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TABLE OF CONTENTS
Chapter # CONTENT Page
#
1 BASIC IDEAS IN STATISTICS……………………….. 01
� Introduction......................................................................... � Meaning of statistics……………………………………… � Applied statistics………………………………………..... � Descriptive statistics……………………………………… � Inferential statistics……………………………………..... � Population………………………………………………… � Sample…………………………………………………..... � Parameter…………………………………………………. � Statistic…………………………………………………… � Ratio……………………………………………………… � Proportion………………………………………………… � Uses or importance of statistics in various fields…..…….. � Constant…………………………………………............... � Variables……………………………………...................... � Collection of data…………………………………….…… � Collection of primary data……………………………..…. � Collection of secondary data…………………………….... � Grouped & ungrouped data……………………………..... � Class, class interval, class boundary…………………….... � Frequency (class frequency)……………………………… � Class magnitude…………………………………………... � Class limit………………………………………………… � Frequency distribution/statistical series…………………... � Tabulation………………………………………………… � Classification………………………………………........... � Steps involve in the construction of classification
according to class interval (frequency distribution)……..... � Exercise…………………………………………………..
01 02 02 02 03 03 03 03 03 03 03 04 04 05 06 06 07 08 09 09 09 09 10 11 13
14 19
2 MEASURES OF CENTRAL TENDENCY……………. 21
� Introduction......................................................................... � Arithmetic mean.................................................................. � Merits and demerits of arithmetic mean..............................
21 22 22
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� Median................................................................................. � Merits & demerits of median.............................................. � Quartiles.............................................................................. � Deciles................................................................................. � Percentiles........................................................................... � Mode.................................................................................... � Merits & demerits of mode................................................. � Exercise…………………………………………………..
26 26 33 34 35 42 43 49
3 MEASURES OF DISPERSION (VARIATION)……… 51
� Introduction......................................................................... � Range................................................................................... � Inter quartile range.............................................................. � Semi-inters quartile range (or) Quartile deviation.............. � Mean deviation (or) average deviation............................... � Variance & standard deviation........................................... � Variance & standard deviation (by short cut method)....... � Co-efficient of variation (dispersion)................................. � Exercise…………………………………………………..
51 52 54 54 58 62 63 63 71
4 SIMPLE CORRELATION & REGRESSION………... 73
� Correlation......................................................................... � Types of correlation...........................................................
⇒ Positive correlation................................................ ⇒ Negative correlation............................................... ⇒ Zero correlation...................................................... ⇒ Perfect correlation...................................................
• Perfect positive correlation........................... • Perfect negative correlation..........................
� Graphic method of measuring correlation........................ � Co-efficient of correlation................................................. � Rank order correlation……………………………………. � Regression………………………………………………... � Regression Equation……………………………………… � Regression line…….……………………………………... � Properties of Regression line……………………………... � Exercise…………………………………………………..
73 74 74 74 74 74 75 75 75 78 87 94 94 95 95 103
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5 STATISTICAL INFERENCE…………………...……... 105
� Introduction......................................................................... � Hypotheses………………………………………………..
⇒ Statistical hypotheses……………………………… ⇒ Null hypothesis……………………………………. ⇒ Alternative hypothesis…………………………….. ⇒ Simple hypothesis…………………………………. ⇒ Composite hypothesis……………………………...
� Type-I error and type-II error…………………………….. � Level of significance……………………………………... � One tailed and two tailed tests…………………………… � Test statistic………………………………………………. � Critical region and non-critical region…………………… � General procedure in testing of hypothesis………………. � Test based on normal distribution……………………….. � Testing hypotheses about difference between two
populations means (normal distribution)………………… � The student-t distribution………………………………… � Degree of freedom………………………………………... � Testing procedure of “t-distribution” for single
population……………………………………………….. � Testing hypothesis about difference of means of two
normal populations with δ1= δ2 but unknown…………… � Testing hypotheses about difference of means of two
normal populations when δ1=δ2 but unknown…………. � Testing hypothesis about difference of means of two
normal populations with δ1≠δ2 but unknown…………… � Testing hypotheses about difference of means of two
normal populations when δ1≠δ2 but unknown………….. � Paired difference t-test…………………………………… � Testing hypotheses about two means with paired
observations……………………………………………… � Exercise…………………………………………………..
105 106 107 108 108 109 109 110 110 111 112 112 113 116
126 132 132
133
138
139
146
147 149
150 157
6 CHI-SQUARE (χχχχ2) DISTRIBUTION………………...... 159
� Introduction......................................................................... � Testing hypotheses about variance of a normal population � Properties of chi-square (χ2) distribution…………………
159 160 160
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� Testing hypotheses about variance of a normal population � χ2-test for goodness of fit………………………………… � χ2-test as test of independence…………………………… � Contingency table………………………………………… � Exercise…………………………………………………..
161 166 169 169 181
Table: Student’s t-distribution ………………………………….... Table: Area for a Standard Normal Distribution………………… Table: Distribution of χ2…………………………………………… Glossary……………………………………………………….……… References……………………………………………………….……
183 184 185 187 195
Atta, M.A Educational Statistics
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