Research Methodology - Dr. Krishan K. Pandey

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Chi-square Test 245 Events or Expected frequencies No. of heads 3 4 5 6 7 8 The value of χ 2 can be worked out as follows: ∴ 8 8 8 8 Table 10.8 3 1 2 3 5 1 2 256 56 C F H G I K J F H G I K J × = 4 1 2 4 4 1 2 256 70 C F H G I K J F H G I K J × = 5 1 2 5 3 1 2 256 56 C F H G I K J F H G I K J × = 6 1 2 6 2 1 2 256 28 C F H G I K J F H G I K J × = 8 7 1 2 7 1 1 2 256 8 C F H G I K J F H G I K J × = 8 8 1 2 8 0 1 2 256 1 C F H G I K J F H G I K J × = No. of heads Observed Expected O – E i i (O – E ) i i 2 /Ei frequency frequency Oi Ei 0 2 1 1 1/1 = 1.00 1 6 8 –2 4/8 = 0.50 2 30 28 2 4/28 = 0.14 3 52 56 –4 16/56 = 0.29 4 67 70 –3 9/70 = 0.13 5 56 56 0 0/56 = 0.00 6 32 28 4 16/28 = 0.57 7 10 8 2 4/8 = 0.50 8 1 1 0 0/1 = 0.00 χ 2 bOi −Eig =∑ E i 2 = 3.13
246 <strong>Research</strong> <strong>Methodology</strong> ∴ Degrees of freedom = (n – 1) = (9 – 1) = 8 The table value of χ 2 for eight degrees of freedom at 5 per cent level of significance is 15.507. The calculated value of χ 2 is much less than this table and hence it is insignificant and can be ascribed due to fluctuations of sampling. The result, thus, supports the hypothesis and we may say that the coins are not biased. ALTERNATIVE FORMULA There is an alternative method of calculating the value of χ 2 in the case of a (2 × 2) table. If we write the cell frequencies and marginal totals in case of a (2 × 2) table thus, then the formula for calculating the value of χ 2 will be stated as follows: b g χ 2 ad − bc ⋅ N = ba + cgbb + dgba + bgbc + dg where N means the total frequency, ad means the larger cross product, bc means the smaller cross product and (a + c), (b + d), (a + b), and (c + d) are the marginal totals. The alternative formula is rarely used in finding out the value of chi-square as it is not applicable uniformly in all cases but can be used only in a (2 × 2) contingency table. YATES’ CORRECTION a b c d ( a + b) ( c + d) ( a + c) ( b + d) N F. Yates has suggested a correction for continuity in χ 2 value calculated in connection with a (2 × 2) table, particularly when cell frequencies are small (since no cell frequency should be less than 5 in any case, through 10 is better as stated earlier) and χ 2 is just on the significance level. The correction suggested by Yates is popularly known as Yates’ correction. It involves the reduction of the deviation of observed from expected frequencies which of course reduces the value of χ 2 . The rule for correction is to adjust the observed frequency in each cell of a (2 × 2) table in such a way as to reduce the deviation of the observed from the expected frequency for that cell by 0.5, but this adjustment is made in all the cells without disturbing the marginal totals. The formula for finding the value of χ 2 after applying Yates’ correction can be stated thus: 2
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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-II 295 Table
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Testing of Hypotheses-II 297 Illust
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Testing of Hypotheses-II 299 Soluti
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Testing of Hypotheses-II 301 r = nu
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Testing of Hypotheses-II 303 where
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Testing of Hypotheses-II 305 Table
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Testing of Hypotheses-II 307 We now
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Testing of Hypotheses-II 309 (ii) I
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Testing of Hypotheses-II 311 all po
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Testing of Hypotheses-II 313 CONCLU
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Multivariate Analysis Techniques 31
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Appendix Summary Chart: Showing the
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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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Research Methodology - Dr. Krishan K. Pandey

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