Statistics – 4

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60 Statistics – 4

Chittaranjan Andrade

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1. Semantic differential scales are used in attitude measurement. image image
2. A cut-off point on the scores of the Present State Examination can be used to define caseness for screening purposes in epidemiological research. image image
3. The chi-squared test could be used in a study of comparison of pay vs. job satisfaction in two groups of workers aged 20 and aged 30. image image
4. Path analysis is used to develop classification systems. image image
5. Correlation between IQ and reading ability in a school-wide sample of children is found to be +0.55. Among a group of learning disabled children of similar age group, one might expect the correlation to be much greater. image image
6. In the design of an experimental study, ‘crossover’ means patients are paired and then swapped. image image
7. For a normally distributed variable the mean and standard deviation provide a sufficient statistical description. image image
8. The halo effect can be a source of error in experimental psychology. image image
9. Incidence is usually higher than prevalence for schizophrenia. image image
10. A Likert scale allows for a 5-point response. image image
11. Two samples significantly different on the Mann–Whitney test can have the same median. image image
12. Multivariate statistics can be measured by least squares. image image
13. In a study of the ego-strength of 16-year-old females working in a clothes factory, as an indicator of the ego-strength of all 16-year-old girls in the same city, the parameter is the mean ego-strength of 16-year-old females in the factory. image image
14. The power of a study is 1 minus type 2 error. image image
15. The Beck Depression Inventory is a self-rated questionnaire. image image
16. Regression is used to compare two groups. image image
17. In the construction of a psychometric rating scale, high test-retest reliability may impair the detection of individual change. image image
18. Every 10th name on a hospital admission register can be used for random sampling. image image
19. Psychiatric screening instruments used in a general hospital should have normative data. image image
20. In the construction of a psychometric rating scale, the type of population chosen for standardization must be different from the population for which the scale is intended. image image
21. A treatment trial shows no significant difference in efficacy between two antidepressants. This may be because the outcome measurement was based on a scale measuring traits rather than state. image image
22. If an association between two variables is statistically significant, it means that a causal association has been established. image image
23. The t-test is used to compare two groups. image image
24. In an experiment to determine whether drug therapy or hypnosis is better as a treatment to stop smoking, the results are measured by the number of cigarettes smoked after treatment. In this study, the number of cigarettes smoked before treatment is a dependent variable. image image
25. In a placebo-controlled trial of a new antidepressant where the subjects are matched in pairs and a suitable rating scale is used, a Wilcoxon test would be more sensitive than a t-test. image image

ANSWERS

1. Semantic differential scales are used in attitude measurement.

True: The semantic differential scale asks a person to express an attitude along a 7-point scale which has a bipolar adjective at the ends. For example, a person may be asked:

Do you believe that women in managerial positions are

1. Competent
2.
3.
4.
5.
6.
7. Incompetent.

Ratings may also be aligned horizontally as:

Good Bad
3 2 1 0 1 2 3

The subject is required to make a choice between the adjectives and along the continuum.

2. A cut-off point on the scores of the Present State Examination can be used to define caseness for screening purposes in epidemiological research.

False: The Present State Examination is a 140-item tool which evaluates different categories of psychopathology towards establishing a clinical diagnosis.

In psychiatry, the most common instrument used to define caseness is presently the DSM-IV. Sometimes, caseness may be defined in terms of a cut-off on a rating scale. For example, a cut-off may be specified on the Goldberg General Health Questionnaire to define caseness when screening for psychiatric disorders in a large sample. A cut-off of 7 on the Mood Disorders Questionnaire may be used to define caseness when screening for bipolar disorders. A cut-off of 18 on the Ham-D may be used to define caseness when recruiting for a clinical trial in which patients who are only mildly depressed are to be screened out.

3. The chi-squared test could be used in a study of comparison of pay vs. job satisfaction in two groups of workers aged 20 and aged 30.

False: Pay and job satisfaction are usually both measured as continuous (quantitative) variables along a ratio scale. The relationship between pay and job satisfaction would be tested using a method of correlation. However, if we wish to determine whether the relationship between pay and job satisfaction differs between two age groups, we would need to use logistic regression with age group as the dependent (grouping) variable, and with pay and job satisfaction as the independent variables. We would need to specify an interaction term between pay and job satisfaction to answer the question asked.

4. Path analysis is used to develop classification systems.

False: Path analysis is used to test a model with several independent and several dependent variables set out in the form of a path.

For example, we know that stress causes depression, that depressed patients are often anxious, and that mood disturbance impairs quality of life. We may hypothesize (a) that stress raises anxiety scores, which in turn raise depression scores, which in turn lower quality of life scores, and (b) that anxiety also directly lowers quality of life scores. In other words, we indicate paths of how different variables directly or indirectly result in downstream effects. Paths can converge, diverge, or intersect. Such models can be tested through correlation coefficients derived through path analysis.

5. Correlation between IQ and reading ability in a school-wide sample of children is found to be +0.55. Among a group of learning disabled children of similar age group, one might expect the correlation to be much greater.

False: Among children with learning disabilities, reading ability is compromised no matter what the IQ is. In consequence, the relationship between IQ and reading ability is much weakened. The result is a lower correlation coefficient.

6. In the design of an experimental study, ‘crossover’ means patients are paired and then swapped.

False: Crossover means that patients are exposed first to one experimental condition, e.g. active drug, and then to the other, e.g. placebo. Patients are usually randomized to one or the other condition and subsequently crossed over to the condition to which they have not been exposed. There is usually a washout interval between exposures to the two conditions. Crossover designs may also involve more than two conditions, e.g. experimental condition, active control and inactive control.

7. For a normally distributed variable the mean and standard deviation provide a sufficient statistical description.

True: The range may be added to provide additional information.

8. The halo effect can be a source of error in experimental psychology.

True: The halo effect is said to occur when the response to one variable influences the response to other variables. For example, when a patient is depressed, he may rate his activities of daily living as being worse than they actually are. This is because depression makes him see everything in a negative light. Another example is when an individual is judged based on a single attribute, e.g. if he tells a single lie, he is judged to be dishonest by nature.

The practice effect is another source of error. If the same ISQ, or a similar ISQ, is administered repeatedly, the subject’s performance improves not because he knows better but because he has ‘learnt’ how to perform in that test. However, knowledge improves if the candidate studies the explanations also.

Subject variables are also a source of error. For example, more intelligent subjects may show certain responses, males may show certain responses, younger persons may show certain responses, etc. These can be controlled for by proper randomization or group matching, or can be reduced through analysis of co-variance if the assumptions of ANCOVA are met.

9. Incidence is usually higher than prevalence for schizophrenia.

False: Incidence describes the occurrence of new cases in a population over a specified time period, while prevalence describes the total number of cases in a population over a specified time period. The chronic nature of schizophrenia is therefore reflected in the prevalence being greater than incidence. Point prevalence is the proportion of cases at a specific point in time. One-year prevalence is the proportion of persons who were already cases or who became cases during that year. Lifetime prevalence is the proportion of persons who become cases during their lifetime.

10. A Likert scale allows for a 5-point response.

True: A Likert scale measures the extent to which a person agrees or disagrees with a statement. The most common scale is 1 to 5. Often the scale will be 1=strongly disagree, 2=disagree, 3=not sure, 4=agree, and 5=strongly agree.

11. Two samples significantly different on the Mann–Whitney test can have the same median.

True: Although the Mann–Whitney test is sometimes described as a test which compares medians between two groups (much as the t-test compares means between two groups), what the Mann–Whitney test actually compares are the mean ranks. The mean ranks can vary even if the medians are the same. This is because the median is a single term; the values of the numbers on either side can differ widely between groups, resulting in differences in mean ranks. If the difference in mean ranks is sizeable, the Mann–Whitney test will emerge significant.

12. Multivariate statistics can be measured by least squares.

True: More specifically, multiple regression analysis uses the least squares method.

13. In a study of the ego-strength of 16-year-old females working in a clothes factory, as an indicator of the ego-strength of all 16-year-old girls in the same city, the parameter is the mean ego-strength of 16-year-old females in the factory.

False: The population of 16-year-old females working in a clothes factory is a biased subset of 16-year-old females in the city. This is because factory workers are likely to belong to a specific socio-economic status, and would therefore differ from girls who work elsewhere in education, income, quality of residence, and other variables.

‘Parameter’ is the term used to describe values such as mean, median, mode, standard deviation, etc. for the population. The equivalent for a sample is ‘statistic’.

14. The power of a study is 1 minus type 2 error.

True: The power of a test is the probability that a type 2 error will not occur, i.e. 1 minus the probability of the type 2 error.

15. The Beck Depression Inventory is a self-rated questionnaire.

True: Other self-rated instruments include personality inventories, e.g. Eysenck Personality Questionnaire, Cattell’s 16-PF self-report questionnaire; quality of life scales, e.g. WHO-QOL; the General Health Questionnaire and the Michigan Alcohol Screening Test.

Clinician-rated instruments include the Ham-D, Ham-A, Montgomery–Asberg Depression Rating Scale, the Young Mania Rating Scale, the Bech–Rafaelson Mania Rating Scale, the Brief Psychiatric Rating Scale, the PANSS, the Clinical Global Impression of severity and the Clinical Global Impression of change.

Neuropsychological measures are almost all clinician-administered, e.g. WAIS, Wechsler Memory Scale, Halstead-Reitan battery, the Luria-Nebraska battery, etc.

The Raven’s Standard and Advanced Progressive Matrices and the Coloured Progressive Matrices are self-administered.

The Zung depression scale has both self-rated and observer-rated versions.

16. Regression is used to compare two groups.

False: Regression is used to explain or predict the value of a dependent variable given the value of an independent variable. For example, we can use regression to derive an equation which explains or predicts the seizure threshold given the patient’s age. Linear regression is used when there is one independent variable and one dependent variable. Multiple regression is used when there are several independent and one dependent variables.

17. In the construction of a psychometric rating scale, high test–retest reliability may impair the detection of individual change.

False: If the test–retest reliability is high, it means that repeated administration of the test to the same individual yields the same or very similar results. The assumption is that the individual has himself not changed, and therefore the test correctly reports the same results.

If the individual does change, a tool with high test–retest reliability must necessarily identify the change. The better the test–retest reliability, the better the tool will be at identifying the change.

18. Every 10th name on a hospital admission register can be used for random sampling.

False: This is systematic sampling, a form of non-random sampling. Systematic sampling is acceptable when it is believed that the distribution of subjects in the sample is reasonably free of bias. For example, in this situation, taking every 10th name is an acceptable form of sampling if it can be reasonably assumed that there is no bias in the manner in which the names are entered in the hospital admission register.

Random sampling assumes that every subject in the population has an equal opportunity of being selected no matter what the previous selections have been. In contrast, in systematic sampling (to use this example), once the initial subject has been chosen, the next 9 subjects have no chance of being chosen, the 10th subject will definitely be chosen, the next 9 will not, etc.

19. Psychiatric screening instruments used in a general hospital should have normative data.

True: Psychiatric screening instruments used in a general hospital should have normative data based on which a cut-off score (with appropriate sensitivity and specificity) can be selected. This cut-off score can be used to separate cases who are likely to have a psychiatric disorder from those who are unlikely to have a psychiatric disorder.

20. In the construction of a psychometric rating scale, the type of population chosen for standardization must be different from the population for which the scale is intended.

False: Psychometric instruments are standardized for the populations for which they are intended. This is because the reliability and validity of a particular version of an instrument can vary across populations.

21. A treatment trial shows no significant difference in efficacy between two antidepressants. This may be because the outcome measurement was based on a scale measuring traits rather than state.

True: Antidepressant drugs treat symptoms such as depression and anxiety. These are states. States are things which alter over time whereas traits are more stable. Antidepressant drugs do not usually influence personality characteristics, i.e. personality traits, and these are therefore unlikely to differ between groups treated with different antidepressant drugs.

22. If an association between two variables is statistically significant, it means that a causal association has been established.

False: There are several possible indicators of causality, and statistical significance is one of them. However, none of the indicators decisively establishes causality.

For example, in children aged 0–2 years, a significant correlation is identified between the number of words the child knows and the number of teeth the child has. This does not establish that vocabulary improves dentition, or that dentition improves vocabulary. Rather, both are explained by a third variable, age.

23. The t-test is used to compare two groups.

True: The independent sample t-test is used to compare means between two groups. The paired t-test, in contrast, is used to compare the means of the same variable obtained from the same group at two different points in time.

The t-test can be used to compare levels of depression measured using Ham-D in a random sample of high school boys and girls. Here, gender is the grouping variable and depression score is the variable being compared between the two groups.

24. In an experiment to determine whether drug therapy or hypnosis is better as a treatment to stop smoking, the results are measured by the number of cigarettes smoked after treatment. In this study, the number of cigarettes smoked before treatment is a dependent variable.

False: The number of cigarettes smoked before treatment is an independent variable. Treatment, i.e. drug therapy vs. hypnosis, is also an independent variable. Whereas treatment is the primary independent variable, pretreatment smoking is a potentially biasing independent variable, and can be treated as a co-variate in the analysis. In this example, the number of cigarettes smoked after treatment is the dependent variable.

25. In a placebo-controlled trial of a new antidepressant where the subjects are matched in pairs and a suitable rating scale is used, a Wilcoxon test would be more sensitive than a t-test.

False: Parametric tests are more powerful than nonparametric tests in the identification of a true difference in means. Therefore, the paired t-test would be superior to the Wilcoxon test.

The Wilcoxon test would be desirable only if the paired t-test cannot be performed, e.g. when the sample size is small or when the distribution of the differences between pairs of values is non-normal.

Incidentally, the paired t-test or the Wilcoxon test are usually performed on pre-vs. post-data, i.e. on repeated measures. A situation in which subjects are matched and compared using a paired test (paired t-test or Wilcoxon test) is unusual in research.

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