Statistics in psychology and education/
MangalmS.K.
- 2
- New Delhi: PHI learning, 2002.
- 404
1. STATISTICS—MEANING AND USE Meaning of Statistics 1 Need and Importance of Statistics in Education and Psychology Evaluation and Measurement 2 Day-to-Day Tasks 2 Reseaich 3 Understanding and Using the Products of Research Prerequisites for Studying Statistics 4 Essential Mathematical Fundamentals 4 Types of Variables Employed in Statistical Measurement Sc^es of Measurement 6 Type of Approximation or Exactness Required in Statistics Various Statistical Symbols 8 Summary 10 Exercises 10 2. ORGANIZATION OF DATA The Meaning of the Term "Data" 12 Methods of Organizing Data 12 Statistical Tables 12 Rank Order 14 Frequency Distribution 15 How to Construct a Frequency Distribution Table 15 Grouping Error 17 Cumulative Frequency and Cumulative Percentage Frequency Distributions IS Summaiy 19 Exercises 21 3. graphical representation of data Meaning of Graphical Representation of Data Advantages of Graphical Representation of Data 23 Modes of Graphical Representation of Data 24 Graphical Representation of Ungrouped Data 24 Graphical Representation of Grouped Data (Frequency Distribution) 28 Smoothing of Frequency Curves—Polygon and Ogive 35 Why Smooth? 35 How to Smooth 35 Explanation 35 Summary 38 Exercises 39 y , 4. MEASURES OF CENTRAL TENDENCY Meaning of the Measures of Central Tendency 41 Arithmetic Mean (M) 41 Median (Mj) 43 Mode (Mo)' 46 Computation of Median and Mode from the Curves of Frequency Distribudon 49 When to Use the Mean, Median and Mode 49 Summary 51 Exercises 52 5. PERCENTILES AND PERCENTILE RANK Meaning of the Term Pencentile 55 Definition 56 Defining Quardles and Deciles 56 ; Computation of Percentiles, Quartiles and Deciles 57 Definition 60 / Percentile Rank 60 Definition 60 Computation of Percentile Rank 60 Utility of Percentiles and Percentile Rank 65 -Summary 65 Exercises 67 6. MEASURES OF VARIABILITY Meaning and Importance of the Measures of Variability 68 Types or Measures of Variability 69 Range (R) 69 Quar'-ile Deviation (Q) 69 Average Deviauon (AD) 70 Standard Deviation (SD) 71 When and Wliere to Use the Various Measures of Variability 74 Range 74 Average Deviauon 74 Quartile Deviation 75 Standard Deviation 75 Summaiy 76 Exercises 77 -ik 7. LINEAR CORRELATION Linear Correlation—Meaning and Types 79 Coefficient of Correlation 80 Computation of Coefficient of Correlation 80 Construction of Scatter Diagram 87 Computation of r 9i ^ Summary 106 Exercises 108 8. THE NORMAL CURVE AND ITS APPLICATIONS What is a Normal Curve? Ill In Terms of Skewness • 112 In Terms of Kurtosis 114 Characteristics and Properties of a Normal Curve 115 Applications of the Normal Curve 117 Use as a Model 117 Computing Percentiles and Percentile Ranks 117 Understanding and Applying the Concept of Standard Errors of Measurement 118 Ability Grouping 118 Transforming and Combining Qualitative Data 118 Converting Raw Scores into Comparable Standard ^ Normalized Scores 118 Determining the Relative Difficulty of Test Items 119 Illustration of the Applications of the Normal Curve 119 Converting Raw Scores into z Scores and Vice Versa 119 Making Use of the Table of Normal Curve 120 Examples of Application of tlie Normal Curve 121 Summary 131 Exercises 133 9. SIGNIFICANCE OF THE MEAN AND OTHER STATISTICS Why is Sampling Needed? 135 Significance of the Sample Mean and Other Statistics 135 Concept of Standard Error in Computing the Significant Value of the Mean or Other Statistics 136 Confidence Intervals 137 Computation of Significance of Mean in Case of Large Samples 138 Significance of Mean for Small Samples 139 Process of Determining the Significance of Small Sample Means 141 Significance of Some Other Statistics 143 Standard Error of a Median 143 Standard Error of a Quartile Deviation 143 Standard Error of a Standard Deviation 143 J Standard Error of the Coefficient of Correlation 143 Coefficient of CoiTelation r 144 Snminary 147 Exercises 149 , 10. SIGNIFICANCE OF THE DIFFERENCE BETWEEN MEANS Need and Importance 151 Fundamental Concepts in Determining the Significance of the Difference between Means 152 Concept of Standard EiTor 152 Concept of Null Hypothesis 152 Setting up the Level of Confidence or Significance 153 Size of the Sample 153 Two-tailed and One-tailed Tests of Significance 154 How to Determine the Significance of Difference between Two Means 157 Smmnary 175 Exercises 177 11. CHI SQUARE AND CONTINGENCY COEFFICIENT Use of Chi Square as a Test of 'Goodness of Bit' 181 Hypothesis of Chance 181 Hypothesis of Equal Probability 182 . • Hypothesis of Normal DisU'ibution 182 y- Procedure of Chi Square Testing 183 Establishing Null Hypothesis 183 Computation of the Value of ^ 183 Determining the Number of Degrees of Freedom 184 Determining the Critical Value of^ 184 Comparing Critical Value of ^ with the Computed Value 184 Use of Chi Square as a Test of Independence between Two Variables 191 Contingency Coefficient 196 How to Compute C 197 Correction for Small Frequencies in a 2 x 2 Table 198 Underlying Assumptions, Uses and Limitations of Chi Square Test 201 Summary 202 Exercises 204 12. FURTHER METHODS OF CORRELATIONS The Biserial Correlation 208 Distinction between Artificial and Natural Dichotomy 209 Computation of Biserial Coefficient of Correlation 210 Alternative Formula for 213 Characteristics of Biserial CoiTelation 213 The Point Biserial Correlation 214 Computation of Point Biserial Correlation CoefTicicnt bis) VVliich One of the Correlation ? bis or bis's Better and Why? 217 The Tetrachoric Correlation 217 Computation of Tetrachoric Correlation 218 y Worksheet for Computation of Tetrachoric Con elation (r,) 219 The Phi (^) Coefficient 220 Computation of Phi {Features and Characteristics of (p Coefficient 222 Summary 222 Exercises 224 13. PARTIAL AND MULTIPLE CORRELATION Need and Importance of Pai tial Correlation 228 Computation of Partial Correlation 229 Application of Partial Correlation 233 Significance of Partial Correlation Coefficient 233 Need and Importance of Multiple Correlation 233 Computation of Multiple Correlation 234 Other Methods of Computing Coefficient of Multiple Correlation 235 Characteristics of Multiple Correlation 238 Significance of Multiple Correlation Coefficient R Suihmary 238 Exercises 240 14. REGRESSION AND PREDICTION Regression 242 Concept of Regression Lines and Regression Equations Procedure for the Use of Regression Lines 243 Error in the Prediction 247 Role of Coefficient of Alienation in Prediction 248 Multiple Regression and Prediction 249 Setting up of a Multiple Regression Equation 249 Steps to Formulate a Regression Equation 250 Standard Error of Esdmate 254 Summary 256 Exercises 258 15. SCORES transformation Need and Importance 260 Standard Scores 261 T-Scores 265 ' How to Construct a T Scale 266 ^ Conversion of the Raw Scores into T Scores 268 C-Scores and Stanine Scores 270 Summary 273 Exercises 274 16. NON-PARAMETRIC TESTS Parametric and Non-parametric Tests 276 / VVlien to Use Parametric and Non-parametric Tests 276 McNcmar Test for the Significance of Change 277 Sign lest 280 Evaluation of Sign Pest 285 Wilcoxon Matched-Pairs Signed Ranks Test 285 Median Test. 288 The Mann-Whitney U Test 290 •. Wild-Wolfowitz-Runs Test 297 Tlie Kolmogrov Smirnov Test (KS Test) 302 KS One-Sample Test 302 Wliat KS One-Sample Test Does? 303 KS Two-Samples Test 306 Summary 311 Exercises 314 17. ANALYSIS OF VARIANCE Need for the Technique of Analysis of Variance 319 Meaning of the Term 'Analysis of Variance' 321 Procedure for Calculating the Analysis of Variance 322 / Two-Way Analysis of Variance 334 Underlying Assumptions in Analysis of Variance 339 Summary 339 Exercises 341 18. ANALYSIS OF COVARIANCE Meaning and Purpose 344 How to Make Use of the Analysis of Covariance 347 Assumptions Underlying Analysis of Covariance 354 Summary 354 Exercises 355