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Psychometric Testing

Psychometric Testing

Solution No. 1

(a)

(b)

(c)

(d)

Solution No. 2

(a) If mental arithmetic is taken as a measure of intelligence then what mental arithmetic score would a child with an IQ of 100 be expected to obtain?

One - Sample Statistics

N

Mean

Std. Deviation

Std. Error Mean

mental arithmetic scores

320

7.51

3.231

.181

From the results of the above mentioned descriptive statistics, the mean of mental arithmetic scores that is used in analyzing the data is given. The most essential and critical values of the One - Sample Statistics is the mean and the standard deviation of the variables, which are imperative to study. Moreover, these values provide the data accuracy; in addition to this, it is also found that observed that the mean of mental arithmetic scores is 7.51 with the standard deviation of 3.2.

One - Sample Test

Test Value = 100

t

df

Sig. (2 - tailed)

Mean Difference

95 % Confidence Interval of the Difference

Lower

Upper

mental arithmetic scores

- 512.108

319

.000

- 92.494

- 92.85

- 92.14

From the above table it can be observed that the significance level is less than 0.05 indicating that there is zero probability that the mean difference of - 93.494 has a zero probability of occurring.

(b) Using the standard deviation (z-score) what proportion of children should have scores between 4.0 and 8.0?

Keeping in view, the standard deviation (z-score), it can be said that there is zero probability that the children will have scores between 4.0 and 8.0, as the standard deviation is 3.231 with the mean value of 7.51.

(c) Use 'frequencies' to determine the mean, median, mode and quartiles for the mental arithmetic score

Statistics

mental arithmetic scores

N

Valid

320

Missing

29

Mean

7.51

Median

7.00

Mode

6

Percentiles

25

5.00

50

7.00

75

10.00

(d) Compute correlations between these variables and comment on the meaning of the correlation between the eowpvt-r and the Crichton scores

Correlations

standard scores eowpvt

crichton vocabulary scores

mental arithmetic scores

standard scores eowpvt

Pearson Correlation

1

.660 **

.352 **

Sig. (2 - tailed)

.000

.001

N

80

80

80

crichton vocabulary scores

Pearson Correlation

.660 **

1

.536 **

Sig. (2 - tailed)

.000

.000

N

80

320

320

mental arithmetic scores

Pearson Correlation

.352 **

.536 **

1

Sig. (2 - tailed)

.001

.000

N

80

320

320

**. Correlation is significant at the 0.01 level (2 - tailed).

From the given correlation table, it can be observed that there is correlation between standard scores eowpvt and crichton vocabulary scores. The basis of this statement is that the level of significance indicates that it is statistically significant as it below 0.5 which represents the significance. Moreover, the Pearson correlation coefficient indicates is in positive that is 0.66, this reflects that there is positive correlation between the standard scores eowpvt and crichton vocabulary scores.

Solution No. 3

Standard Error = = = 16

If the test ...

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