Statistics in Psychology and Education/ Garrett,Henry E.

THE FREQUENCY DISTRIBUTION
3BCnON
I. The Tabulation op Measures into a Frequency Distribu
tion .
1. Measures in General: Continuous and Discrete
2. Classification of Measures in Continuous Series
3. Three Ways of Expressing the Limits of a Step-interval
4. The Meaning of a Single Score in a Continuous Series
n. Measures of Central Tendency .
1. The Average, or Arithmetic Mean
2. The Median .
3. The Mode .
in. Measures of Variability
1. The Range .
2. The Quartile Deviation, or Q .
3. The Average Deviation, or AD
4. The Standard Deviation, or SD
TV. The Short Method of Finding the Average, AD, and
SDic)
1. The Calculation of the Average by the Short Method
2. The Calculation of the AD by the Short Method
A. The Calculation of the AD from the Average
B. The Calculation of the AD from the Median
3. The Calculation of the Standard Deviation by the Short
Method
4. The Short Method Applied to Discrete Series
V. The Comparison op Groups .
1. The Measurement of Relative Variability
2. The Comparison of Two Groups in Terms of Central
Tendency and Variability .
3. The Comparison of Two Groups in Terms of Overlapping
VI. The Calculation op the Percentilbs in a Frequency Dis
tribution
BECriON
VTI. When to Use the Different Measures of Central Ten
dency AND Variability .
VIIL Summary of Formulas for Finding the Measures of Cen
tral Tendency and Variabiuty .
IX. Illustrative Problems
CHAPTER II
GRAPHIC METHODS AND THE NORMAL CURVE
I. The Graphic Representation of the Frequency Distribu
tion
1. The Frequency Polygon .
2. The Histogram or Column Diagram .
3. The Ogive, or Cumulative Frequency Graph .
II. Other Uses of Graphical Methods: the Compabattvb Line
Graph
m. The Normal Probability Curve . .
1. Elementary Principles of Probability .
2. Why the Probability Curve is Employed in Psychological
Measurement
3. Important Properties of the Normal Curve
4m' The Measurement of Skewness
IV. Some Practical Applications of the Normal Curve .
1. The Construction and Use of Tables X and XI . . . .
2. A Variety of Problems Solved by Means of Tables X and XI
3. The Arrangement of Problems or other Test Items into a
Scale in Which the Difficulty of Each Item is ICnown with
Reference to Each Other Item as Well as Some Selected
Zero Point
4. The Conversion of Judgments by Ilelative Position—or
Relative Merit—into <r or PE Positions on the Scale .
5. The Scaling of Total Scores on a Test .
V. The Transmutation of Measures by Relative Position
(in Order op Merit) into Units of Amount on the
Assumption of Normality in the Trait Measured .
CHAPTER HI
THE RELIABILITY OF MEASURES
I. What is Meant by the Reuabiuty of a Mbaburb . . ,
SECTION
11. The Reliability op Measures of Central Tendency .
1. The Reliability of the Average or Mean .
A. In Terms of the Standard Error, 0^7. .
B. In Terms of the Probable Error, P^av.
2. The Reliability of the Median
III. The Reliability op Measures op Variability
1. The Standard Deviation, or tr
2. The QuartUe Deviation, or Q
IV. The Reliability op the Difference between Two Measures
1. The Reliability of the Difference between Two Averages
A. In Terms of the a(din.)
B. In Terms of the PE((iio.) .
2. The Reliability of the Difference between Two Medians
V. Some Problems which Involve Measures of Reliability
W. Limitations to the Reliability Formulas, and Cautions to
BE Observed in Interpreting Them .
/II. Summary of Reliability Formulas .
CHAPTER IV
CORRELATION
I. What is Meant by Correlation
II. The Coefficient op Correlation: What it is, and what it
Does
1/ The Coefficient of Correlation as a Ratio
2. Graphical Representation of the Coefficient of Correlatioii
III. The Calculation op the Coefficient op Correlation by
the Product-moment Method
1. The Product-moment Formula when Deviations are
Taken from the Guessed Averages of the Two Distri
butions
2. The Product-moment Formula when Deviations are
Taken from the Actual Averages of the Two Distribu
tions
rv. The Probable Error op a Coefficient of Correlation .
1. The PE,
2. The PE of the Difference between Two r's .
V. The Rboresbion Equations
1. In Deviation Form
2. The Regression Equations in Score Form
3. The Reliability of the "Predictions" made from the
Regression Equations "
SECTION
VI. The Complete Solution of a Correlation Problem .
VII. Methods of Measuring Correlation which Take Account
only of the Relative Position or Rank
1. The Method of Rank-differences
2. The Method of Gains, or the Spearman Footrule
3. Summary of the Rank'Methods
VIII. A Method of Measuring Relationship when the Data are
Grouped into Classes or Categories. The Contingbnct
Method
IX. Non-linear Relationship . .
1. The Correlation Ratio .
2. The Correction of "raw" eta .
3. Test of Linearity of Regression
X. The Correction op a Coefficient of Correlation for
"Attenuation."
XI. Summary op Formulas in Chapter IV
CHAPTER V
PARTIAL AND MULTIPLE CORRELATION
/
I. The Meaning of Partial and Multiple Correlation . .
II. A Correlation Problem Involving 3 Variables . . .
III. General Formulas for Use in Partial and Multiple Corre
lation
1. General Formulas for Partial r's . . . .
2. General Formulas for Partial a's of any Order
3. General Formulas for the Regression Equation, and Co
efficients of Regression
4. General Formulas for Standard and Probahle Errors of
Estimate
5. General Formula for R, the Coefficient of Multiple Correla
tion
6. Outline of the Formulas Needed in Correlation Problems
which Involve (a) Four Variables, (6) Five Variables .
IV. A Multiple Correlation Problem Involving 4 Variables .
V. The Value and Use of Partial and Multiple Correlation
VI. Spurious Correlation
1. Spurious Correlation Due to Heterogeneity of Material .
2. Spurious Index Correlation
SBCnON
3. Spurious Correlation of a Single Test^ith a Composite of
which it is a Member
VTI. Summary of Formulas in Chapter V .
CHAPTER VI
SOME APPLICATIONS OF STATISTICAL METHOD AND
TECHNIQUE TO TESTS AND TEST RESULTS
I. The Validity op Test Scores
1. Validity Determined through Correlation with a Criterion .
2. Indirect Measures of Validity
11. The Reliability of Test Scores
1. The Reliability of a Test as Measured by its Self-Correla
tion
(A) The "Reliability Coefficient"
{B) Effect on Reliability of Lengthening or Repeating the
Test
(C) Coefficient of Reliability from One Application of a
Test
(D) Dependence of the Reliability Coefficient on the Size
and Variability of the Group
2. The Index of Reliability
3. The Standard Error and Probable Error of Measurement:
and PE{iiS)
III. CoMhiNiNQ the Scores from Dipeterent Tests . . . .
1. Combining Test Scores by Percentiles
2, Combining Test Scores by the Method of Median Mental
Age
3. Combining Tests which have been Weighted According to
the Variability of the Test Scores
4, Combining Test Scores by Converting the Scores of Dif
ferent Tests into Comparable Series
IV. The <r OP THE Sum or Difference op Corresponding Values
OF Two Series of Test Scores
V. How to Interpret the Coefficient of Correlation between
Two Tests or Other Measures
1. The Interpretation of a Coefficient of Correlation in Terms
of 0"{€at.)
2. The Interpretation of a Coefficient of Correlation in terms
of the Standard Error of Measurement, <^(4o . . . .
3. Interpretation of a Coefficient of Correlation in Terms of the
Percentage of Common (Overlapping) Elements or Fac
tors