Chapter 8, STATISTICS IN PSYCHOLOGY AND EDUCATION Video Solutions, Fundamentals of Applied Statistics

Problem 1

(a) Why is it considered desirable to convert gross scores to some standard scores ? Define 'standardised scores' and 'normalised scores' and describe how they are derived.
(b) Explain the concept of a percentile scale and describe a practical method of its computation from raw scores.

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Problem 2

Explain the various methods of scaling scores bringing out the underlying importance of normal distribution.

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Problem 3

Describe the errors of measurement, estimation, substitution and prediction, along with their standard deviations, in a psychological test.

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Problem 4

(a) How are the items of a test scaled in terms of difficulty, assuming that the underlying trait has a normal distribution? How does such scaling help in item selection?
(b) Why is the scaling of raw scores considered necessary? Describe any two of the commonly used derived scales, mentioning their advantages and disadvantages. What are the advantages of reporting percentile norms while standardising a test?

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02:50

Problem 5

(a) Distinguish between $\sigma$-scores, standard scores and Mc-Call $T$ scores. Describe how $T$ scores are to be found given that test scores are in the form of a frequency table.
(b) What do you understand by a $T$-scale ? Explain clearly the method of converting raw test scores into $T$-scores.
Show that this scaling procedure helps in the process of normalising a skew distribution.

Jameson Kuper

Numerade Educator

Problem 6

(a) Explain briefly the concepts of reliability and validity of scores in educational and psychological experiments.
(b) Explain the importance of reliability and validity in test standardisation. What is their relationship to each other? Describe the different methods of obtaining the reliability coefficient and the validity coefficient.
(c) What is the effect of the lengthening of a test on (i) reliability, and (ii) validity?

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02:57

Problem 7

(a) Describe the Kuder-Richardson methods of assessing the reliability of a test. Give a brief account of (i) Test-retest, (ii) Parallel form, and (iii) Split-half method of assessing the reliability, commenting on their merits and demerits.
(b) Describe the experimental methods usually used for estimating the reliability of a test and indicate their relative merits.

Jeremiah Mbaria

Numerade Educator

Problem 8

Define reliability and validity of tests. Explain reliability in terms of true error and observed variance of test scores.

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Problem 9

Write brief answers to the following questions :
(i) Is it true that a test can have high reliability and low validity ? If so, explain how?
(ii) Is it true that a test can have high validity and low reliability ? If so, explain how?
(iii) Does a test battery with low test intercorrelations have more predicative value than a test battery with high test intercorrelations?

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Problem 10

Define relability and validity of a test. Deseribe and compare the following methods of assessing the reliability of a test :
(i) Test-Retest method. (ii) Parallel Form. (iii) Split-Half technique. (iv) Rational equivalence.

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Problem 11

(a) Explain the concept of reliability of a test and obtain the expressions for (i) coefficient of reliability, and (ii) index of reliability.
(b) Describe briefly how reliability can be estimated from empirical data.

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Problem 12

Write short notes on:
(i) Summation score as a function of ability. (ii) Relation of validity coefficient to error of measurement. (iii) Reliability of composite score. (iv) Percentile score.

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01:48

Problem 13

Show that the reliability $\rho_k$ of a test at length $k$ in terms of its reliability $\rho_k^{\prime}$ at length $k^{\prime}$ is :
$$
\rho_k=\frac{k \rho_k^{\prime}}{k^{\prime}+\left(k-k^{\prime}\right) \rho_k^{\prime}}
$$

Narayan Hari

Numerade Educator

Problem 14

(a) Explain the important properties of parallel tests.
(b) Briefly describe the procedures available for comparing and combining examination scores.

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01:39

Problem 15

Let $Y_1$ and $Y_2$ be measurements with true scores $T_1$ and $T_2$ and let $X=Y_1+Y_2$ be a composite measurement with true score $T$. Then prove that-
$$
[r(X, T)]^2 \geq 2\left[1-\frac{\sigma^2\left(Y_1\right)+\sigma^2\left(Y_2\right)}{\sigma^2(X)}\right]
$$
where $r(X, T)=$ the correlation coefficient between $X$ and $T ; \sigma\left(Y_i\right)=$ the standard deviation of $Y_i^{\prime} i=$ 1,$2 ; \sigma(X)=$ the standard deviation of $X$.

Manik Pulyani

Numerade Educator

02:21

Problem 16

Suppose a test contains $p$ items and a sub-test is formed with $q(q<p)$ items out of this test. If $r$ be the reliability of each item included in the test, show that
$$
r_{p q}=\sqrt{\frac{q}{p} \cdot \frac{1+(p-1) r}{(q-1) r}},
$$
where $r_{p q}$ is the correlation between the test and the sub-test. Assume items to be parallel.

Karen Song

Numerade Educator

01:29

Problem 17

What do you mean by intelligence quotient (I.Q.). Describe the procedure and tests for measuring I.Q.

Dwijendra Rao

Numerade Educator

Problem 18

How is intelligence measured ? How does an aptitude test differ from an intelligence test ? Explain the terms 'mental age' and 'intelligence quotient'. How is the validity of an intelligence test

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