Statistics – 2

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58 Statistics – 2

Chittaranjan Andrade

	T	F
1. Analysis of variance enables a test of significance of multiple repeated mean scores on a measure of a normally distributed variable.
2. The Barnum effect explains in part people’s belief in astrology.
3. The chi-squared test can be used to compare the Ham-D scores between patients treated with an experimental antidepressant drug and placebo.
4. The chi-squared test could be used in a study of response to a new antidepressant at four 3-monthly intervals in one hospital population.
5. Correlation coefficient refers to how one variable alters with change in another paired variable.
6. Correlation coefficient ‘r’ may be used when studying non-linear relationships.
7. In a normal distribution, 68% of the population lie within one standard deviation of the mean.
8. Standard error of a proportion will depend on the proportion in the wider population.
9. The Hawthorne effect can be a source of error.
10. The least squares method is used for normally distributed continuous data.
11. Logistic regression is used for categorical variables.
12. The arithmetic mean is equal to the median when the distribution of scores is unimodal and symmetrical.
13. The null hypothesis is that the two populations being compared are different.
14. Parametric statistics are generally more powerful than non-parametric tests.
15. If, in a 60-year-old man, the probability of having A is 0.2, and B is 0.1, and both are independent, then the probability of having neither is 0.7.
16. Logistic regression is done by the least squares method.
17. In the design of an experimental study, prospective methods are relatively inexpensive.
18. In psychological assessment, the response set is the responses the subject believes the interviewer wants.
19. Snowballing can be used for random sampling.
20. 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 sample is biased.
21. A treatment trial shows no significant difference in efficacy between two antidepressants. This may be because the sample size considerations were based on active drug versus placebo comparison.
22. A result statistically significant at a level of 5% implies that the result could not be accepted as valid.
23. A specific test has a low number of false negatives.
24. Instruments need to result in a normal distribution of results to have validity.
25. A researcher investigates the effect of smoking marijuana on motivation. He finds motivation levels lower in smokers than in a control population. In this study, marijuana smoking is the independent variable.

ANSWERS

1. Analysis of variance enables a test of significance of multiple repeated mean scores on a measure of a normally distributed variable.

True: For example, if we obtain Ham-D scores in one or more groups of patients at several different points in time, we may want to know whether there has been a significant change in the scores across time. If there is more than one group, we may also want to know if the rate of change across time differs between groups. We use repeated measures analysis of variance (RMANOVA) for this design. To examine changes in only one group across time, we use a one-way RMANOVA; the ‘one way’ refers to differences across time. To examine changes in two or more groups across time, we use a two-way RMANOVA; one of the ‘two ways’ refers to differences across time, and the other to differences between groups.

2. The Barnum effect explains in part people’s belief in astrology.

True: The Barnum effect is named after the American circus proprietor P. T. Barnum, some of whose exhibits were frauds which preyed upon the gullibility of the audience. Astrological columns present generalizations which apply to most people; people who read these columns are struck by the seeming relevance of the column to their own life and experiences, and therefore credit astrology with the status of a science.

The Barnum effect is also known as the Forer effect, after psychologist B. R. Forer who found that people tend to accept vague and general personality descriptions as uniquely applicable to themselves without realizing that the same description could be applied to almost anyone.

This effect is also known as the subjective validation effect, or the personal validation effect, because the validation of the construct under consideration is based on subjectivity, personal experience, and credulity.

3. The chi-squared test can be used to compare the Ham-D scores between patients treated with an experimental antidepressant drug and placebo.

False: The chi-squared test is used to compare proportions between two or more groups. For example, it could be used to compare the proportion of responders to non-responders in antidepressant- and placebo-treated groups.

The chi-squared test cannot be used to compare a quantitative variable, such as Ham-D scores, between groups.

For example, suppose 10 men and 15 women were randomized to receive a new antidepressant drug and 12 men and 12 women were randomized to receive placebo. We wish to find out whether the two treatment groups were similar in sex distribution at baseline. We use the chi-squared test to determine whether the sex distribution differed significantly between antidepressant- and placebo-treated groups.

4. The chi-squared test could be used in a study of response to a new antidepressant at four 3-monthly intervals in one hospital population.

False: Antidepressant response is commonly assessed as a continuous variable using measures such as the Ham-D. Repeated assessments of the same variable across time are tested using RMANOVA. As there is only one group being tested, the test would be one-way RMANOVA.

5. Correlation coefficient refers to how one variable alters with change in another paired variable.

False: Linear regression tests how one variable alters with changes in another paired variable. Correlation examines only the strength of association between two paired variables. Linear regression and correlation are related procedures.

6. Correlation coefficient ‘r’ may be used when studying non-linear relationships.

False: The Pearson’s product-moment correlation coefficient is used only when the relationship between the variables is linear (hence the concept of linear regression). It cannot be used when the relationship between the variables is nonlinear (hence the concept of curvilinear regression). Curvilinear relationships may be U-shaped, sigmoid, or of other shapes.

7. In a normal distribution, 68% of the population lies within one standard deviation of the mean.

True: In general, continuous variables in nature are normally distributed. This means that 68.3% of the population lies within one standard deviation of the mean; 95.5% lies within two standard deviations of the mean; and 99.7% lies within three standard deviations of the mean. A characteristic of the normal distribution is that the curve of variable value (X-axis) and frequency (Y-axis) is bilaterally symmetrical and shaped like a bell. Hence, the normal distribution is also known as the bell-shaped curve. It is also called the Gaussian distribution, after the mathematician Gauss. In the normal distribution, the mean, median, and mode coincide.

8. Standard error of a proportion will depend on the proportion in the wider population.

True: The standard error of a proportion is given by the square root of: P(1–P)/n where P is the value of the proportion and n is the sample size.

9. The Hawthorne effect can be a source of error.

True: The Hawthorne effect can be a source of error in any type of research. The Hawthorne effect is said to occur when the act of measurement influences that which is being measured. For example, when the behaviour of subjects is measured by observation, the subjects know that they are being observed, they become self-conscious and behave less naturally. Another example is when the pupil of the eye is measured. When light is thrown into the eye so that the pupil can be visualized, the pupil constricts. When measuring the length of the penis, touching can alter the variable being measured.

10. The least squares method is used for normally distributed continuous data.

True: The least squares method is used in regression to examine the relationship between continuous variables. One of the assumptions of the procedure is that the variables are normally distributed. If this assumption is not met, the procedure is carried out after log-transforming one or both variables. Alternatively, the procedure can be applied on the ranked data.

11. Logistic regression is used for categorical variables.

True: Logistic regression is used to predict or explain the value of a categorical variable which is dichotomous. It cannot be used when the variable is classified into three or more categories.

12. The arithmetic mean is equal to the median when the distribution of scores is unimodal and symmetrical.

True: A unimodal distribution has only one mode, and a symmetrical distribution is a normal distribution. In a normal distribution, the mean, median, and mode coincide.

13. The null hypothesis is that the two populations being compared are different.

False: The null hypothesis states that the populations under comparison do not differ significantly, or that the relationship between two variables is not significant. It is the alternative hypothesis which states that the populations are different, or that there is a significant relationship between variables.

14. Parametric statistics are generally more powerful than non-parametric tests.

True: This is why, wherever possible, variables should be operationalized along interval or ratio scales. Data so collected should never be split into categories unless there is a very definite reason to do so (e.g. a non-normal distribution, or a non-linear relationship between variables to be compared, or the existence of natural categories within the data).

Note that ‘powerful’ tests are those which are less vulnerable to a type II (false negative) error.

15. If, in a 60-year-old man, the probability of having A is 0.2, and B is 0.1, and both are independent, then the probability of having neither is 0.7.

False: The probability of NOT having A is 1.0 – 0.2 = 0.8. The probability of NOT having B is 1.0 – 0.1= 0.9. The probability of occurrence of BOTH of two independent events is given by the product of their individual probabilities. Therefore, the probability of occurrence of both ‘A absent’ and ‘B absent’ is 0.8 × 0.9 = 0.72. Note that the value of probability can range from 0 to 1. A probability of 1 means that the event will certainly occur, whereas a probability of 0 means that the event will certainly not occur.

16. Logistic regression is done by the least squares method.

False: Linear and multiple regression, which are applied to continuous variables, employ the least squares method. Logistic regression makes use of the binomial distribution in making its parameter estimates.

17. In the design of an experimental study, prospective methods are relatively inexpensive.

False: In retrospective designs, data are drawn from the charts of subjects already treated in the past. Prospective methods require a fresh sample to be drawn from the population. This may take much time, especially if the study selection criteria are rigorous. Longitudinal prospective studies are even more lengthy than cross-sectional studies. As a result, expenses mount. The advantages of retrospective designs are lower time and financial costs. Furthermore, more data may be available with retrospective designs. Retrospective research has many disadvantages. Subjects would not have been randomized. Data might not have been obtained in a standardized fashion. Data might not have been reliably recorded. All the relevant variables might not have been addressed. Appropriate assessment tools might not have been used. Situations might have changed. Cohort effects might be present due to changes in patterns of patient attendance, changes in assessment and treatment styles down the years, etc. Overall, therefore, retrospective studies are good when we want a large body of data, or data to formulate hypotheses. Prospective studies are preferable when we want to confirm hypotheses.

18. In psychological assessment, the response set is the responses the subject believes the interviewer wants.

False: Response set is a source of error in self-rated and certain other instruments. The simplest example of response set is when a subject answers ‘yes’ to a borderline question after answering ‘yes’ to a series of preceding questions; or, in the Wisconsin Card Sorting Test, when the subject sticks to the same rule of card sorting even after the rules have changed. Thus, a series of questions puts the subject into a frame of mind, and this frame of mind influences his responses to subsequent questions. Rating scales in which closely similar items are placed together are prone to ‘response sets’.

19. Snowballing can be used for random sampling.

False: Snowball sampling is the procedure whereby one subject recruits those of his contacts who are willing to participate in the study, and each of these contacts recruits further contacts. Snowballing is biased because only persons known to or through the initial contact are eligible for recruitment and they may not be representative of the population.

Snowballing is useful when it is hard to locate the population, e.g. to locate homosexuals in a society which does not allow the open expression of gay behaviour.

20. 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 sample is biased.

True: The ego-strength is likely to vary between, for example, girls who study in college and those who work in a factory. Therefore, girls who work in a factory cannot be considered representative of all girls of that age in the city.

21. A treatment trial shows no significant difference in efficacy between two antidepressants. This may be because the sample size considerations were based on active drug versus placebo comparison.

True: The difference between an antidepressant drug and placebo is likely to be large and, hence, a smaller sample size will be sufficient to adequately power the study to identify the difference to a statistically significant extent. In contrast, the difference between two antidepressant drugs is likely to be small and, therefore, larger sample sizes will be required to demonstrate the statistical significance of the difference. If power calculations are based on antidepressant vs. placebo, the sample size will not be adequate to identify true differences between two antidepressants.

22. A result statistically significant at a level of 5% implies that the result could not be accepted as valid.

False: It means that the null hypothesis is rejected and the alternative hypothesis is accepted.

23. A specific test has a low number of false negatives.

True: Specificity is the ability of the test to identify the absence of disease.

Specificity = true negatives/total non-cases. See Q23 in Statistics – 1.

24. Instruments need to result in a normal distribution of results to have validity.

False: If the Ham-D is administered to persons in the general population, most will obtain very low scores, but those who are depressed will obtain high scores. Thus, the distribution will be non-normal. However, Ham-D is still a valid measure of the severity of depression.

25. A researcher investigates the effect of smoking marijuana on motivation. He finds motivation levels lower in smokers than in a control population. In this study, marijuana smoking is the independent variable.

True: And motivation is the dependent variable.

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