Research Methodology - Dr. Krishan K. Pandey

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Testing of Hypotheses-II 311 all possible pairs. The relationship between the average of Spearman’s r’s and Kendall’s W can be put in the following form: average of r’s = (kW – 1)/(k – 1) But the method of finding W using average of Spearman’s r’s between all possible pairs is quite tedious, particularly when k happens to be a big figure and as such this method is rarely used in practice for finding W. Illustration 11 Using data of illustration No. 9 above, find W using average of Spearman’s r’s. Solution: As k = 4 in the given question, the possible pairs are equal to k(k – 1)/2 = 4(4 – 1)/2 = 6 and we work out Spearman’s r for each of these pairs as shown in Table 12.10. Now we can find W using the following relationship formula between r’s average and W Average of r’s = (kW – 1)/(k – 1) or 0.655 = (4W – 1)/(4 – 1) or (0.655) (3) = 4W – 1 b gbg 0. 655 3 + 1 2. 965 or W = = = 0. 741 4 4 [Note: This value of W is exactly the same as we had worked out using the formula: W = s/[(1/12) (k2 ) (N3 – N)] CHARACTERISTICS OF DISTRIBUTION-FREE OR NON-PARAMETRIC TESTS From what has been stated above in respect of important non-parametric tests, we can say that these tests share in main the following characteristics: 1. They do not suppose any particular distribution and the consequential assumptions. 2. They are rather quick and easy to use i.e., they do not require laborious computations since in many cases the observations are replaced by their rank order and in many others we simply use signs. 3. They are often not as efficient or ‘sharp’ as tests of significance or the parametric tests. An interval estimate with 95% confidence may be twice as large with the use of nonparametric tests as with regular standard methods. The reason being that these tests do not use all the available information but rather use groupings or rankings and the price we pay is a loss in efficiency. In fact, when we use non-parametric tests, we make a trade-off: we loose sharpness in estimating intervals, but we gain the ability to use less information and to calculate faster. 4. When our measurements are not as accurate as is necessary for standard tests of significance, then non-parametric methods come to our rescue which can be used fairly satisfactorily. 5. Parametric tests cannot apply to ordinal or nominal scale data but non-parametric tests do not suffer from any such limitation. 6. The parametric tests of difference like ‘t’ or ‘F’ make assumption about the homogeneity of the variances whereas this is not necessary for non-parametric tests of difference.
Table 12.10: Difference between Ranks |d | Assigned by k = 4 Judges and the Square i 2 Values of such Differences (d ) for all Possible Pairs of Judges i Individuals Pair 1 – 2 Pair 1 – 3 Pair 1 – 4 Pair 2 – 3 Pair 2 – 4 Pair 3 – 4 |d | d 2 |d | d 2 |d | d 2 |d | d 2 |d | d 2 |d | d 2 A 1 1 2 4 0 0 1 1 1 1 2 4 B 1 1 1 1 1 1 0 0 2 4 2 4 C –1 1 1 1 3 9 0 0 4 16 4 16 D –2 4 3 9 1 1 1 1 1 1 2 4 E 0 0 0 0 1 1 0 0 1 1 1 1 F 1 1 2 4 1 1 1 1 2 4 3 9 G 0 0 1 1 1 1 1 1 1 1 2 4 Spearman’s Coefficient of Correlation 6 ∑d i r = 1 − 2 N N − 1 2 2 ∑ di = 2 8 ∑ di = 2 20 ∑ di = 2 14 ∑ di = 2 4 ∑ di = 2 28 ∑ di = e j r 12 = 0.857 r 13 = 0.643 r 14 = 0.750 r 23 = 0.929 r 24 = 0.500 r 34 0.857 + 0.643 + 0.750 + 0.929 + 0.500 + 0. 250 Average of Spearman’s r’s = 6 3929 . = = 0. 655 6 42 = 0.250 312 <strong>Research</strong> <strong>Methodology</strong>
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In loving memory of my revered fath
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Preface to the Second Edition vii P
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Preface to the First Edition ix Pre
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Contents xi Contents Preface to the
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Contents xiii Selection of Appropri
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Contents xv ANOVA in Latin-Square D
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Research Methodology: An Introducti
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Define research problem I Review th
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Defining the Research Problem 25 Ov
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Defining the Research Problem 27 so
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Defining the Research Problem 29 (a
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Research Design 31 MEANING OF RESEA
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Research Design 33 FEATURES OF A GO
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Research Design 35 of students and
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Research Design 37 Now, what sort o
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Research Design 39 The difference b
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Research Design 41 Important Experi
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Research Design 43 extraneous facto
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Research Design 45 From the diagram
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Research Design 47 equal. This redu
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Research Design 49 The graph relati
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Research Design 51 The dotted line
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Appendix: Developing a Research Pla
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Sampling Design 55 CENSUS AND SAMPL
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Sampling Design 57 would like to ma
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Sampling Design 59 Element selectio
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Sampling Design 61 successive drawi
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Sampling Design 63 The following th
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Sampling Design 65 where C 1 = Cost
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Sampling Design 67 Table 4.1 City n
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Measurement and Scaling Techniques
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Methods of Data Collection 95 6 Met
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Methods of Data Collection 97 There
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Methods of Data Collection 99 (viii
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Methods of Data Collection 101 2. I
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Methods of Data Collection 103 inst
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Methods of Data Collection 105 is g
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Methods of Data Collection 107 amon
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Methods of Data Collection 109 Holt
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Methods of Data Collection 111 COLL
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Methods of Data Collection 113 usin
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Methods of Data Collection 115 (v)
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Methods of Data Collection 117 2.
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Appendix (ii): Guidelines for Succe
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Appendix (iii): Difference Between
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Processing and Analysis of Data 123
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Editing Coding Processing of Data (
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Sampling Fundamentals 153 1. Univer
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Sampling Fundamentals 155 should no
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Sampling Fundamentals 157 certain l
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Sampling Fundamentals 159 (i) Stati
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Sampling Fundamentals 161 (ii) To t
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Sampling Fundamentals 163 2 (ii) Sq
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Sampling Fundamentals 165 (ii) Stan
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Sampling Fundamentals 167 σ s 1⋅
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Sampling Fundamentals 169 mean is c
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Sampling Fundamentals 171 08 . = ×
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Sampling Fundamentals 173 We now il
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Sampling Fundamentals 175 (v) Stand
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Sampling Fundamentals 177 where N =
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Sampling Fundamentals 179 Since $p
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Sampling Fundamentals 181 (i) Find
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Sampling Fundamentals 183 25. A tea
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Testing of Hypotheses I 185 Charact
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Testing of Hypotheses I 187 when th
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Testing of Hypotheses I 189 Mathema
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Testing of Hypotheses I 191 PROCEDU
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Testing of Hypotheses I 193 MEASURI
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Testing of Hypotheses I 195 We can
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Testing of Hypotheses I 197 HYPOTHE
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1 2 3 4 5 z OR X − X 1 2 2 2 p p
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1 2 3 4 5 z = p q 0 0 p$ − p$ F H
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Testing of Hypotheses I 203 to have
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Testing of Hypotheses I 205 S. No.
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Testing of Hypotheses I 207 S. No.
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Testing of Hypotheses I 209 nX + nX
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Testing of Hypotheses I 211 (Since
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Testing of Hypotheses I 213 Table 9
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Testing of Hypotheses I 215 σ diff
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Testing of Hypotheses I 217 Solutio
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Testing of Hypotheses I 219 Hence t
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Testing of Hypotheses I 221 of succ
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Testing of Hypotheses I 223 Thus, q
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Testing of Hypotheses I 225 the val
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Testing of Hypotheses I 227 and 2 X
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Testing of Hypotheses I 229 LIMITAT
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Testing of Hypotheses I 231 20. Ten
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Chi-square Test 233 10 Chi-Square T
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Chi-square Test 235 S. No. 1 2 3 4
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Chi-square Test 237 As a test of go
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Chi-square Test 239 (i) First of al
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Chi-square Test 241 The expected fr
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Chi-square Test 243 Show that the s
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Chi-square Test 245 Events or Expec
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Chi-square Test 247 c h χ 2 N ⋅
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Chi-square Test 249 from a number o
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Chi-square Test 251 Questions 1. Wh
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Chi-square Test 253 No. of boys 5 4
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Chi-square Test 255 23. For the dat
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Analysis of Variance and Co-varianc
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Analysis of Variance and Co-varianc
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The Computer: Its Role in Research
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Appendix 375 Appendix (Selected Sta
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Appendix 377 Table 2: Critical Valu
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Appendix 379 v 2 Table 4(a): Critic
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Appendix 381 Table 5: Values for Sp
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s l Min Max 0 1 2 3 4 5 6 7 8 9 10
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Appendix 385 Table 8: Cumulative Bi
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Appendix 387 Table 9: Selected Crit
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Appendix 389 1 2 3 4 5 6 40 0.368 0
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Selected References and Recommended
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Selected References and Recommended
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Author Index 395 Ackoff, R.L., 25,
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Author Index 397 Murphy, James L.,
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Subject Index 399 Content analysis,
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Subject Index 401 Research Plan, 53
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Research Methodology - Dr. Krishan K. Pandey

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