## Q n #1

### Highlight the importance of Statistics in social research. Define the difference Between the Descriptive and inferential statistics with example.

Scientific research involves a systematic process that focuses on being objective and gathering a

multitude of information for analysis so that the researcher can come to a conclusion. This

process is used in all research and evaluation projects, regardless of the research method

(scientific method of inquiry, evaluation research, or action research). The process focuses on

testing hunches or ideas in a park and recreation setting through a systematic process. In this

process, the study is documented in such a way that another individual can conduct the same

study again. This is referred to as replicating the study. Any research done without documenting

the study so that others can review the process and results is not an investigation using the

scientific research process. The scientific research process is a multiple-step process where the

steps are interlinked with the other steps in the process. If changes are made in one step of the

process, the researcher must review all the other steps to ensure that the changes are reflected

throughout the process. Parks and recreation professionals are often involved in conducting

research or evaluation projects within the agency. These professionals need to understand the

eight steps of the research process as they apply to conducting a study. Table 2.4 lists the steps of

the research process and provides an example of each step for a sample research study.

Step 1: Identify the Problem

The first step in the process is to identify a problem or develop a research question. The research

problem may be something the agency identifies as a problem, some knowledge or information

that is needed by the agency, or the desire to identify a recreation trend nationally. In the

example in table 2.4, the problem that the agency has identified is childhood obesity, which is a

local problem and concern within the community. This serves as the focus of the study.

Step 2: Review the Literature

Now that the problem has been identified, the researcher must learn more about the topic under

investigation. To do this, the researcher must review the literature related to the research

problem. This step provides foundational knowledge about the problem area. The review of

literature also educates the researcher about what studies have been conducted in the past, how

these studies were conducted, and the conclusions in the problem area. In the obesity study, the

review of literature enables the programmer to discover horrifying statistics related to the long-

term effects of childhood obesity in terms of health issues, death rates, and projected medical

costs. In addition, the programmer finds several articles and information from the Centers for

Disease Control and Prevention that describe the benefits of walking 10,000 steps a day. The

information discovered during this step helps the programmer fully understand the magnitude of

the problem, recognize the future consequences of obesity, and identify a strategy to combat

obesity (i.e., walking).

Step 3: Clarify the Problem

Many times the initial problem identified in the first step of the process is too large or broad in

scope. In step 3 of the process, the researcher clarifies the problem and narrows the scope of the

study. This can only be done after the literature has been reviewed. The knowledge gained

SOCIAL STATISTICS (4689) END TERM ASSESSMENT 2019

through the review of literature guides the researcher in clarifying and narrowing the research

project. In the example, the programmer has identified childhood obesity as the problem and the

purpose of the study. This topic is very broad and could be studied based on genetics, family

environment, diet, exercise, self-confidence, leisure activities, or health issues. All of these areas

cannot be investigated in a single study; therefore, the problem and purpose of the study must be

more clearly defined. The programmer has decided that the purpose of the study is to determine

if walking 10,000 steps a day for three days a week will improve the individual’s health. This

purpose is more narrowly focused and researchable than the original problem.

Step 4: Clearly Define Terms and Concepts

Terms and concepts are words or phrases used in the purpose statement of the study or the

description of the study. These items need to be specifically defined as they apply to the study.

Terms or concepts often have different definitions depending on who is reading the study. To

minimize confusion about what the terms and phrases mean, the researcher must specifically

define them for the study. In the obesity study, the concept of “individual’s health” can be

defined in hundreds of ways, such as physical, mental, emotional, or spiritual health. For this

study, the individual’s health is defined as physical health. The concept of physical health may

also be defined and measured in many ways. In this case, the programmer decides to more

narrowly define “individual health” to refer to the areas of weight, percentage of body fat, and

cholesterol. By defining the terms or concepts more narrowly, the scope of the study is more

manageable for the programmer, making it easier to collect the necessary data for the study. This

also makes the concepts more understandable to the reader.

Step 5: Define the Population

Research projects can focus on a specific group of people, facilities, park development,

employee evaluations, programs, financial status, marketing efforts, or the integration of

technology into the operations. For example, if a researcher wants to examine a specific group of

people in the community, the study could examine a specific age group, males or females, people

living in a specific geographic area, or a specific ethnic group. Literally thousands of options are

available to the researcher to specifically identify the group to study. The research problem and

the purpose of the study assist the researcher in identifying the group to involve in the study. In

research terms, the group to involve in the study is always called the population. Defining the

population assists the researcher in several ways. First, it narrows the scope of the study from a

very large population to one that is manageable. Second, the population identifies the group that

the researcher’s efforts will be focused on within the study. This helps ensure that the researcher

stays on the right path during the study. Finally, by defining the population, the researcher

identifies the group that the results will apply to at the conclusion of the study. In the example in

table 2.4, the programmer has identified the population of the study as children ages 10 to 12

years. This narrower population makes the study more manageable in terms of time and

resources.

Step 6: Develop the Instrumentation Plan

The plan for the study is referred to as the instrumentation plan. The instrumentation plan serves

as the road map for the entire study, specifying who will participate in the study; how, when, and

where data will be collected; and the content of the program. This plan is composed of numerous

decisions and considerations that are addressed in chapter 8 of this text. In the obesity study, the

researcher has decided to have the children participate in a walking program for six months. The

group of participants is called the sample, which is a smaller group selected from the population

specified for the study. The study cannot possibly include every 10- to 12-year-old child in the

community, so a smaller group is used to represent the population. The researcher develops the

plan for the walking program, indicating what data will be collected, when and how the data will

be collected, who will collect the data, and how the data will be analyzed. The instrumentation

plan specifies all the steps that must be completed for the study. This ensures that the

programmer has carefully thought through all these decisions and that she provides a step-by-

step plan to be followed in the study.

Step 7: Collect Data

Once the instrumentation plan is completed, the actual study begins with the collection of data.

The collection of data is a critical step in providing the information needed to answer the

research question. Every study includes the collection of some type of data—whether it is from

the literature or from subjects—to answer the research question. Data can be collected in the

form of words on a survey, with a questionnaire, through observations, or from the literature. In

the obesity study, the programmers will be collecting data on the defined variables: weight,

percentage of body fat, cholesterol levels, and the number of days the person walked a total of

10,000 steps during the class.

The researcher collects these data at the first session and at the last session of the program. These

two sets of data are necessary to determine the effect of the walking program on weight, body

fat, and cholesterol level. Once the data are collected on the variables, the researcher is ready to

move to the final step of the process, which is the data analysis.

Step 8: Analyze the Data

All the time, effort, and resources dedicated to steps 1 through 7 of the research process

culminate in this final step. The researcher finally has data to analyze so that the research

question can be answered. In the instrumentation plan, the researcher specified how the data will

be analyzed. The researcher now analyzes the data according to the plan. The results of this

analysis are then reviewed and summarized in a manner directly related to the research

questions. In the obesity study, the researcher compares the measurements of weight, percentage

of body fat, and cholesterol that were taken at the first meeting of the subjects to the

measurements of the same variables at the final program session. These two sets of data will be

analyzed to determine if there was a difference between the first measurement and the second

measurement for each individual in the program. Then, the data will be analyzed to determine if

the differences are statistically significant. If the differences are statistically significant, the study

validates the theory that was the focus of the study. The results of the study also provide valuable

information about one strategy to combat childhood obesity in the community.

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As you have probably concluded, conducting studies using the eight steps of the scientific

research process requires you to dedicate time and effort to the planning process. You cannot

conduct a study using the scientific research process when time is limited or the study is done at

the last minute. Researchers who do this conduct studies that result in either false conclusions or

conclusions that are not of any value to the organization.

4689 AIOU end term assessments 2019

## Q No # 2

### WHAT IS SAMPLING ? EXPLAIN THE DIFFERENCE TYPE OF PROBABILITY SAMPLING TECHNIQUES ?

SAMPLING:-

Sampling method refers to the way that observations are selected from a population to be in

the sample for a sample survey.

The main types of probability sampling methods are simple random sampling, stratified

sampling, cluster sampling, multistage sampling, and systematic random sampling. The key

benefit of probability sampling methods is that they guarantee that the sample chosen is

representative of the population. This ensures that the statistical conclusions will be valid.

Simple random sampling. Simple random sampling refers to any sampling method that

has the following properties.

The population consists of N objects.

The sample consists of n objects.

If all possible samples of n objects are equally likely to occur, the sampling

method is called simple random sampling.

There are many ways to obtain a simple random sample. One way would be the lottery

method. Each of the N population members is assigned a unique number. The numbers

are placed in a bowl and thoroughly mixed. Then, a blind-folded researcher selects n

numbers. Population members having the selected numbers are included in the sample.

Stratified sampling. With stratified sampling, the population is divided into groups,

based on some characteristic. Then, within each group, a probability sample (often a

simple random sample) is selected. In stratified sampling, the groups are called strata.

As a example, suppose we conduct a national survey. We might divide the population

into groups or strata, based on geography – north, east, south, and west. Then, within each

stratum, we might randomly select survey respondents.

Cluster sampling. With cluster sampling, every member of the population is assigned to

one, and only one, group. Each group is called a cluster. A sample of clusters is chosen,

using a probability method (often simple random sampling). Only individuals within

sampled clusters are surveyed.

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Note the difference between cluster sampling and stratified sampling. With stratified

sampling, the sample includes elements from each stratum. With cluster sampling, in

contrast, the sample includes elements only from sampled clusters.

Multistage sampling. With multistage sampling, we select a sample by using

combinations of different sampling methods.

For example, in Stage 1, we might use cluster sampling to choose clusters from a

population. Then, in Stage 2, we might use simple random sampling to select a subset of

elements from each chosen cluster for the final sample.

Systematic random sampling. With systematic random sampling, we create a list of

every member of the population. From the list, we randomly select the first sample

element from the first k elements on the population list. Thereafter, we select

every kth element on the list.

This method is different from simple random sampling since every possible sample

of n elements is not equally likely.

## Q NO # 3

## Q NO # 4

### WHAT ARE THE DIFFERENT MEASURES OF VARIABILITY ? BRIEFLY DISCUSS THE MOST COMMON MEASURES OF VARIABILITY?

The terms variability, spread, and dispersion are synonyms, and refer to how spread out a

distribution is. Just as in the section on central tendency where we discussed measures of the

center of a distribution of scores, in this chapter we will discuss measures of the variability of a

distribution. There are four frequently used measures of variability: the range, interquartile

range, variance, and standard deviation. In the next few paragraphs, we will look at each of these

four measures of variability in more detail. The range is the simplest measure of variability to

calculate, and one you have probably encountered many times in your life. The range is simply

the highest score minus the lowest score. Let’s take a few examples. What is the range of the

following group of numbers: 10, 2, 5, 6, 7, 3, 4? Well, the highest number is 10, and the lowest

number is 2, so 10 – 2 = 8. The range is 8. Let’s take another example. Here’s a dataset with 10

numbers: 99, 45, 23, 67, 45, 91, 82, 78, 62, 51. What is the range? The highest number is 99 and

the lowest number is 23, so 99 – 23 equals 76; the range is 76. Now consider the two quizzes

shown in Figure 1. On Quiz 1, the lowest score is 5 and the highest score is 9. Therefore, the

range is 4. The range on Quiz 2 was larger: the lowest score was 4 and the highest score was 10.

Therefore the range is 6.

The interquartile range (IQR) is the range of the middle 50% of the scores in a distribution. It is

computed as follows:

IQR = 75th percentile – 25th percentile

For Quiz 1, the 75th percentile is 8 and the 25th percentile is 6. The interquartile range is

therefore 2. For Quiz 2, which has greater spread, the 75th percentile is 9, the 25th percentile is

5, and the interquartile range is 4. Recall that in the discussion of box plots, the 75th percentile

was called the upper hinge and the 25th percentile was called the lower hinge. Using this

terminology, the interquartile range is referred to as the H-spread.

A related measure of variability is called the semi-interquartile range. The semi-interquartile

range is defined simply as the interquartile range divided by 2. If a distribution is symmetric, the

median plus or minus the semi-interquartile range contains half the scores in the distribution.

Variability can also be defined in terms of how close the scores in the distribution are to the

middle of the distribution. Using the mean as the measure of the middle of the distribution, the

variance is defined as the average squared difference of the scores from the mean. The data from

Quiz 1 are shown in Table 1. The mean score is 7.0. Therefore, the column “Deviation from

Mean” contains the score minus 7. The column “Squared Deviation” is simply the previous

column squared.

The standard deviation is simply the square root of the variance. This makes the standard

deviations of the two quiz distributions 1.225 and 2.588. The standard deviation is an especially

useful measure of variability when the distribution is normal or approximately normal (see

Chapter on Normal Distributions) because the proportion of the distribution within a given

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number of standard deviations from the mean can be calculated. For example, 68% of the

distribution is within one standard deviation of the mean and approximately 95% of the

distribution is within two standard deviations of the mean. Therefore, if you had a normal

distribution with a mean of 50 and a standard deviation of 10, then 68% of the distribution would

be between 50 – 10 = 40 and 50 +10 =60. Similarly, about 95% of the distribution would be

between 50 – 2 x 10 = 30 and 50 + 2 x 10 = 70. The symbol for the population standard deviation

is σ; the symbol for an estimate computed in a sample is s. Figure 2 shows two normal

distributions. The red distribution has a mean of 40 and a standard deviation of 5; the blue

distribution has a mean of 60 and a standard deviation of 10. For the red distribution, 68% of the

distribution is between 35 and 45; for the blue distribution, 68% is between 50 and 70.

4689 AIOU end term assessments 2019