Research Methodology - Dr. Krishan K. Pandey

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Testing of Hypotheses-II 299 Solution: To apply the H test or the Kruskal-Wallis test to this problem, we begin by ranking all the given figures from the highest to the lowest, indicating besides each the name of the ball as under: Table 12.7 Bowling results Rank Name of the ball associated 302 1 B 297 2 D 282 3 A 279 4 D 276 5 B 275 6 B 271 7 A 270 8 D 268 9 B 266 10 C 262 11 A 260 12 C 258 13 D 257 14 A 255 15 C 252 16 B 248 17 A 246 18 C 242 19 D 239 20 C For finding the values of R i , we arrange the above table as under: Table 12.7 (a): Bowling Results with Different Balls and Corresponding Rank Ball A Rank Ball B Rank Ball C Rank Ball D Rank 271 7 252 16 260 12 279 4 282 3 275 6 255 15 242 19 257 14 302 1 239 20 297 2 248 17 268 9 246 18 270 8 262 11 276 5 266 10 158 13 n 1 = 5 R 1 = 52 n 2 = 5 R 2 = 37 n 3 = 5 R 3 = 75 n 4 = 5 R 4 = 46 Now we calculate H statistic as under:
300 <strong>Research</strong> <strong>Methodology</strong> k 2 12 Ri H = ∑ − 3 n+ 1 nn b + 1g b g ni i= 1 R S| T| = 2 2 2 2 12 52 37 75 46 + + + − 320+ 1 20b20 + 1g b g 5 5 5 5 = (0.02857) (2362.8) – 63 = 67.51 – 63 = 4.51 As the four samples have five items * each, the sampling distribution of H approximates closely with χ 2 distribution. Now taking the null hypothesis that the bowler performs equally well with the four balls, we have the value of χ 2 = 7.815 for (k – 1) or 4 – 1 = 3 degrees of freedom at 5% level of significance. Since the calculated value of H is only 4.51 and does not exceed the χ 2 value of 7.815, so we accept the null hypothesis and conclude that bowler performs equally well with the four bowling balls. 6. One Sample Runs Test One sample runs test is a test used to judge the randomness of a sample on the basis of the order in which the observations are taken. There are many applications in which it is difficult to decide whether the sample used is a random one or not. This is particularly true when we have little or no control over the selection of the data. For instance, if we want to predict a retail store’s sales volume for a given month, we have no choice but to use past sales data and perhaps prevailing conditions in general. None of this information constitutes a random sample in the strict sense. To allow us to test samples for the randomness of their order, statisticians have developed the theory of runs. A run is a succession of identical letters (or other kinds of symbols) which is followed and preceded by different letters or no letters at all. To illustrate, we take the following arrangement of healthy, H, and diseased, D, mango trees that were planted many years ago along a certain road: HH DD HHHHH DDD HHHH DDDDD HHHHHHHHH 1st 2nd 3rd 4th 5th 6th 7th Using underlines to combine the letters which constitute the runs, we find that first there is a run of two H’s, then a run of two D’s, then a run of five H’s, then a run of three D’s, then a run of four H’s, then a run of five D’s and finally a run of nine H’s. In this way there are 7 runs in all or r = 7. If there are too few runs, we might suspect a definite grouping or a trend; if there are too many runs, we might suspect some sort of repeated alternating patterns. In the given case there seems some grouping i.e., the diseased trees seem to come in groups. Through one sample runs test which is based on the idea that too few or too many runs show that the items were not chosen randomly, we can say whether the apparently seen grouping is significant or whether it can be attributed to chance. We shall use the following symbols for a test of runs: n = number of occurrences of type 1 (say H in the given case) 1 n = number of occurrences of type 2 (say D in the given case) 2 * For the application of H test, it is not necessary that all samples should have equal number of items. U V| W|
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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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Interpretation and Report Writing 3
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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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