurements
taken from the same individual, object, or related units
• These "paired" measurements can represent thing like:
oA measurement taken at two different times (e.g., pre-test and post-
test score with an intervention administered between the two time
points)
• The purpose of the test is to determine whether there is statistical
evidence that the mean difference between paired observations is
significantly different from zero. The Paired Samples t Test is a
parametric test

79. Applications
The Paired Samples t Test is commonly used to test the following:
• Statistical difference between two time points
• Statistical difference between two conditions
• Statistical difference between two measurements
• Statistical difference between a matched pair

80. Hypotheses
• The hypotheses can be expressed in two different ways that express
the same idea and are mathematically equivalent:
• H0: µ1 = µ2 ("the paired population means are equal")
H1: µ1 ≠ µ2 ("the paired population means are not equal")
• OR
• H0: µ1 - µ2 = 0 ("the difference between the paired population means
is equal to 0")
• H1: µ1 - µ2 ≠ 0 ("the difference between the paired population means
is not 0")

81. • Formula Where Sx
x¯diff = Sample mean of the differences
n = Sample size (i.e., number of observations)
sdiff= Sample standard deviation of the differences
sx¯ = Estimated standard error of the mean (s/sqrt(n))

82. Z-test-Professor Fisher
• In case of large sample, where sample size is greater than 30,we apply
Z-test which is based on normal distribution
• A technique used to test the hypothesis that proportions are
significantly different for two independent groups
• When a researcher wants to test the sample correlation against any
other value of r or if it is desired to test whether the two given sample
have come from same population or not, the Z-test is used.

83. Chi-Square Test
• The Chi-Square Test of Independence determines whether there is an
association between categorical variables (i.e., whether the variables
are independent or related)
• The Chi-Square Test of Independence is commonly used to test the
following:
• Statistical independence or association between two or more
categorical variables

84. Hypotheses
• The null hypothesis (H0) and alternative hypothesis (H1) of the Chi-
Square Test of Independence can be expressed in two different but
equivalent ways:
• H0: "[Variable 1] is independent of [Variable 2]"
H1: "[Variable 1] is not independent of [Variable 2]"
• OR
• H0: "[Variable 1] is not associated with [Variable 2]"
H1: "[Variable 1] is associated with [Variable 2]"

85. Example
• In the sample dataset, respondents were asked their gender and
whether or not they were a cigarette smoker. There were three
answer choices: Nonsmoker, Past smoker, and Current smoker.
Suppose we want to test for an association between smoking
behavior (nonsmoker, current smoker, or past smoker) and gender
(male or female) using a Chi-Square Test of Independence (we'll
use α = 0.05).