Statistics in psychology and education/ MangalmS.K.

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
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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
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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 {<p) Coefficient 220
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