MAP 604 8

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2 M.A.(Psy) Research Methods and Statistics-I Course Code: MAP 604 Semester: First E- Lesson: 6 SLM Unit: 8 https://images.app.goo.gl/ibaW7YhjJ7LmSLJV6 www.cuidol.in Unit-8(MAP 604) All right are reserved with CU-IDOL

RESEARCH METHODS 33 AND STATISTICS OBJECTIVES INTRODUCTION Understand the basic concept and importance of In this unit will help you to understand research, the basics of research design and the different concepts under data evaluate types of research designs analysis ie, descriptive statistics and standard deviation. Understand and evaluate the process of research and sampling. The unit further discusses other concepts of data analysis which are Understand the concepts and explore the types skewness, Kurtosis and range. of reliability and validity and evaluate the data analysis. Understand and explore Correlation and Regression and parametric and nonparametric test www.cuidol.in Unit-8(MAPP 604) INASlTl ITriUgThEt OarFeDrIeSsTeArNvCeEd AwNitDh OCNUL-IIDNOE LLEARNING

TOPICS TO BE COVERED 4 > Data Analysis: Descriptive statistics > Standard deviation and variance > Skewness and kurtosis > Range https://images.app.goo.gl/qhiaHBQmdQUHqGr8A www.cuidol.in Unit-8(MAP 604) All right are reserved with CU-IDOL

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DATA ANALYSIS: 6 DESCRIPTIVE STATISTICS  Descriptive statistics are used to describe the basic features of the data in a study.  It provides simple summaries about the sample and the measures.  Its also relate to quantitative analysis of data.  Descriptive statistics are typically distinguished from inferential statistics.  Descriptive statistics are typically distinguished from inferential statistics.  With descriptive statistics we simply describing what is or what the data shows.  Descriptive Statistics are used to present quantitative descriptions in a manageable form.  Descriptive statistics help us to simplify large amounts of data in a sensible way www.cuidol.in Unit-8(MAP 604) All right are reserved with CU-IDOL

DATA ANALYSIS: DESCRIPTIVE STATISTICS 7 • So, Descriptive statistics are used to describe or summarize data in ways that are meaningful and useful. • For example, it would not be useful to know that all of the participants in our example wore blue shoes. However, it would be useful to know how spread out their anxiety ratings were. • Descriptive statistics is at the heart of all quantitative analysis. • There are two ways: measures of central tendency and measures of variability, or dispersion. 1. Measures of central tendency use a single value to describe the center of a data set. The mean, median, and mode are all the three measures of central tendency 2. Standard deviation is the measurement of average distance between each quantity and mean. That is, how data is spread out from mean. https://images.app.goo.gl/A7bUCDkdJiPmAYQQ9 www.cuidol.in Unit-8(MAP 604) All right are reserved with CU-IDOL

MEASURES OF CENTRAL 8 TENDENCY In Descriptive Statistics, Mean, median, and mode are three kinds of \"averages\". There are many \"averages\" in statistics, but these are, I think, the three most common, and are certainly the three you are most likely to encounter in your pre-statistics courses, if the topic comes up at all. 1. The \"mean\" is the \"average\" you're used to, where you add up all the numbers and then divide by the number of Numbers. • For Ex. The mean is the usual average, so I'll add and then divide: (13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13) ÷ 9 = 15 www.cuidol.in Unit-8(MAP 604) http://www.peoi.org/Cou All right are reserved with CU-IDOL

MEASURES OF CENTRAL 9 TENDENCY 2. The \"median\" is the \"middle\" value in the list of numbers. To find the median, your numbers have to be listed in numerical order from smallest to largest, so you may have to rewrite your list before you can find the median. • The median is the middle value, so first I'll have to rewrite the list in numerical order: 13, 13, 13, 13, 14, 14, 16, 18, 21 • There are nine numbers in the list, so the middle one will be the (9 + 1) ÷ 2 = 10 ÷ 2 = 5th number: 13, 13, 13, 13, 14, 14, 16, 18, 21 • So the median is 14. https://images.app.goo.gl/VfQE94jsy9PjNLGD6 www.cuidol.in Unit-8(MAP 604) All right are reserved with CU-IDOL

MEASURES OF CENTRAL 10 TENDENCY 3. The mode is the number that is repeated more often than any other, so 13 is the mode. • The largest value in the list is 21, and the smallest is 13, so the range is 21 – 13 = 8. https://images.app.goo.gl/oUzCdNajr5Tdurnu9 www.cuidol.in Unit-8(MAP 604) All right are reserved with CU-IDOL

MEASURES OF VARIABILITY 11 STANDARD DEVIATION AND VARIATION Standard deviation is the measurement of average distance between each quantity and mean. That is, how data is spread out from mean. • A low standard deviation indicates that the data points https://images.app.goo.gl/VioR1Y5Q72pTnmRk7 tend to be close to the mean of the data set, while a high standard deviation indicates that the data points are spread out over a wider range of values. • There are situations when we have to choose between sample or population Standard Deviation. • When we are asked to find SD of some part of a population, a segment of population; then we use sample Standard Deviation. • When we are asked to find SD of some part of a population, a segment of population; then we use sample Standard Deviation. www.cuidol.in Unit-8(MAP 604) All right are reserved with CU-IDOL

VARIANCE 12 All right are reserved with CU-IDOL • The variance is computed by finding the difference between every data point and the mean, squaring them, summing them up and then taking the average of those numbers. • The squares are used during the calculation because they weight outliers more heavily than points that are near to the mean. This prevents that differences above the mean neutralize those below the mean. • The problem with Variance is that because of the squaring, it is not in the same unit of measurement as the original data www.cuidol.in Unit-8(MAP 604)

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SKEWNESS 14 • Skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. The skewness value can be positive or negative, or undefined. • In a perfect normal distribution, the tails on either side of the curve are exact mirror images of each other. • When a distribution is skewed to the left, the tail on the curve’s left-hand side is longer than the tail on the right-hand side, and the mean is less than the mode. This situation is also called negative skewness. • When a distribution is skewed to the right, the tail on the curve’s right-hand side is longer than the tail on the left-hand side, and the mean is greater than the mode. This situation is also called positive skewness. www.cuidol.in Unit-8(MAP 604) All right are reserved with CU-IDOL

SKEWNESS 15 www.cuidol.in https://miro.medium.com All right are reserved with CU-IDOL Unit-8(MAP 604)

SKEWNESS 16 • How to the skewness coefficient? To calculate skewness coefficient of the sample, there are two methods: 1] Pearson First Coefficient of Skewness (Mode skewness) 2] Pearson Second Coefficient of Skewness (Median skewness) www.cuidol.in https://miro.medium.com All right are reserved with CU-IDOL Unit-8(MAP 604)

KURTOSIS 17 The exact interpretation of the measure of Kurtosis used to be disputed, but is now settled. Its about existence of outliers. Kurtosis is a measure of whether the data are heavy-tailed (profusion of outliers) or light-tailed (lack of outliers) relative to a normal distribution. There are three types of Kurtosis 1. Mesokurtic: Meso-kurtic is the distribution which has similar kurtosis as normal distribution kurtosis, which is zero. 2. Leptokurtic: Distribution is the distribution which has kurtosis greater than a Mesokurtic distribution. Tails of such distributions are thick and heavy. If the curve of a distribution is more peaked than Mesokurtic curve, it is referred to as a Leptokurtic curve. 3. Platykurtic: Distribution is the distribution which has kurtosis lesser than a Mesokurtic distribution. Tails of such distributions thinner. If a curve of a distribution is less peaked than a Mesokurtic curve, it is referred to as a Platykurtic curve. www.cuidol.in Unit-8(MAP 604) All right are reserved with CU-IDOL

KURTOSIS 18 Diagram showing the three types of kurtosis:- www.cuidol.in https://mvpprograms.com All right are reserved with CU-IDOL Unit-8(MAP 604)

RANGE 19 • The simplest and the easiest method of measuring dispersion of the values of a variable is the Range. • It is measured just as the difference between the highest and the lowest values of a variable. The extent of dispersion increases as the divergence between the highest and the lowest values of the variable increases. • We thus express the magnitude of Range as: • Range = (highest value – lowest value) of the variable. • For determining Range of a variable, it is necessary to arrange the values in an increasing order. It will enable us to avoid mistakes in calculation and give us the best result. www.cuidol.in Unit-8(MAP 604) All right are reserved with CU-IDOL

RANGE 20 Here are two separate examples both the grouped and the ungrouped data separately. • Example 1: Consider the following series of numbers:1, 2, 4, 6, 8, 10, 12. • Solution: Here, the highest value of the series is 12 and the lowest is 1. Therefore, the Range = 12 – 1 = 11 i.e. the values of the variable are scattered within 11 units. • Example 2: For the data presented with their respective frequencies, the idea is to measure the same as the difference between the mid-values of the two marginal classes. • Consider the following table: Fre. 0-9 10-19 20-29 30-39 40-49 50-59 Scores 4 7 11 6 8 10 www.cuidol.in Unit-8(MAP 604) All right are reserved with CU-IDOL

RANGE 21 • The required Range is 54.5 – 4.5 = 50 or the observations on the variable are found scattered within 50 units. • It is to be noted that any change in marginal values or the classes of the variable in the series given will change both the absolute and the percentage values of the Range. www.cuidol.in Unit-8(MAP 604) All right are reserved with CU-IDOL

SUMMARY 22 • Thus introduction to descriptive statistics is very important type of Research and Statistics. We have gained knowledge about the three different kinds of averages (mean, mode and median), also called the Central Tendency. • Afterwards, we learned about the range, interquartile range, variance and standard deviation. • Then we discussed the three types of modality and that you can describe how much a distribution differs from a normal distribution in terms of Skewness. • Lastly, we learned about Leptokurtic, Mesokurtic and Platykurtic distributions. www.cuidol.in Unit-8(MAP 604) All right are reserved with CU-IDOL

MULTIPLE CHOICE QUESTIONS 23 1. Mean and median are related to measures of central tendency. a) True b) False 2. Since the mode is the most frequently occurring data value, it a. can never be larger than the mean b. is always larger than the median c. is always larger than the mean d. must have a value of at least two e. None of the above answers is correct. Answers: 1. a) 2. e) www.cuidol.in Unit-8(MAP 604) All right are reserved with CU-IDOL

MULTIPLE CHOICE QUESTIONS 24 3. The difference between the largest and the smallest data values is the a. Variance b. interquartile range c. Range d. coefficient of variation e. None of the above answers is correct. 4. distribution which has kurtosis greater than a _________ distribution. a. Meso kurtic b. Platy kurtic c. Lepto kurtic • Answers: 3. c) 4.c) www.cuidol.in Unit-8(MAP 604) All right are reserved with CU-IDOL

FREQUENTLY ASKED QUESTIONS 25 1. Name the measures of descriptive statistics. 2. Formula of mean and median measures in descriptive statistics. 3. What is the difference between mean and standard deviation? 4. What are types of kurtosis and it is relate to which statistics ? 5. What is skewness and kurtosis? 6. What is relation between standard deviation and variance? www.cuidol.in Unit-8(MAP 604) All right are reserved with CU-IDOL

REFERENCES 26 • Singh A.K. (2006). 5th ed. Tests, Measurement and Research Methods in Behavioral Sciences. Patna: BharatiBhavan. methods_fig1_317905066 • https://link.springer.com/10.978-94-007-0753-5_2241 • https://www.ncbi.nim.nih.gov/pmc/artic;es/PMC4797036/ • https://www.investopedia.com/terms/d/descriptive_statistics.asp • https://conjointly.com/kb/descriptive-statistics/ www.cuidol.in Unit-8(MAP 604) All right are reserved with CU-IDOL

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