- What are important concepts of research? - ExamTests 1
- How can data be described and explored? - ExamTests 2
- Why and how is a normal distribution used? - ExamTests 3
- How can you test hypotheses? - ExamTests 4
- What are the basic concepts of probability? - ExamTests 5
- When and how to use the Chi-square test? - ExamTests 6
- How to test hypotheses about means? - ExamTests 7
- What is the power of a statistical test? - ExamTests 8
- How to calculate the relationship between variables? - ExamTests 9
- Which other correlation techniques can be used? - ExamTests 10
- How to apply the analysis of variance? - ExamTests 11
- How to compare means for different treatment groups? - ExamTests 12
- How to use the ANOVA for two or more independent variables? - ExamTests 13
- How to apply the analysis of variance for repeated-measures designs? - ExamTests 14
- What is the procedure for multiple regression? - ExamTests 15
- How can the analysis of (co)variance be viewed as a special case of multiple regression? - ExamTests 16
- When and how to use log-linear models? - ExamTests 17
- Which techniques are used for resampling and nonparametric approaches to data? - ExamTests 18

## What are important concepts of research? - ExamTests 1

### MC-questions

#### Question 1

To estimate the percentage of Spanish inhabitants in the United States, we draw a sample from a small town in Nebraska. What is lacking in this case?

- Internal validity
- Random assignment
- External validity
- Non-random assignment

#### Question 2

A study is designed to examine the relationship between weight and length. In this study, 20 men and 20 women participate and they men and women are compared to each other. What type of variables are used here?

- Discrete variables
- Continuous variables
- Both
- Neither

#### Question 3

A researcher wants to examine the relationship between extraversion and self-esteem. For his study, 100 children fill out a questionnaire about extraversion, on which they can score between 1 and 10. A score of 1 means "introvert". A score of 10 means "very extravert". After filling out this questionnaire, the researchers asks the children to indicate how much self-esteem they have, again on a scale of 1-10. The researcher expects that children who score high on the questionnaire about extraversion, also indicate to have high self-esteem. What is the measurement scale here?

- Nominal
- Ordinal
- Interval
- Ratio

#### Question 4

For a research study of the University of Leiden, the BMI of 50 students is calculated. To do so, the weight and length are compared for different age groups. Which measurement scale is applicable here?

- Nominal
- Ordinal
- Interval
- Ratio

#### Question 5

Which term is used for a measure that refers to the population?

- Statistic
- Parameter
- Variable
- Sample

#### Question 6

Someone claims that the score of Elise on a certain variable is twice as high as the score of Adriaan. Which measurement scale is minimally required to make such a statement?

- Nominal
- Ordinal
- Interval
- Ratio

#### Question 7

For a research study, the variable intelligence is measured as follows:

1 = IQ below 70

2 = IQ between 71 and 90

3 = IQ between 91 and 110

4 = IQ between 111 and 120

5 = IQ above 120

What is the measurement scale of this variable?

- Nominal
- Ordinal
- Interval
- Ratio

### Open questions

#### Question 1

What is correlational research?

#### Question 2

A researcher wants to examine the extent to which giftedness of children in primary school associates with behavioral problems in the classroom. What type of research is appropriate to examine this research question?

### Answer indication MC-questions

#### Question 1

C. External validity. The sample does not represent the population well.

#### Question 2

C. both. Gender is discrete. Weight and length are continuous.

#### Question 3

B. ordinal. There is a order in the scale. However, there is not a legitimate difference between points on the scale. Neither does this scale have a "true" zero.

#### Question 4

C. ratio. There are legitimate differences between points on the scale. Yet, there is no "true" zero for BMI.

#### Question 5

B. parameter.

#### Question 6

D. ratio.

#### Question 7

B. ordinal.

### Answer indication Open questions

#### Question 1

With correlational research, the relationship between two (or more) variables is examined without making statements about cause and effect.

#### Question 2

Correlational research.

## How can data be described and explored? - ExamTests 2

### MC-questions

#### Question 1

Which statement is true?

I. A normal curve takes the mean and standard deviation of the data into account.

II. A kernel density plot takes the mean and standard deviation into account.

- Only statement I is true
- Only statement II is true
- Both statement I and II are true
- Both statement I and II are false

#### Question 2

Characteristics of a normal curve are (multiple answers may be applicable):

- A symmetric distribution
- A bimodal distribution
- Positive skewness
- Mesokurtosis

#### Question 3

Which measure of central tendency can be used for a variable with a nominal measurement scale?

- Variance
- Median
- Mode
- Mean

#### Question 4

Examine the following scores: 11 15 19 26 37

Which statement is true?

- The median is 19
- The first quartile is 15
- The distribution is positively skewed
- The interquartile range is 26

#### Question 5

A study is designed to examine the mean IQ of children on a school in Leiden. A sample is drawn that consists of six children. Their IQ scores are: 110 105 80 85 90 100.

What is the variance?

- 140
- 10,95
- 120
- 11,83

#### Question 6

Suppose the following scores: 3 4 6 8 19

I. The inner fence is -2 to 14

II. The score of 19 is an outlier

Which statement is true?

- Only statement I is true
- Only statement II is true
- Both statement I and II are true
- Both statement I and II are false

#### Question 7

The collected data is multiplied by 3. The old standard deviation is 1.41. The score of Floor is 5. What is the new variance?

- 15
- 18
- 36
- 45

### Open questions

#### Question 1

After the exam of M&T, we examined for 11 students how many of the 40 questions they answered correctly. Their scores are depicted in a stem-and-leaf diagram:

0 | 2 | 6 | 6 | |

1 | 0 | 8 | 9 | |

2 | 1 | |||

3 | 4 | 6 | 8 | 9 |

What is the median?

#### Question 2

What is the median of the scores: 4-6-8-10-18?

#### Question 3

What is the median of the scores: 8, 9, 14, 15?

### Answer indication MC-questions

#### Question 1

A. A kernel density plot does not take into account the mean and standard deviation, but aim to plot the data with a smooth curve, taking into account that each measurement may have random noise.

#### Question 2

A and D. Normal curves have a symmetric distribution and tails that are not too thick or too thin. In addition, there are not too many or too few scores centered in the middle of the distribution.

#### Question 3

C. The mode represents the most common score, which is the only relevant measurement for variables with a nominal measurement scale.

#### Question 4

D. The IQR is 26 - 15 = 11 (instead of 26).

#### Question 5

A. The mean is 9, so:

Sigma (X -)2 = (110 - 95)2 + (105 - 95)2 + (80 - 95)2 +95)2 + (90 95)2 + (100 - 95)2 = 225 + 100 + 225 + 100 + 25 + 25 = 700.

700/n-1 = 700/5 = 140.

#### Question 6

C. The first quartile is 4, the third quartile is 8. The inner fence lies 4 x 1.5 = 6 points above the first and third quartile, thus it runs from -2 to 14. Score 19 is then an outlier, because it lies outside the inner fence.

#### Question 7

C. Variance is: s^{2} = 1,412 is approximately 2 and s^{2}_{new} = 32 x s^{2}_{old} = 9 x 4 = 36

### Answer indication Open questions

#### Question 1

19

#### Question 2

8

#### Question 3

11.5

## Why and how is a normal distribution used? - ExamTests 3

### MC-questions

#### Question 1

Which statement is true?

I. The normal distribution is a symmetric, unimodal distribution.

II. T-scores have a mean of 0 and a standard deviation of 1.

- Only statement I is true.
- Only statement II is true.
- Both statements are true.
- Both statements are false.

#### Question 2

For a study about the IQ of primary school students, one child scores an exceptional score of 145. The mean IQ is 100, the standard deviation is 15. How many standard deviations does the child's score deviate from the mean?

- 45
- 3
- 1.96
- 3

#### Question 3

What is the size of the are under the normal curve from z = 1.5 onward?

- 0,4394
- 0,9394
- 0,0606
- 0,1200

#### Question 4

We asked 20 women living in Groningen about their weight. The mean weight of these women is 87 kg with a standard deviation of 5. Between which values will 95% of the women score?

- 77,2 - 96,8
- 82,3 - 91,8
- 72,5 - 101,5
- 74,5 - 99,5

#### Question 5

What does an ordinate (one of the axis of a histogram) represent?

- The different values of X
- The density of X
- The frequency of X
- The chance on X

### Open questions

#### Question 1

You are comparing the sizes of mussels in the sea in two mussel populations using a z-test; the test statistic has the value z = 3.5. What is the most correct conclusion?

#### Question 2

A professional choice agency uses a standardized IQ test for HAVO students from the highest class. This test has a variance of 225. The scores obtained with this are normally distributed. A sample of 25 students from the group who registered at this agency for advice scores an average of 119 on this test. What is the 95% confidence interval of the population average?

### Answer indication MC-questions

#### Question 1

A. The normal distribution is symmetric and has only one mode (peak). Statement II does not belong to t-scores, but to z-scores.

#### Question 2

B. Z = (145-100)/15 = 3

#### Question 3

C. 2,050X + 0,835

#### Question 4

A. X = mu +/11,96sigma, so X = 87 +/- 1,96 x 5 = 87 +/- 9,8 = 77,2 until 96,8

#### Question 5

B. The density of X. This axis is related to the frequency and probability, but is not exactly the same. The possible values of X are shown in the horizontal axis, or abcissa.

### Answer indication Open questions

#### Question 1

Because a z-test has been used you can assume that the shell sizes are normally distributed and that this is the difference in average shell size between the two populations (the median is used for non-normally distributed quantities). The chance of exceeding s = 3.5 is 0.00023, and this is much smaller than 0.05; there is a significant difference in average shell size between the two populations.

#### Question 2

113.12 ≤ mu ≤124.88

## How can you test hypotheses? - ExamTests 4

### MC-questions

#### Question 1

Which statement is true?

I. With a sampling distribution of the differences between means, we can test the chance that the data occur, assuming that the null hypothesis is true.

II. If the null hypothesis is rejected, this implies that the population means are equal.

- Only statement I is true.
- Only statement II is true.
- Both statements are true.
- Both statements are false.

#### Question 2

Which statement is true?

I. A type-I error is the chance to reject H0, while in fact H0 is true.

II. Raising alfa lowers the chance on type-II errors

- Only statement I is true.
- Only statement II is true.
- Both statements are true.
- Both statements are false.

#### Question 3

Why are two-sided tests often used in research?

- Because it is often unclear what the direction of the effect will be.
- Because researchers want to test as conservatively as possible.
- Both the above options are correct.
- Both of the above options are incorrect.

#### Question 4

Complete the sentence below:

A sampling distribution is the distribution of ... at ... samples.

- averages; repeated
- variance; repeated
- averages; replications of
- variance; replications of

### Open questions

#### Question 1

Which steps are taken during hypothesis testing?

#### Question 2

A person is judged and found guilty in a court case. After a few months it appears that this person is innocent and is acquitted. Has a mistake been made here, and if so, which mistake has been made here?

#### Question 3

The statistical power of a test to demonstrate a certain difference of at least 50% between control group and treated group in an experiment is 0.4. What does this mean?

#### Question 4

For a research study, the affinity with eating meat was examined for a sample of 134 students. To half of the sample, films were shown before the study about how meat is made. The other half watched a comedy movie. The following data is known: The average of the first group is 4.78 with a standard deviation of 1.61. The average of the second group is 4.54 with a standard deviation of 1.56. Perform the appropriate t-test on this data. Can you reject the null hypothesis when you test one-sided with a = 0.05?

#### Question 5

A certain matched pairs t-test yields a significant result with a significance level of 5%. The power of this test with a reasonable effect size is 0.12. What is the probability of incorrectly rejecting the null hypothesis?

#### Question 6

The time that students need to solve an exam question is normally distributed with an average of 30 seconds and a standard deviation of 3 seconds. You want to examine whether the average time mu changes after exercise. You do this by having 9 randomly selected students practice for 30 minutes with the exam question. Then you let them make the specific question and you measure the time, X, that it takes to solve this question. Assume that the standard deviation remains 3 seconds. For which values of x do you reject the null hypothesis that mu equals 30 seconds for a two-sided test with a = 0.01?

### Answer indication MC-questions

#### Question 1

A. Only statement I is correct. If the null hypothesis is rejected, then the means are not the same.

#### Question 2

C. Both statements are true.

#### Question 3

C. Both are correct.

#### Question 4

A. Averages; repeated. It is a distribution of values (the sample means) for a certain variable, with repeated samples (passing through the same experiment for a large number of samples).

### Answer indication Open questions

#### Question 1

- Set up a research hypothesis, for example: People take longer to leave if someone waits for their parking space.
- Collect samples of both conditions (time with waiting people / no waiting people).
- Set up up a null hypothesis (H0) that the samples come from populations with the same average: departure times do not depend on whether someone is waiting.
- Obtain a sampling distribution of differences between averages, assuming H0 is true.
- Calculate the probability of an average difference at least as large as that we found in the sample.
- Decide on the basis of that probability whether we can reject or retain H0. If we reject H0, it means that the population means are not the same.

#### Question 2

A type-I error was made. He was charged while he was not guilty. The null hypothesis is based on our legal system. This states: "You are innocent until your guilt is proven."

#### Question 3

This means that if there really is a 50% difference, the test gives a significant result in 40% of the cases. The null hypothesis H0 in this test is: there is a difference of less than 50% between control group and treated group; the alternative hypothesis says that there is at least a 50% difference between the two groups. A power of 0.4 means that the probability of rejecting an incorrect H0 is 0.4. To reject H0, a significant result must be found. Because the chance of this is 0.4, this is expected to happen in 40% of the cases.

#### Question 4

No, p > .05

#### Question 5

5%

#### Question 6

For all x values that are less than 27,424 or greater than 32,576

## What are the basic concepts of probability? - ExamTests 5

### MC-questions

#### Question 1

There are 100 smarties in a bag: 20% is brown, 19% is yellow, 12% is green, 9% is red and 25% is blue and 15% is orange. What is the chance that I will take a red and a yellow smartie, regardless of the order?

- 0.034
- 0.280
- 0.090
- 0.191

#### Question 2

3000 students enroll at Leiden University. 40% of that is male. 800 students enroll in psychology, including 45 men. 1) What is the joint probability that someone is a woman and will study psychology p (V and Psy), and 2)? What is the conditional probability that a man will study something other than psychology p (And | M)?

- p (V and Psy) = 0.57; p (And | M) = 0.99
- p (V and Psy) = 0.25; p (And | M) = 0.96
- p (V and Psy) = 0.57; p (And | M) = 0.96
- p (V and Psy) = 0.25; p (And | M) = 0.99

#### Question 3

- Probability that the patient has cancer p (Y +): 15%
- Probability that the patient has no cancer p (Y-): 85%
- Probability of positive diagnosis given that patient has cancer p (X + | Y +): 95%
- Probability of positive diagnosis given that patient has no cancer p (X + | Y-): 5%

Calculate the probability that the patient has given cancer that the patient has received a positive diagnosis p (Y + | X +).

- 0.52
- 0.65
- 0.77
- 0.90

#### Question 4

What is the mean and standard deviation of a binomial distribution with n = 12 and p = 0.30?

- Mean = 6 ; standard deviation = 1.59
- Mean = 3.6; standard deviation = 1.59
- Mean = 6; standard deviation = 1.73
- Mean = 3.6; standard deviation = 1.73

#### Question 5

Which statement is true?

I. When it comes to probability calculation with discrete variables, we speak of the probability of an outcome within an interval.

II. With combinations, the order of object selection is more important than with permutations.

- Only statement I is true
- Only statement II is true
- Both statements are correct
- Both statements are false

### Answer indication MC-questions

#### Question 1

A. p (red, yellow) = 0.09 x 0.19 = 0.0171 and p (yellow, red) = 0.19 x 0.09 = 0.017. The total probability is 0.0171 + 0.0171 = 0.0342.

#### Question 2

B. Of the 3000 students, 40% are men (= 1200) and 60% are women (= 1800). 800 students enroll in psychology, 45 of them male and 755 female. The probability that someone is a woman and will study psychology is 755/3000 ≈ 0.25. The conditional probability that a man will study something else is (1200-45) / 1200 = 1155/2000 ≈ 0.96

#### Question 3

C. p (Y+|X+) = (0.95)(0.15)/((0.95)(0.15)+(0.05)(0.85)) = 0.1425/(0.1425 + 0.0425) ≈ 0.77

#### Question 4

B. Mean = 12 x 0.30 = 3,6. Standard deviation: ≈ 1,59

#### Question 5

D. Both statements are incorrect. With discrete variables you can speak of the probability of a specific outcome, with continuous variables you can speak of the probability of an outcome within an interval. With permutations, the order is more important in comparison with combinations.

## When and how to use the Chi-square test? - ExamTests 6

### MC-questions

#### Question 1

Men | Women | |

A | 34 | 51 |

B | 23 | 67 |

C | 87 | 43 |

What are the expected frequencies for men?

- 50.83 for all three
- 40.13 - 42.49 - 61.37
- 48 for all three
- 42.35 - 43.02 - 59.28

#### Question 2

It is being examined whether the 'male / female' ratio among students differs between the law, social sciences and arts faculties. The proportion of men is 0.37 for law, 0.18 for social sciences and 0.24 for art. 100 students were studied in law and social sciences and 50 students in art. Can the H0 be rejected with a = .05?

- No, P> .05
- Yes .025
- Yes, .01
- Yes, P <.01>

#### Question 3

The relationship between the degree of extraversion and self-confidence (four and three categories respectively) of 30 subjects is examined. The Chi-square value is 12.01. How many degrees of freedom are there?

- 5
- 6
- 7
- 8

#### Question 4

Which statement is true?

I. An assumption of the chi-squared test is that the variables are independent of each other.

II. The expected frequencies are the frequencies that you would expect if the null hypothesis were true.

- Only statement I is true
- Only statement II is true
- Both statements are true
- Both statements are false

#### Question 5

It is said that cholesterol greatly increases the risk of cardiovascular disease. For example, cholesterol is in eggs. This study looks at how often people who eat an egg four times a week later develop cardiovascular disease and how often people who never eat eggs get heart disease.

Cardiovasuclar disease | No cardioviscular disease | Total | |

Eggs | 520 | 390 | 910 |

No eggs | 410 | 625 | 1035 |

Total | 930 | 1015 | 1945 |

What is the risk ratio for cardiovascular disease?

- 1.23
- 1.35
- 1.43
- 1.56

### Open questions

#### Question 1

A researcher examines the relationship between the degree of alcohol consumption and the study result (both variables have three categories). He has examined 15 people, and finds a chi-square value of 1.3. How many degrees of freedom does he have to test?

#### Question 2

To test whether there is an association between sex and smoking behavior (smoking or not) you count the number of smokers and non-smokers in a group of 75 men and 69 women. Then you perform a chi-square test. What is the number of degrees of freedom?

#### Question 3

One wants to know whether the "male / female" ratio among employees of company A and B is different. On a sample basis, it is established that the proportion of men in company A is 0.40 and company B is 0.52. In both cases, 100 students were examined. Test the null hypothesis with the chi-square test. What value does the test statistic have?

#### Question 4

A researcher checks whether the moment of birth influences whether someone becomes a professional gymnast. For this, random 220 gymnasts have been selected who have trained during the past 10 years. The quarter in which they were born is determined: first quarter 62, second quarter 69, third quarter 40 and the fourth quarter 49. Test the null hypothesis with the chi-square test. What is the value of the test statistic?

### Answer indication MC-questions

#### Question 1

B. 85 x 144/305 = 40,13; 90 x 144/305 = 42,49; 130 x 144/305 = 61,37

#### Question 2

D. χ² = ∑ (O-E)2/E = 61,24. df = 2. P

An example table with associated proportions is provided below.

Men | Women | Total | |

Law | 37 (50) | 63 (50) | 100 |

Social sciences | 18 (50) | 82 (50) | 100 |

Art | 12 (25) | 38 (25) | 50 |

Total | 67 | 183 | 250 |

#### Question 3

B. (R-1)(C-1) = (4-1)(3-1) = 6

#### Question 4

B. Only statement II is correct. The Chi-square test examines the independence of variables. An important assumption to perform the test is that the observations are independent.

#### Question 5

C. 520/910 = .57; 410/1035 = .40; RR = .57/.4 = 1.43

### Answer indication Open questions

#### Question 1

4

#### Question 2

The variable gender has 2 classes (male, female), and the variable blow also 2 (blow, not blow). The number of degrees of freedom is then (2 - 1) x (2 - 1) = 1. (In other words: there are four possible combinations with the 2 x 2 classes: woman and blow, woman and not blow, man and blow, and man If you know the numbers in one of the four classes, then the numbers in the other three classes are fixed because you know how large the numbers of men and women you have interviewed for your test are. Hence, the degrees of freedom is 1.

#### Question 3

2.899

χ² = (40-46)2/46 + (52-46)2/46 + (60-54)2/54 + (48-54)2/54

χ² = 36/46 + 36/46 + 36/54 + 36/54 = .782 + .782 + .667 + 667 = 2.889

#### Question 4

9.20

## How to test hypotheses about means? - ExamTests 7

### MC-questions

#### Question 1

In a study with 120 people, the population mean is 35 with a standard deviation of 3. What are the mean and the variance of the sample distribution from the mean?

- 35 and 0.075
- 30 and 0.244
- 35 and 0.274
- 30 and 0.075

#### Question 2

Suppose we have a t-value of 1.965 in a study with 40 people. Is this a significant result with unilateral testing with a = 0.05?

- No, P> .05
- Yes .025
- Yes, .01
- Yes, P <.01>

#### Question 3

Suppose we have = 5, s = 1.3 and n = 20. We test on both sides with a = .05. What is the 95% confidence interval?

- 4.23 - 5.45
- 4.34 - 5.54
- 4.39 - 5.61
- 4.43 - 5.65

#### Question 4

A study is being conducted with 30 children into the number of hours of watching television per day. In America the average is 4.5 hours. The average in the Netherlands is thought to be lower. It appears that mu = 3.5 hours and s2 = 1.2. Can the H0 be rejected with a = 0.05 if left-side testing is done?

- No, P> .05
- Yes .025
- Yes, .01
- Yes, P <.01>

#### Question 5

It is examined whether two populations have a different mean. It is known that n1 = 35 and n2 = 43 and s1 = 3 and s2 = 4.5. This hypothesis can best be tested with a:

- Z test for two independent samples
- T-test for two dependent samples
- T-test for two independent samples with pooled variances
- T-test for two independent samples with separate variances

### Answer indication MC-questions

#### Question 1

A. Sample average is equal to population average. Variance is: 32/120 = 0.07

#### Question 2

B. Yes, 0.025

#### Question 3

C. t.025 (19) = 2,09 +/- 2,093.

Rewrite to = +/- 2,093(0,291) + 5 = +/- 0,609 + 5

Upper = + 0,609 + 5 = 5,61;

Lower = - 0,609 + 5 = 4,39

#### Question 4

D. H0 = muN t,05 (29) = 1,699. So p

#### Question 5

C. T-test for two independent samples with pooled variances. We are interested in two different populations; so we use an independent t-test sample for that. The sample sizes are uneven, so we use pooled variance to get a more accurate estimate of the population variance.

## What is the power of a statistical test? - ExamTests 8

### MC-questions

#### Question 1

It is examined for 40 people how many hours of driving lessons they had before they passed. According to the CBR, the distribution is n (50.5), but the driving examiners think this is higher. With an a of 0.05, H0: mu = 80 and Ha: mu = 90, what is the effect size (Cohen's d)?

- -3
- -2
- 1
- 2

#### Question 2

We perform a one sample t-test on 30 clients with psychological problems. We look for at least an eight point difference between the general population and this group. It is known that mu0 = 120, sigma = 23, mu1 = 130 and a = 0.05 (two-sided). What is the chance that the null hypothesis will be wrongly not rejected?

- 0,35
- 0,41
- 0,45
- 0,52

#### Question 3

What is d in a study with mu0 = 10, mu1 = 8, and sigma = 0.5 with two research groups of 20 participants?

- 11,23
- 12,65
- 13,78
- 14,25

#### Question 4

Which of the variables does not influence the power?

- The alpha level
- The alternative hypothesis
- The sample size
- The effect size

### Open questions

#### Question 1

The scores of a certain variable are normally distributed in the population with a standard deviation of 12. Suppose that the right-hand side testing is done with the null hypothesis that the population mean is equal to 80. The null hypothesis is known to be rejected from a sample mean of 82.5. What would the power be if the population average was 86?

#### Question 2

A certain matched pairs t-test yields a significant result at a significance level of 5%. The power of this test with a reasonable effect size of 0.12. What is the probability of incorrectly rejecting the null hypothesis?

### Answer indication MC-questions

#### Question 1

B. d = (80-90)/5 = -2

#### Question 2

A. d = (130-120)/23 ≈ 0,43. δ = 0,43 ≈ 2,36

The power thus lies between 0,63 and 0,67, so on average 0,65. The type-II error probability = 0.35

#### Question 3

B. d = (10-8)/0,5 = d = 4 ≈ 12,65

#### Question 4

D. The effect size

### Answer indication Open questions

#### Question 1

0.99

#### Question 2

5%

## How to calculate the relationship between variables? - ExamTests 9

### MC-questions

#### Question 1

Which statement is true?

I. If the correlation is examined, two random variables are involved.

II. In a regression, Y is predicted based on X.

- Only statement I is true.
- Only statement II is true.
- Both statements are true.
- Both statements are false.

#### Question 2

Six people participate in a study focusing on the relationship between extraversion and self-confidence. For both variables, scores range between 1 and 10. The scores of these individuals are:

Individual | 1 | 2 | 3 | 4 | 5 | 6 |

Extraversion (X) | 6 | 2 | 7 | 9 | 10 | 5 |

Self-confidence (Y) | 5 | 4 | 9 | 6 | 7 | 4 |

What is the covariance?

- 2,5
- 3,5
- 4,5
- 5,5

#### Question 3

The correlation between X (educational level) and Y (income) is 0,65. Further, it is known that sx = 1.00 and sy = 1,50. What is the regression equation?

- 1,950X + 0,675
- 2,035X + 0,755
- 2,050X + 0,835
- 2,075X + 0,975

#### Question 4

In a study with 20 participants, we find a correlation of 0.67. What is the correlation coefficient of the population?

- 0,59
- 0,61
- 0,63
- 0,65

#### Question 5

The regression equation is Y = 3,55X + 1,30. What is the predicted score of an individual with score 10 on X?

- 33,25
- 36,80
- 40,35
- 43,90

### Answer indication MC-questions

#### Question 1

C. Both statements are true.

#### Question 2

B. = 6,5 en ≈ 5,83. ∑(X-)(Y-) / (N-1) = (0,415 + 8,235 + 1,585 + 0,425 + 4,095 + 2,745) / (6-1) = 17,5 / 5 = 3,5

#### Question 3

D. 0,65 = covxy / 1 x 1,5. Dus covxy = 1,5 x 0,65 = 0,975

b = 0,975 / 1,002 = 0,975 and a = 5 - 0,975 x 3 = 2,075 = 2,075X + 0,975

#### Question 4

D.

#### Question 5

B. 3,55 x 10 + 1,30 = 36,80

## Which other correlation techniques can be used? - ExamTests 10

### MC-questions

#### Question 1

A study with 15 participants found a point-biserial correlation of .45 between economic status and physical health. We test the null hypothesis (ρ = 0). Is the t value significant with an a = 0.05?

- No, P> .05
- Yes .025
- Yes, .01
- Yes, P <.01>

#### Question 2

We examine twenty men and twenty women for alcohol consumption. It is checked whether they drink more than two glasses of alcohol per day (much) or less (little). The hypothesis is that women drink less than men. The x2 is determined. What is correct with an a = .05?

Female (X = 0) | Male (X = 1) | |

Few (Y = 0) | 13 | 9 |

Many (Y = 1) | 7 | 11 |

- X
^{2}significant and*p*= 0.22 - X
^{2}significant and*p*= 0.32 - X
^{2}not significant and*p*= 0.22 - X
^{2}not significant and*p*= 0.32

#### Question 3

Country | Whiskey (1) | Wine (2) | Rank 1 | Rank 2 | Conversions |

A | 3,21 | 4,78 | 1 | 2 |

What is Kendall’s Tau coefficient (t)?

- 0,00
- 0,10
- 0,15
- 0,20

#### Question 4

Which type of correlation is used if one of the two variables is dichotomous?

- Pearson’s r
- The point-biserial correlation
- The Phi coefficient
- Spearman’s Rho

#### Question 5

Anne conducts research on problem behavior in children. To study this, she had eight observers rank the problem behavior of the children. Which correlation measure can Anne best use to determine to what extent the observers agree?

- Kendall’s tau
- Kendall's W
- Spearman’s Rho
- Spearman’s Rs

### Open questions

#### Question 1

The (Pearson's) correlation coefficient for two variables x and y is 0.7. What is the percentage of variability in y that is explained by variable x?

#### Question 2

For the following three pairs of observations (x, y) you determine the Spearman rank correlation coefficient: (1, 1), (2, 2) and (3, 3). What happens to this correlation coefficient when you change the last pair to (3, 25)?

### Answer indication MC-questions

#### Question 1

t = 0.45/ = 1,51/0,89 ≈ 1,70

t.05 (13) = 1,77. So the t-value is not significant.

#### Question 2

C. The expected value in each cell is 10.

X^{2} = 0,9 + 0,9 + 0,1 + 0,1 = 2,0. X2 (1) = 3,84. = 0,22

#### Question 3

A. The number of conversions is: A = 1, B = 2, C = 0, D = 0.

Total number ofconversions is: 3

Number of pairs of scores: 4(4-1)/2 = 12/2 = 6

t = 1 - 2(3)/6 = 1 - 6/6 = 0. T is significant.

#### Question 4

B. The point-biserial correlation. You use Pearson’s R with continuous variables with a linear relationship. The Phi coefficient is used with two dichotomous variables. Spearman's rho is used with ordered data.

#### Question 5

B. Kendall’s W. The other techniques are used when there are two sets of scores (X and Y).

### Answer indication Open questions

#### Question 1

49%. The percentage variability in one variable that is explained by the other variable is equal to (squared correlation coefficient) x100%.

#### Question 2

The Spearman rank correlation coefficient does not change, because the change from y = 3 to 25 has no influence on the differences in the rank numbers with which the correlation coefficient is calculated.

## How to apply the analysis of variance? - ExamTests 11

### MC-questions

#### Question 1

Which statement is true?

I. An assumption of ANOVA is that the variances are homogeneous.

II. If the largest variance is no more than four times as large as the smallest, the ANOVA is still valid.

- Only statement I is true
- Only statement II is true
- Both statements are true
- Both statements are false

#### Question 2

A study is being conducted with 120 people who are divided into three groups. Complete the table below and see if F is significant with a = .05

Source | df | SS | MS | F |

Treatment | 23,45 |

- No, P > .05
- Yes, .025
- Yes, .01
- Yes, P

#### Question 3

Which statement is true?

I. Logarithmic transformations reduce standard deviations more with large samples than with small samples.

II. Square root transformations ensure that outliers have less effect on the size of the standard deviation.

- Only statement I is true
- Only statement II is true
- Both statements are true
- Both statements are false

#### Question 4

We investigate the influence of three different antidepressants on the degree of depression and find the following averages and standard deviations:

Condition | Mean | Si | Ni |

1 | 2,8 | 0,9 | 10 |

Perform the ANOVA (SS_{total} = 120.3). Can H0 be rejected with α = .05 and what is the effect size?

- F is significant and n
^{2}is 0.31 - F is significant and n
^{2}is 0.69 - F is not significant and n
^{2}is 0.31 - F is not significant and n
^{2}is 0.69

#### Question 5

Which effect size is most suitable for variance analyses with a balanced design?

- Eta squared
- Percent Reduction in error (PRE)
- Omega squared
- Root-mean-square standardized effect (RMSSE)

### Answer indication MC-questions

#### Question 1

C. Both statements are correct. This assumption of homogeneity is also called homoscedasticity.

#### Question 2

D. df_{treatment} = k - 1 = 2, df_{total} = N - 1 = 119, df_{error} = 117

MS_{treatment} = 23.45 / 2 = 11.725; MS_{error} = 0.480

F = 24,427. F.01 (2.177) = 4.79. So F is significant

#### Question 3

A. Only statement I is correct. This difference in logarithmic transformations is caused by the fact that the right-hand side of the distribution (with positive values) is compressed more strongly than the left-hand side.

#### Question 4

B. = 3.8

Source | df | SS | MS | F |

Treatment | 2 | 83,4 | 41,70 | 30,44 |

F.01 (2, 27) = 5,45. So F is significant.

η² is 83,4/120,3 = 0,69

#### Question 5

C. Omega squared. This method often results in less distortion.

## How to compare means for different treatment groups? - ExamTests 12

### MC-questions

#### Question 1

Which statement is true?

I. Linear contrasts are generally priori comparisons

II. The Bonferroni test is an a priori comparison

- Only statement I is true
- Only statement II is true
- Both statements are true
- Both statements are false

#### Question 2

Which statement is true?

I. Orthogonal coefficients are independent of each other, because ∑ajbj = 0.

II. Using the Bonferroni correction reduces the chance of type I errors.

- Only statement I is true
- Only statement II is true
- Both statements are true
- Both statements are false

#### Question 3

We conduct a survey with 30 people. The standard error is 4.5. = 25, = 20. What is the studentized range (q)?

- 11.50
- 12.30
- 12.90
- 13.40

#### Question 5

Condition | df | SS | MS | F |

Treatment | 4 | 35,67 | 8,92 | 12,93 |

There are five conditions with the following averages:

1 = 1.23 - 2 = 1.30 - 3 = 0.80 - 4 = 0.95 - 5 = 1.11

Is the linear component significant with α = .05?

- No, P> .05
- Yes .025
- Yes, .01
- Yes, P <.01>

### Answer indication MC-questions

#### Answer 1

A. Only statement I is correct. Linear contrasts are usually calculated with a priori tests. The Bonferonni t-test can be used either a priori or a posteriori.

#### Answer 2

C. Both statements are correct.

#### Answer 3

C. t = (25-20) / = 5 / 0.548 = 9.12. q = 9.12 ≈ 12.90

#### Answer 4

A. linear = (-2) 1.23 + (-1) 1.30 + (0) 0.80 + (1) 0.95 + (2) 1.11 = - 0.59

SSlinear = 30 ∙ (-0.59) 2/10 = 1.044. F = 1.044 / 0.69 = 1.513. F.05 (1.25) = 4.26

So F, the linear component, is not significant.

## How to use the ANOVA for two or more independent variables? - ExamTests 13

### MC-questions

#### Question 1

Which statement is true?

I. A simple effect is the effect of one variable on one level of another variable.

II. A significant interaction effect means that the effect of one variable depends on the level of the other variable.

- Only statement I is true
- Only statement II is true
- Both statements are true
- Both statements are false

#### Question 2

Research is being conducted into the reaction speed of two age groups. When a blue number appears on the screen, they must press the left key and, with a yellow number, the right key. How many degrees of freedom are used with the interaction effect?

- 1
- 2
- 3
- 4

#### Question 3

Which statement is true?

I. The same F value is always calculated for random factors.

II. A fixed effect changes the test for the random effect.

- Only statement I is true
- Only statement II is true
- Both statements are true
- Both statements are false

#### Question 4

A 2 x 5 factorial design has ... factors with respectively ... levels.

- 7; 7
- 2; 7
- 5; 2
- 2; 7

#### Question 5

A combination of the levels of the variables is also called a ....

- Factor
- Cell
- Mixed model
- Conditional effect

### Answer indication MC-questions

#### Question 1

C. Both statements are true.

#### Question 2

A. df_{L∙C} = (2-1)(2-1) = 1

#### Question 3

D. Both statements are false.

#### Question 4

B. Two factors with 2 and 5 levels; so 7 levels total.

#### Question 5

B. Cell.

## How to apply the analysis of variance for repeated-measures designs? - ExamTests 14

### MC-questions

#### Question 1

Which statement is true?

I. For repeated measures, the different scores are independent of each other.

II. Within subjects variances consists of variance by treatments and error variance.

- Only statement I is true
- Only statement II is true
- Both statements are true
- Both statements are false

#### Question 2

We investigate the effect of psychotherapy on the severity of depression among ten participants. We have four measurement moments. The first measurement is the baseline, the second is immediately after the psychotherapy sessions, the third is two weeks after the psychotherapy sessions and the last measurement is a follow-up half a year after the sessions. We compare the first measurement moment with the last three measurement moments. MS_{error} = 8.20. Is the t-value significant?

Measurement 1 | Measurement 2 | Measurement 3 | Measurement 4 |

12,50 | 25,33 | 23,60 | 19,45 |

- No, P > .05
- Yes, .025
- Yes, .01
- Yes, P

#### Question 3

Source | df | SS | MS | F |

Between subjects | 7 | 50,230 | 7,176 | 36,20 |

What is the reliability?

- 0,54
- 0,62
- 0,73
- 0,79

#### Question 4

Under what name is the condition known that states that there is compound symmetry?

- Heteroscedasticity
- Sphericity
- Homogeneity of variances
- Multicollinearity

#### Question 5

The interclass correlation can be used to check whether a measurement is ....

- Reliable
- Content valid
- Predictive
- Convergent valid

### Answer indication MC-questions

#### Question 1

B. Only statement II is true. For repeated measures, scores are actually *dependent* on each other.

#### Question 2

D. = (-1)12,50 + (1/3)25,33 + (1/3)23,60 + (1/3)19,45 = -12,50 + 8,44 + 7,87 + 6,48 = 10,29. t = 10,29 / = 10,29/1,044 = 9,86. dferror = (n-1)(k-1) = 9 x 3 = 27. t.01 (27) = 2,473. So t-value is significant at p = 0,01.

#### Question 3

C. Intraclass correlation = (7,176 - 0,096)/(7,176 + (5-1)0,096 + 5(3,475 - 0,096)/8) = 7,08 / (7,176 + 0,384 + 2,112) = 7,08 / 9,672 ≈ 0,7

#### Question 4

B. Sphericity (constant variance between and within treatments).

#### Question 5

A. Reliable. It specifically concerns inter-reliability here.

## What is the procedure for multiple regression? - ExamTests 15

### MC-questions

#### Question 1

Unstandardized | Standardized | t | Sig. | ||

Model | B | Std. Error | Beta | ||

Constant | 35.00 | 2.30 | .350 | 26.00 | .000 |

What is the regression equation?

- = 35,00 + 13,45X1 + 11,13X2
- = 2,30 + 1,50X1 + 0,96X2
- = 35,00 - 13,45X1 - 11,13X2
- = 2,30 - 1,50X1 - 0,96X2

#### Question 2

We want to study why some people with depression recover sooner than others. We take a questionnaire from 30 participants to measure the severity of the depression. We do this at two moments, to track progress or decline. We think three things are important: psychotherapy, medication and social support. We include these three variables in our analysis. The multiple correlation coefficient is .85. Is the effect of these three variables on the severity of depression significant?

- No, P > .05
- Yes .025
- Yes, .01
- Yes, P

#### Question 3

Which statement is true?

I. The degree of mutual correlation between predictors is called multicollinearity.

II. With a regression analysis we want the lowest possible tolerance.

- Only statement I is true
- Only statement II is true
- Both statements are true
- Both statements are false

#### Question 4

Take a look at the table below. Which point do we prefer to remove?

Observation | X | Y | Residual | Distance | Leverage | Influence | Cook's D |

A | 1 | 1 | 2 | 2.30 | 1.63 | 0.10 | 0.99 |

- Point A
- Point B
- Point C
- Point D

#### Question 5

Which statement is true?

I. In mediating relationships, the relationship between the independent and dependent variable has to be significant.

II. A mediator influences the direct relationship between the independent and dependent variable.

- Only statement I is true
- Only statement II is true
- Both statements are true
- Both statements are false

### Answer indication MC-questions

#### Question 1

A. = 35,00 + 13,45X1 + 11,13X2.

#### Question 2

D. F = ((30-3-1).852) / 3(1-.852) = 18,785/0,833 = 22,55

df = 3 and df = 30-3-1 = 26. F.01(3,26) = 4,64.

#### Question 3

A. Only statement I is true. It is desirable to have a high tolerance, implying little overlap between the predictors.

#### Question 4

C. Point C.

#### Question 5

A. Only statement I is true. Mediation concerns a indirect relationship.

## How can the analysis of (co)variance be viewed as a special case of multiple regression? - ExamTests 16

### MC-questions

#### Question 1

Which statement is true?

I. The rows, columns, and interaction-effects in a design matrix are independent of each other.

II. A design matrix shows to which group a participant belongs

- Only statement I is true
- Only statement II is true
- Both statements are true
- Both statements are false

#### Question 2

We have a 2x3 factorial design with 30 participants. Complete the table below and see if the F-values are significant with a = .05.

Source | df | SS | MS | F |

A | 34.67 238.94 |

- Only effect A is significant
- Only effect B is significant
- Only effects A and B are significant
- Both effect A, B and AB are significant

#### Question 3

Treatment | Mean | SD | N |

A | 9.30 | 2.50 | 20 |

Is it useful to use the above variable as a covariate?

- No, because the standard deviations differ little from each other
- No, because there are equal group sizes
- Yes, because the means differ from each other
- Yes, because it is always useful to include a covariate in the study

#### Question 4

When do you use the true-score covariance analysis?

- If the covariate has been measured with error.
- If participants are not randomly assigned to groups.
- If the participants are not randomly selected.

#### Question 5

Which procedure can be used as an alternative to dealing with data that contains a covariate? (multiple answers possible).

- Stratification
- Sequentialization
- Difference scores
- Stochastization

### Answer indication MC-question

#### Question 1

B. Only statement II is true. The rows, columns, and interaction-effects are *not* independent of each other.

#### Question 2

D. Both effect A, B, and AB are significant. See the table below.

Source | df | SS | MS | F |

A | 1 | 34.67 | 34.37 | 14.51* |

* p <.05>

#### Question 3

C. Yes, because the means differ from each other.

#### Question 4

A. If the covariate has been measured with error.

#### Question 5

A and C.

## When and how to use log-linear models? - ExamTests 17

### MC-questions

#### Question 1

Which model usually best fits the data?

- Equiprobability model
- Conditional equiprobability model
- Mutual dependence model
- Saturated model

#### Question 2

Which model is referred to with: ln(F_{ij}) = λ + ln(F_{ij}) + λ_{i}^{V} + λ_{iF}

- Equiprobability model
- Conditional equiprobability model
- Mutual dependence model
- Saturated model

#### Question 3

A research study is being conducted into the relationship between family composition (number of brothers/sisters) and the chance to break through as a professional athlete.

We obtain the following data:

Professional athlete | Total | ||

Number of brothers/sisters | Yes | No | |

2 or less | 8 | 37 | 45 |

more than 2 | 25 | 30 | 55 |

Total | 33 | 67 | 100 |

What are the odds voor breaking through as a professional athlete, given that one has more than two brothers or sisters?

- 25/55 = 0.45
- 25/30 = 0.83
- 25/100 = 0.25
- 25/33 = 0.76

#### Question 4

Considering the same table as provided for question 3, what is the odds ratio for breaking through as a professional athlete (use >2 brothers/sisters as benchmark)?

- 3.85
- 1.84
- 3,32
- 1.00

### Answer indication MC-questions

#### Question 1

D. The saturated model is the most complex model and therefore best fits the data. However, this is not directly the preferred model because parsimony is often an important criterion for model selection as well. Therefore, one usually starts with this model to see which (interaction) effects can be eliminated to obtain a more parsimonious model that still fits the data well.

#### Question 2

C.

#### Question 3

B. The question concerns a conditional odds, being 25/55 = 0.83

#### Question 4

A. The odds ratio is 0.83 / 0.22 = 3.85. Be aware that the reverse could also be possible, but then the interpretation is also reversed. Usually, the >1 odds ratio is preferred, as it is easier to interpret. Here: the odds for breaking through as a professional athlete are 3.85 times greater for athletes with more than 2 brothers and sisters, compared to athletes with 2 or less brothers and sisters

## Which techniques are used for resampling and nonparametric approaches to data? - ExamTests 18

### MC-questions

#### Question 1

What is not a characteristic of a non-parametric test?

- There is no distribution of this test
- It has general assumptions about the sample distribution
- It is suitable for research into means
- It has a lower power than parametric tests

#### Question 2

Which of the answers below is not correct?

- Bootstrapping is mainly used for research into the median
- With bootstrapping, we do not use replacing when sampling
- If the population is not normally distributed, bootstrapping is a good solution
- Bootstrapping is often used when estimating parameters

#### Question 3

Which of the following statements is correct?

- Unlike bootstrapping, permutation testing draws samples without replacing.
- As well as bootstrapping, permutation testing takes samples without replacing.
- As well as bootstrapping, permutation testing takes samples with replacement.

#### Question 4

The Wilcoxon’s Rank-Sum Test is almost analogous to the...

- F-test
- T-test
- Z-test
- B-test

### Answer indication MC-question

#### Question 1

C. It is suitable for research into means.

#### Question 2

B. Bootstrapping *does* use replacing when drawing a new sample from the same population.

#### Question 3

A. Unlike bootstrapping, permutation testing draws samples without replacing.

#### Question 4

B. The T-test. This test is suitable for two independent samples.

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