Assignment Code: BPCC-104/Asst /TMA /July 2022-January 2023

Course Code: BPCC-104

Assignment Name: Statistical Methods for Psychological Research- I

Year: 2022-2023

Verification Status: Verified by Professor

Assignment One

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

1. Explain the role of statistics in research.

Ans) The field of statistics is quite broad in scope and application. Although one of its main uses is in research, it also finds use in areas such as policy making, management, education, marketing, agriculture, and medicine. As a result, the majority of our discussion in this regard will centre on psychological research. However, before we discuss the significance of statistics in psychological research, we will first make an effort to comprehend the term "research," particularly as it relates to psychology.

At several stages of the research process, statistics is crucial. For instance, statistics can be effectively employed while selecting a sample from the population for research. Statistics can be used to calculate the sample size for a study. To calculate sample size, a specific formula can be employed. Additionally, statistics can be applied to test development to determine the validity and reliability of the test. Factor analysis is a technique that works well for data reduction and is also utilised in the creation of psychological assessments. You can utilise the normal distribution to create norms. As a result, statistics might be crucial to the process of developing tests.

When a researcher collects quantitative data, statistics is crucial to the analysis of that data. Using a variety of statistical approaches, the data can be arranged, categorised, and analysed to make inferences, come to conclusions, and aid in decision-making. Thusly collected results can be summarised in a meaningful way, and from them, inferences and predictions can be made. The data can be analysed using descriptive and inferential statistics. The degree of precision can be increased by using statistics to estimate the likelihood of errors while forming inferences.

According to the goals of the study, measures of central tendency and measures of variability can be applied to the raw data in descriptive statistics after they have been categorised and tabulated. Additionally, the data can be visually displayed for clear presentation and comprehension. It is possible to compare two or more sample subgroups using inferential statistics. Additionally, statistics can be used by researchers who wish to predict one or more variables from other variables (s).

Depending on whether or not certain assumptions are true, statistics can also be divided into parametric and nonparametric categories. These methods work well under a variety of circumstances. For instance, parametric statistics has certain requirements, including that the variables be assessed using an interval or ratio scale, that the data be normally distributed, and that the sample be homogeneous. When a sample is heterogeneous in nature, the data is not normally distributed, there are outliers, and the variables are measured using a nominal or ordinal scale, for example, nonparametric statistics can be employed effectively.

Additionally, statistics might be multivariate, bivariate, or univariate. One variable is considered univariate, two variables are considered bivariate, and numerous variables are considered multivariate. Therefore, a variety of statistical approaches, from the simplest, like computing the mean and mode, to the most complex, like factor analysis, discriminant analysis, and so on, can be utilised depending on the goals and nature of the research. Therefore, statistics plays a vital and major function in research.

2. Compute Spearman’s rho for the following data:

Ans) Solution of the given problem is as follows:

The formula used to compute Rho is

Rho= 1- [(6Σd2) / [N (N2 - 1)]

The formula used to compute Rho is

p = 1- [(6Σd2) / [N (N2 - 1)]

So,

p = 1- [(6×139) / [10 (102 - 1)]

= 1- (834) / [10 (100-1)]

= 1- (834) / (10×99)

= 1-(834/990)

= 1-0.84

p = 0.16

Thus, the correlation of coefficient (Rho) obtained for the above data is 0.16, thus denoting a significant and positive correlation between data 1 and data 2.

Assignment Two

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

3. Explain the scales of measurement with the help of examples.

Ans) In the process of measuring, numbers are meaningfully assigned to observations. The characteristics of the quantification of the observations can vary. Wheat is measured in terms of weight here, therefore 1 kilogramme is equal to 1/2 of 2 kilos. On the other hand, grades can be given to pupils based on how well they perform in math. For instance, a student who placed first might have earned 95 marks, but a student who placed second might have earned 80 marks, and a student who placed third might have earned 79 marks. As can be observed, the numerical characteristics of the two cases vary.

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

5. Explain the merits, limitations and uses of average deviation.

Ans) Merits, Limitations and uses of the AD as follows:

1. Merits of Average Deviation

2. It is simple to comprehend and calculate AD or MD.

3. Unlike R or QD, it is based on all observations.

4. Given that it averages the absolute deviations, it is a reliable indicator of variability.

5. Extreme observations have less of an impact on it.

6. It is based on average, making it a better metric to compare on how various distributions are formed.

Limitations of Average Deviation

1. We ignore the plus and negative signs while computing average deviation and treat all numbers as positive. It is not utilised in inferential statistics because of this mathematical characteristic.

2. For classes with open ends, AD cannot be computed.

3. It usually grows as the sample size does.

Use of Average Deviation

Despite these drawbacks, economists and business statisticians still utilise AD or MD. The distribution of individual wealth within a society or country is also computed using this method. The National Bureau of Economic Research claims that the most useful measure of dispersion for this use is MD.

6. Compute standard deviation for the following data.

Ans) Solution of the given problem is as follows:

Standard Deviation =√Σx2/N

N=10

SD= √(Σx2) /N

So,

SD= √(Σx2) /N

SD= √203.96 /10

SD= √20.39

SD= 4.51

Thus, the standard deviation for this data is 4.51.

7. What is correlation? Describe the other methods of correlation with the help of suitable examples.

Ans) The link between two or more variables can be studied using correlations. It is a measurement of the relationship between two or more variables, and it takes into account both the relationship's magnitude and direction, whether positive or negative. However, it won't reveal any details regarding any causal connection between the variables.

Other Methods of Correlation

Partial Correlation: In partial correlation, the influence of a third variable is controlled in order to examine the link between two variables. For instance, if we are researching the connection between teenagers' self-concept and emotional intelligence, we may leave out or manipulate the third component, such as home environment.

Partiality: This is sometimes referred to as semi-partiality. This is somewhat similar to partial correlation, however in this case the influence of the third variable on one of the variables is controlled when examining the correlation between two variables. Using the partial correlation example, it can be seen that only emotional intelligence is influenced by the familial environment, not self-concept.

Multiple correlation: Multiple correlation occurs when several variables are correlated with one another. Self-concept, for instance, will be linked to a number of other factors, such as emotional intelligence, motivation for success, quality of life, and so forth.

8. Explain the concept, properties and uses of z scores.

Ans)

Concept

The standard score, also known as the z-score, is a modified score that displays how many standard deviation units the raw score (the value of the observation) deviates from the mean. The likelihood that a score will fall inside the normal distribution can be estimated using the standard score. Comparing results from several normal distributions is aided by it as well.

Properties

1. The z-scores' average is always equal to zero.

2. It's also crucial to remember that the z-scores' standard deviation is always 1.

3. Additionally, the z-score distribution graph consistently resembles the initial distribution of sample values.

4. Sample values above the mean are represented by z-scores above 0; sample values below the mean are represented by z-scores below 0; and so forth.

5. The z-score distribution will have a similar or exact shape to the original raw score distribution. As a result, the z-score distribution will also be normal if the original distribution is normal. As a result, normalising the distribution of any data by converting it to a z-score does not normalise the data.

Uses

1. It aids in pinpointing an observation's or observations' location within a population distribution.

2. The raw data is standardised using it.

3. It facilitates the comparison of scores from various normal distributions.