Assignment Code: BPCC-134/Asst/TMA/2021-22

Course Code: BPCC-134

Assignment Name: Statistical Methods and Psychological Research

Year: 2021-22

Verification Status: Verified by Professor

Total Marks: 70

Assignment One

Answer the following questions in about 500 words each (wherever applicable). Each question carries 20 marks. (2 x 20 = 40)

Q1. Explain the concept of sampling and discuss various sampling techniques.

Ans) The process of taking a sample from a population is known as sampling. Sampling can also be defined as the process of selecting a representative sample from a population. It may also be described as a procedure in which a proportion of the population is drawn, and it is a process that involves the selection of a sample. Because the population may be heterogeneous in character, with people of diverse genders, religions, ages, socioeconomic status, and so on, sampling must be done properly.

Sampling Techniques

Probability Sampling: Probability sampling mainly involves random selection of the sample from the population. Thus, each and every individual in the population has an equal chance of being selected for the sample. Technique used for such a selection is called randomisation. In probability sampling, every individual who is part of the population has an equal chance of being included in the sample. Sample is thus assumed to be representative of the population. Thus, if the population for a research is students in class 9th of a school, each and every student has equal chance of being selected for the research.

The various types of probability sampling are:

1. Participants are randomly picked from the population using procedures such as the lottery method in simple random sampling.

2. Systematic random sampling: In this technique, a random order list of persons in the population is formed, and a sample is chosen based on a random number, keeping the sampling fraction and interval size in mind.

3. Stratified random sampling: In stratified random sampling, the population is separated into homogeneous groups before a random sample is chosen.

4. Cluster sampling divides the population into groups, which are then randomly picked, and all of the individuals who fall into those clusters are taken.

5. Multistage random sampling: As the name implies, this method involves sampling at various levels.

Non-probability Sampling: There is no random selection of participants to be included in the sample in non-probability sampling. As a result, the sample may not be representative of the general public. For example, if a study is to be conducted on female survivors of domestic abuse, randomization cannot be employed, so the participants are chosen based on their availability and consent.

The various types of non-probability sampling are:

1. Convenient Sampling: In convenient sampling, an individual's inclusion or exclusion from the sample is determined by his or her availability.

2. Voluntary Sampling: Participants that agree to be a part of the study are included in the sample via voluntary sampling.

3. Sample Selection is carried out by an individual who has a thorough understanding of the sample in this sort of sampling.

4. Quota Sampling: This method selects a sample based on a predetermined quota. For example, the study's sample could consist of 100 junior managers and 50 senior managers from a corporation (for a total of 150 junior managers and 100 senior managers).

5. Snowball Sampling: In snowball sampling, a researcher approaches an individual who has qualities that match the sample's requirements, and then asks this individual to refer others who have similar features.

Q2. What is nonlinear correlation? Compute Spearman’s rho for the following data:

Ans) Correlation is said to be non-linear if the ratio of change is not constant. In other words, when all the points on the scatter diagram tend to lie near a smooth curve, the correlation is said to be non-linear (curvilinear).

Calculation:

R = CoVariance / (XRa St. Dev. x YRa St. Dev.)

Key:

XRa = Ranks of X Values; YRa = Ranks of Y Values

XRa - Mx = X rank minus mean of X ranks

YRa - My = Y rank minus mean of Y ranks

Sum Diffs = (XRa - Mx) x (YRa - My)

Result Details:

X Ranks:

Mean: 5.5

Standard Dev: 2.98

Y Ranks:

Mean: 5.5

Standard Dev: 2.92

Combined:

Covariance = 20 / 9 = 2.22

R = 2.22 / (2.98 x 2.92) = 0.255

rs = 0.25482, p (2-tailed) = 0.47738.

Assignment Two

Answer the following questions in about 100 words each (wherever applicable). Each question carries 5 marks. (6 x 5 = 30)

Q3. Discuss the methods of qualitative research.

Ans) The methods of qualitative research are:

A case study approach can be used to investigate a strange event or a person with an uncommon disorder or sickness, for example. It can also be used to research specific organisations. Because a case study is lengthy, it necessitates not just the researcher's time but also his or her undivided attention. A case study can be used to obtain a lot of information.

Ethnography is a method of research that focuses on a certain community. It's more of a close field observation that aims to understand a sociocultural phenomenon. This method mostly entails observing people in their naturalistic setting. In ethnography, observation is commonly used, yet it is also less regimented. The researcher takes an active involvement in the process, and participant observation is frequently used.

Grounded Theory is a qualitative method that focuses on 'discovering' and researching the relationship between empirical research and theory. As a result, data collecting is carried out with the goal of promoting the development of theory based on the data gathered.

A focus group is a type of qualitative research in which a group of people debate a certain question or issue. Focus groups can be structured or unstructured, and the nature of the group might be heterogeneous or homogeneous. It could include specialists discussing critical issues or citizens from a certain community/area discussing a specific issue.

Phenomenology: This method explains behavioural phenomena using conscious experience of occurrences rather than theories, computations, or assumptions from other disciplines. One of the research that was done in which patients were asked to characterise caring and noncaring nurses in hospitals helped to better understand the notion. Patients described those nurses as caring because they demonstrate their existential presence rather than just their bodily presence.

Content analysis can be used to investigate a variety of issues ranging from social to cultural, values and events, and so on, using text, news, ads, and other sources. It can also be used to analyse and extract useful information from a variety of texts and documents. It entails a systematic review of texts and documents, in which qualitative data is translated to quantitative data through coding, allowing for valid interpretations.

Discourse Analysis: A study that focuses on the use of written and spoken language between individuals is referred to as discourse analysis. As a result, it mostly entails examining individual interactions, texts, social practises, face-to-face interactions, photos, documents, and so on.

Q4. Describe interview as a method of data collection.

Ans) One of the most prevalent ways of data collection is the interview. Various data collection methods can be classified according to how direct they are. For example, one method of gathering data is to ask participants questions, while another is to use projective techniques such as the Rorschach inkblot series. An interview can be described as a direct way for getting useful information directly from participants. However, it's likely that some of the participants won't be able or ready to share specific details. In this instance, a direct procedure such as an interview will not be effective.

"A face-to-face interpersonal role setting in which one person, the interviewer, asks a person being interviewed, the respondent, questions meant to get answers important to the study subject," according to Kerlinger. The major features in this definition are that there are two main individuals participating in a face-to-face contact, the interviewer, and the interviewee. During this engagement, the interviewer will ask the interviewee a series of questions in order to elicit responses.

The interview schedule is one of the most important components of the interview. The interview schedule consists of questions that the interviewer must ask as well as specific rules for how the interviewer should conduct the interview. Preparing an interview schedule is a difficult task that necessitates a great deal of organisation and effort. When creating an interview schedule, make sure the sentences are detailed and unambiguous, and that there are no terms with two meanings or ambiguous words. Despite the fact that interview schedules are expensive and time intensive, the amount of information that can be collected with the use of an interview schedule is substantial.

Q5. Describe frequency polygon with the help of a diagram.

Ans) Frequency polygon is a line graph used to display frequency distributions. A frequency polygon can be created by drawing a straight line through the midpoints of the upper base of the histogram or by drawing a straight line through the midpoints of the upper base of the histogram.

The following are the steps of drawing a frequency polygon:

1. Step 1: The frequency polygon is based on frequency distribution, as we all know. Two further class intervals, one below and one above, are added before creating a frequency polygon in the case of frequency polygons.

2. Step 2: Midpoints are calculated for all of the class intervals.

3. Step 3: A frequency polygon, like any other graph, has an x and y axis. The midpoints will be depicted on the x axis, while the frequencies will be represented on the y axis.

4. Step 4: Based on the midpoints on the y axis, the appropriate frequencies of the class intervals are plotted.

5. Step 5: Finally, the points are connected to form a line.

Q6. Compute mean, median and mode for the following data

Ans)

Mean

The mean of a data set is commonly known as the average. You find the mean by taking the sum of all the data values and dividing that sum by the total number of data values. The formula for the mean of a population is µ = ∑/N

The formula for the mean of a sample is  = ∑/n

Both of these formulas use the same mathematical process: find the sum of the data values and divide by the total. For the data values entered above, the solution is: = 450/10 = 45

Median

The median of a data set is found by putting the data set in ascending numerical order and identifying the middle number. If there are an odd number of data values in the data set, the median is a single number. If there are an even number of data values in the data set, the median is the average of the two middle numbers. Sorting the data set for the values entered above we have: 22,34,43,43,43,45,45,45,65,65

Since there is an even number of data values in this data set, there are two middle numbers. With 10 data values, the middle numbers are the data values at positions 5 and 6. These are 43 and 45. The median is the average of these numbers. We have: 43+45/2

Therefore, the median is: 44

Mode

The mode is the number that appears most frequently. A data set may have multiple modes. If it has two modes, the data set is called bimodal. If all the data values have the same frequency, all the data values are modes. Here, the mode(s) is/are: 43,45.

Q7. Compute standard deviation for the following data.

Ans)

Count, N:                                                                            10

Sum, Σx:                                                                             281

Mean, μ:                                                                             28.1

Variance, σ^2:                                                                     102.69

σ =1/N=∑_(i=1)^N(x_i-µ)^2

σ2 = Σ(xi-μ)^2/N

= (43-28.1)^2 + (23-28.1)^2/10

= 1026.9/10

=102.69

σ = √102.69

σ = 10.133607452433

Standard Deviation, σ: 10.133607452433

Q8. Explain the concept and nature of normal probability distribution with help of suitable diagram.

Ans) The normal probability distribution, or simply normal distribution, is a continuous probability distribution for a variable. Gaussian/ Gauss or LaPlace – Gauss distribution are some names for it. The mean and variance are the two factors that determine the normal distribution. The normal distributions are used to model real-valued random variables with uncertain distributions. They are extensively employed in the natural and social sciences.

The normal probability distribution curve, or simply normal curve, is the graph representation of the normal distribution. A normal curve is a continuous frequency distribution curve with a bell shape and bilateral symmetry. Plotting the frequencies of scores of a continuous variable in a large sample yields such a curve. Because the y ordinates represent relative frequencies or probabilities rather than observed frequencies, the curve is known as a normal probability distribution curve. If the histogram of a continuous random variable's relative frequency takes the shape of a normal curve, it is said to be normally distributed.

In the domains of mental measurement and experimental psychology, it is critical to comprehend the properties of the Normal Probability Curve (NPC) frequency distribution.