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Robin beaumont C:\web_sites_mine\HIcourseweb new\stats\basics\MCQS_statistics_course1_student_ver.docx
- MCQS - Statistics course
- Date last updated Wednesday, 03 November Written by: Robin Beaumont e-mail: [email protected] - Version:
- Defining data Contents
- Defining the centre
- Graphics
- Spread
- Sample / Populations.......................................................................................................................
- Assessing a single mean
- Assessing two means
- Assessing Ranks
- Correlation
- Simple regression
- Proportions and Chi square..........................................................................................................
- Risk, rates and odds
- Survival analysis...........................................................................................................................
- Hypotheses, Power and sample size
- Simple logistic regression.............................................................................................................
Robin beaumont C:\web_sites_mine\HIcourseweb new\stats\basics\MCQS_statistics_course1_student_ver.docx
1. Defining data
- I suggest two reasons why I feel people fall foul at the first hurdle of learning statistics. Which of the following are they? (two correct choices)
a. 'user friendly' introductions under emphasising basic concepts b. 'user friendly' introductions incorrectly explaining basic concepts c. statistics presented as a poorly defined subjective discipline d. over emphasis on the use of computers e. statistics presented as a clear cut subject with clearly defined rules
- Which of the following is an example of nominal data? (one correct choice)
a. Number of people on a course b. Cancer staging scale c. List of different species of bird visiting a garden over the past week d. Popularity rating of UK top ten television programmes e. Heart rate
- Which of the following are examples of Interval/Ratio data? (two correct choices)
a. Number of people on a course b. Cancer staging scale c. List of different species of bird visiting a garden over the past week d. Popularity rating of UK top ten television programmes e. Heart rate
- Which of the following are examples of Ordinal data? (two correct choices)
a. Number of people on a course b. Cancer staging scale c. List of different species of bird visiting a garden over the past week d. Popularity rating of UK top ten television programmes e. Heart rate
- Which of the following is the correct listing of data from the simplest to the most complex? (one correct choice)
a. Nominal -> Ordinal -> Interval -> Transcendental b. Nominal -> Ordinal -> Interval -> Ratio c. Qualitative -> Ordinal -> Interval -> Discrete d. Qualitative -> Ordinal -> Interval -> Ratio e. Nominal -> Ordinal -> Interval -> Quantitative
- Which of the following is an incorrect statement about Ranking a dataset? (one correct choice)
a. You can rank any dataset as long it is not Nominal b. Each value in a dataset should only occur once c. The process of ranking a dataset involves ordering it and then assigning a 'rank' value to each score from 1 to the number of scores in the dataset. d. When ranking a dataset tied scores receive the average of the rank value given to the ties. e. The result of ranking a dataset means that you loose the effect of magnitude if the data were Interval/Ratio
Robin beaumont C:\web_sites_mine\HIcourseweb new\stats\basics\MCQS_statistics_course1_student_ver.docx
- To work out the median by inspecting the scores what must you first do to the dataset?
a. Remove any negative values
b. Rank
c. Work out the mean
d. Count the total number of scores
e. Know the formula to use
- What is the main difference between the median and mean?
a. The median uses the ranked values whereas the mean uses the frequencies
b. The median uses the ranked values whereas the mean uses the actual values
c. The mean uses the ranked values whereas the median uses the actual values
d. There is no difference
e. The median uses deviations whereas the mean uses the actual values
- When calculating the median for a dataset consisting of an even number of scores (i.e. 2,4,6 etc.) which of the following is correct?
a. Calculate the average value of the three middle ranked scores
b. Calculate the mean for the whole dataset which would provide the same answer in this
instance
c. Calculate the average value of the two middle ranked scores
d. Calculate the mode and use instead
e. Choose either the upper or lower value of the two
- Which of the following statements concerning the mean is incorrect (choose one)?
a. The mean is not suitable for nominal data
b. The mean is sensitive to a single extreme value
c. The mean should always be used as the preferred measure to indicate a typical score
d. The mean is a more complex descriptive statistic than either the mode or median
e. The mean provides the most sensible result when the interval/ratio dataset has a symmetrical
set of scores
- The mean can be interpreted as (choose one)?:
a. The centre of gravity of a dataset
b. The average of the mode and median values of a dataset
c. The weight of all the scores
d. The weight of all the positive deviations
e. The relative frequency with the highest value
- In a positively skewed dataset the various measures suggesting a typical value lie in the following order (choose one)
a. median -> mode -> mean
b. mode -> median -> mean
c. mean -> mode -> median
d. mean -> median -> mode
e. mode -> mean -> median
Robin beaumont C:\web_sites_mine\HIcourseweb new\stats\basics\MCQS_statistics_course1_student_ver.docx
3. Graphics
Exercise 2
The following four boxplots provide summary information from four datasets. Please answer the following multiple choice questions (MCQs).
- Which sample has the highest median (one correct answer)?
a. Sample
b. Sample
c. Sample
d. Sample
e. None of them
- Which sample has a median value of 2 (one correct answer)?
a. Sample
b. Sample
c. Sample
d. Sample
e. None of them
- Which sample has outliers with low scores (one correct answer)?
a. Sample
b. Sample
c. Sample
d. Sample
e. None of them
- Which sample has outliers with high scores (one correct answer)?
a. Sample
b. Sample
c. Sample
d. Sample
e. None of them
- Which sample has 50% of its scores which do not overlap the other sets of scores to a great extent (one correct answer)?
a. Sample
b. Sample
c. Sample
d. Sample
sample1 sample2 sample3 sample
12
10
8
6
4
2
0
15 14
23 24 22
Robin beaumont C:\web_sites_mine\HIcourseweb new\stats\basics\MCQS_statistics_course1_student_ver.docx
- Which one of the charts suggests that the data form a uniform distribution (one correct answer)?
a. Chart 1
b. Chart 2
c. Chart 3
d. Chart 4
- Which one of the charts suggests that the data form a normal distribution (one correct answer)?
a. Chart 1
b. Chart 2
c. Chart 3
d. Chart 4
- Which two of the charts suggests that the data form a negative exponential distribution (one correct answer)?
a. Chart 1 and 2
b. Chart 2 and 3
c. Chart 3 and 4
d. Chart 3 and 1
Robin beaumont C:\web_sites_mine\HIcourseweb new\stats\basics\MCQS_statistics_course1_student_ver.docx
4. Spread
- The interquartile range includes the following scores? (one correct choice)
a. 50% of the un ranked scores b. 25% of the ranked scores c. 70% of the rank scores d. 50% of the ranked scores e. 70% of the un ranked scores
- Summing (adding together) all the deviations from the mean produces the following value? (one correct choice)
a. half the standard deviation b. the standard deviation c. 0 d. the mean value for the set of scores e. the median value for the set of scores
- What is an alternative name for the deviation from the mean? ( two correct choices)
a. residual from the mean b. derivation from the mean c. residual from the median d. error from the mode e. error from the mean
- Why does the standard deviation formula have a square root as part of it? ( one correct choice)
a. to make it add up to the mean b. to reverse the effect of squaring the deviations c. to provide a standard (i.e. mean=0; sd=1) unit of measure d. to provide a smaller value e. none of these
- Which of the following Greek letters represents the mean of a population? ( one correct choice)
a. β b. α c. μ d. ε e. λ
- Sigma squared represents? ( one correct choice)
a. Population variance b. Sample standard deviation c. Population standard deviation d. Population range e. Sample variance
Robin beaumont C:\web_sites_mine\HIcourseweb new\stats\basics\MCQS_statistics_course1_student_ver.docx
5. Sample / Populations
- The total area represented by a probability histogram is equal to: (one correct choice)
a. The p value b. undefined c. infinity d. 1 e. n
- Within statistics the term pdf stands for: (one correct choice)
a. Probability disease function b. Probability deviance function c. Portable Document format a. Probability density function b. Portable density function
- The pdf is a function that considers all the values for a particular random variable and allocates the following: (one correct choice)
a. A residual b. A Probability c. A odds d. A odds ratio e. A survival function
- The normal pdf takes two parameters to fully define it, they are: (two correct choices)
a. Mean b. Median c. Mode d. Variance e. Range f. Skewness g. Kurtosis h. M estimator i. t value
- For the normal pdf a value of 1.96 standard deviations each side of the mean is where approximately X percent of the scores lie. X is equal to: (one correct choice)
j. 25% k. 50% l. 75% m. 85% n. 95% o. 100%
- The degrees of freedom concept can be summed up as: (one correct choice)
a. The number of data items that are not free to vary, that is the parameter estimates b. The number of data items that are free to vary plus those used for parameter estimation c. The number of data items that are not free to vary plus those used for parameter estimation d. The number of data items that are free to vary e. None of the above
Robin beaumont C:\web_sites_mine\HIcourseweb new\stats\basics\MCQS_statistics_course1_student_ver.docx
- Which of the following best describes what is ment by the sampling distribution of the mean? : (one correct choice)
a. The theoretical process of non-randomly sampling from a population and recording the mean value of each sample to produce a distribution of sample means b. The theoretical process of randomly sampling from a population and recording the range of values of each sample to produce a distribution. c. The theoretical process of randomly sampling from a population and recording the mean value of each sample to produce a standard deviation d. The theoretical process of non-randomly sampling from a population and recording the median value of each sample to produce a distribution of sample medians e. The theoretical process of randomly sampling from a population and recording the mean value of each sample to produce a distribution of sample means
- When we theoretically consider an infinite number of sample means the estimate of the standard deviation of them is called the: (one correct choice)
a. Standard error of the sample b. Standard error of the median c. Standard deviation of the mean d. Standard error of the population e. Standard error of the mean
- The standard error of the mean (SEM) has the following formula: (one correct choice)
a. Sample variance divided by the square root of number in sample a. Standard deviation of sample divided by the square root of number in sample b. Standard deviation of sample divided by the number in sample c. Estimated standard deviation of population divided by the number in sample d. Standard deviation of sample multiplied by the square root of number in sample
- The standard error of the mean (SEM) is related to sample size, specifically: (one correct choice)
a. As sample size increases, SEM increases b. As sample size increases, SEM stays constant c. As sample size increases, SEM becomes less stable d. As sample size increases, SEM decreases e. None of the above
- Standardized scores (also called Z scores) allow values to be compared with the standard normal pdf. They are calculated in the following manner: (one correct choice)
a. (Score mean – population mean)/standard deviation b. (Score – mean)/standard deviation c. ((Score – mean)/standard error d. ((Score – mean)/SEM e. ((Score – mean)/n
- The process of estimation is an essential aspect of inferential statistics, it can be defined as: (one correct choice)
a. The process of calculating unbiased, efficient, consistent values from populations to sample parameters b. The process of calculating uniquely varying sensitive values from samples of population parameters c. The process of calculating unbiased, efficient, consistent values from both samples or populations d. The process of calculating unbiased, efficient, consistent values from samples of population means e. The process of calculating unbiased, efficient, consistent values from samples of population parameters
Robin beaumont C:\web_sites_mine\HIcourseweb new\stats\basics\MCQS_statistics_course1_student_ver.docx
- The one sample t statistic, is suitable in the following situation: (one correct choice)
a. Comparison of a sample mean to that of a population mean b. Comparison of a sample proportion to that of a population proportion c. Comparison of a sample mean to that of a population one, where the sampling distribution is exponential d. Comparison of a sample distribution to that of a population e. Comparison of a sample mean to that of a population one over a time period
- The one sample t statistic, has a degrees of freedom equal to: (one correct choice)
a. Number of observations in sample plus one b. Number of observations in sample c. Number of observations in sample minus one d. Number of observations in sample minus two e. Number of observations in sample minus three
- The p value associated with the one sample t statistic, assumes the following: (one correct choice)
a. Mean of sample is not equal to the comparator b. Mean of sample less than that of the comparator c. Mean of sample greater than that of the comparator d. Mean of sample and comparator are identical e. None of the above
- The effect size measure (i.e. clinical importance measure) associated with the one sample t statistic, is calculated as: (one correct choice)
a. (sample mean – population mean)/standard error b. (sample mean – population mean)/standard deviation c. (sample mean – population mean)/number in sample d. (sample mean – population mean)/sample mean e. (sample mean – population mean)/
- The effect size measure (i.e. clinical importance measure) associated with the one sample t statistic, provides: (one correct choice)
a. The difference between the hypothesised and observed mean b. The probability of obtaining the observed difference in means c. The probability of obtaining the effect size observed d. The probability of the null hypothesis being true e. A standardised measure of the difference between the hypothesised and observed mean
Robin beaumont C:\web_sites_mine\HIcourseweb new\stats\basics\MCQS_statistics_course1_student_ver.docx
- The paired sample t statistic, is suitable in the following situation: (one correct choice)
a. Comparison of a sample proportion to that of a population proportion of 0. b. Comparison of a sample mean to that of a population one, where the sampling distribution is exponential c. Comparison of a sample distribution to that of a population d. Comparison of a sample mean of zero to that of a population one over a time period e. Comparison of a sample mean to that of a population mean of zero
- If we obtained a p-value of 0.034 (n= 13, two tailed) from a paired sample t statistic, how would we initially interpret this outside of the decision rule approach (i.e. hypothesis testing): (one correct choice)
a. We will obtain the same t value from a random sample of 13 observations 34 times in every thousand on average, given that the population mean is zero. b. We will obtain the same t value from a random sample of 13 observations 34 times, or more in every thousand on average, given that the population mean is zero. c. We will obtain the same of a more extreme t value from a random sample of 13 observations 34 times in every thousand on average. d. We will obtain the same or a more extreme t value from a random sample of 13 observations 34 times in every thousand on average, given that the population mean is zero. e. We are 0.966 (i.e. 1-.034) sure that the null hypothesis is true.
- If interval/ratio data are paired in a research design such as pre and post test a paired sample t statistic.. : (one correct choice)
a. Is the most appropriate test, regardless of the differences being normally distributed a. Is the most appropriate test, if the differences are normally distributed b. Is the most appropriate test, if the differences are NOT normally distributed c. Is sometimes the appropriate test, if the differences are normally distributed and centred around zero d. Is the least appropriate test, regardless of the differences being normally distributed
- A p value is a special type of probability with two fundamental characteristics what are they.. : (one correct choice)
a. Conditional probability, range of values representing area(s) under PDF curve b. Conditional probability, of a specific single value representing a x value along the PDF curve c. Non-conditional probability, range of values representing area(s) under PDF curve d. Conditional probability, always representing a single area under PDF curve e. Non-conditional probability, representing a x value along the PDF curve
- The conditional probability for a p value, is usually re-interpreted as.. : (one correct choice)
a. Parameter value = zero = specific alternative hypothesis b. Parameter value = zero = alternative hypothesis c. Parameter value = zero = null hypothesis d. Parameter value = zero = not related to any hypothesis e. Parameter value not equal to zero = probability of the null hypothesis being true
- Before calculating a single sample or paired sample t statistic it is essential to.. : (one correct choice)
a. Perform graphical statistics. Review study design. b. Perform descriptive/graphical statistics to assess assumptions. Review study design. c. Not perform descriptive/graphical statistics to assess assumptions. Review study design. d. Assess the difference between the mean and median. Review study design. e. Not perform description statistics to assess assumptions nor review study design.
Robin beaumont C:\web_sites_mine\HIcourseweb new\stats\basics\MCQS_statistics_course1_student_ver.docx
- The two independent samples t statistic, has a degrees of freedom equal to: (one correct choice)
a. Number of observations in both samples plus one b. Number of observations in both samples c. Number of observations in both samples minus one d. Number of observations in s both samples minus two e. Number of observations in both samples minus three
- The p value (two sided) associated with the two independent samples t statistic, assumes the following: (one correct choice)
a. Mean of samples identical b. Mean of sample one is not equal to that of sample two c. Mean of sample one is less than that of sample two d. Mean of sample one is greater than that of sample two e. None of the above
- Given that s 1 = sample one and s 2 = sample 2. The effect size measure (i.e. clinical importance measure) associated with the two independent samples t statistic, is calculated as: (one correct choice)
a. (s 1 mean – s 2 mean)/standard error
b. (s 1 mean – s 2 mean)/standard deviation
c. (s 1 mean – s 2 mean)/number in sample
d. (s 1 mean – s 2 mean)/sample mean
e. (s 1 mean – s 2 mean)/
- Given that s 1 = sample one and s 2 = sample 2. The effect size measure (i.e. clinical importance measure) associated with two independent samples t statistic, provides: (one correct choice)
a. The difference between s 1 mean and s 2 mean
b. The probability of obtaining the observed difference in means c. The probability of obtaining the effect size observed d. The probability of the null hypothesis being true
e. A standardised measure of the difference between s 1 mean and s 2 mean
- The two independent samples t statistic, is suitable in the following situation: (one correct choice)
a. Comparison of a sample mean to that of a population mean of zero b. Comparison of more than two sample means c. Comparison of a sample mean to that of another sample mean d. Comparison of a sample distribution to that of a population e. Comparison of two sample means to that of zero
- If we obtained a p-value of 0.034 (n=7,8, two tailed) from an independent samples t statistic, how would we initially interpret this outside of the decision rule (i.e. hypothesis testing) approach: (one correct choice)
a. We will obtain the same t value from two independent random samples of the specified size 34 times in every thousand on average, given that both samples come from a population with the same mean. b. We will obtain the same, or a more extreme, t value from two independent random samples of the specified size 34 times in every thousand on average. c. We will obtain the same or a more extreme t value from a single random sample of the specified size 34 times, or more in every thousand on average, given that both samples come from a population with the same mean. d. We are 0.966 (i.e. 1-.034) sure that the null hypothesis is true. e. We will obtain the same, or a more extreme t value from two independent random samples of the specified size 34 times in every thousand on average, given that both samples come from a population with the same mean.
Robin beaumont C:\web_sites_mine\HIcourseweb new\stats\basics\MCQS_statistics_course1_student_ver.docx
- If two independent samples (both less than 30 observations) of interval/ratio data are produced in a research design an independent samples t statistic.. : (one correct choice)
a. Is the most appropriate test, regardless of the scores being normally distributed or not b. Is the most appropriate test, if the scores are normally distributed c. Is the most appropriate test, if the scores are NOT normally distributed d. Is sometimes the appropriate test, if the scores are normally distributed and centred around zero e. Is the least appropriate test, regardless of the scores being normally distributed
8. Assessing Ranks
- Rank order statistics assume the scale of measurement is.. : (one correct choice)
a. Nominal b. Ordinal c. Interval d. Ratio e. Binary
- Which of the following gives the reasons for using rank order statistics.. : (one correct choice)
a. Normal distributions, or not ordinal data or sample size less than 20 b. Non normal distributions, or ordinal data or sample size greater than 20 c. Non normal distributions, or not ordinal data or sample size less than 20 d. Normal distributions, or ordinal data, or sample size greater than 20 e. Non normal distributions, or ordinal data, sample size irrelevant
- Which of the following statistics is often called the non parametric equivalent to the two independent samples t statistic? (one correct choice)
a. Wilcoxon b. Chi square c. Mann Whitney U d. Sign e. Kolmogorov – Smirnov (one sample)
- Non parametric statistics use the ranks of the data, in so doing which of the following characteristics of the original dataset may be lost? (one correct choice)
a. Range/ magnitude b. Median c. Rank order d. Group membership e. Number in each group
- When investigating an ordinal data set which of the following is the most appropriate method of assessing values graphically? (one correct choice)
a. Barchart with SEM bars b. Barchart with CI bars c. Boxplots d. Histograms e. Funnel plots
Robin beaumont C:\web_sites_mine\HIcourseweb new\stats\basics\MCQS_statistics_course1_student_ver.docx
9. Correlation
- Correlation is a measure that makes use of a particular distribution, what is it? (one correct choice)
a. Normal b. Exponential c. Chi square ( df =1) d. Bivariate normal e. Uniform
- Correlation is often assessed by eye, which type of plot is usually used for this purpose? (one correct choice)
a. Histogram b. Bar chart c. Boxplot d. Scatter plot e. Funnel plot
- Which of the following statements is true concerning correlation? (one correct choice)
a. A correlation is always between -2 and 2, a zero value indicates no clustering towards line b. A correlation is always between -1 and 1, a zero value indicates all points on line c. A correlation is always between -2 and 2, a zero value indicates all points on line d. A correlation is always between -1 and 1, a zero value indicates no clustering towards line e. A correlation is always between -1 and 1, a zero value indicates all points on a horizontal line
- The correlation coefficient is based upon another measure, what is it? (one correct choice)
a. Variance b. Co-relation c. Contingency coefficient d. Covariance e. Cooks distance
- The calculation of the confidence interval for the correlation coefficient is...? (one correct choice)
a. No different from other statistics b. More complex than usual because of the restricted range c. Needs to be interpreted with extreme caution d. Un-defined e. Equivalent to the coefficient of determination
- There are a number of effect size measures for the correlation coefficient. Which of the following is not considered to be one? (one correct choice)
a. Coefficient of determination (r^2 ) b. Cohens d c. Correlation coefficient d. Cooks distance e. Correlation coefficient squared
- The coefficient of determination can be interpreted a number of ways. Which of the following is one of them? (one correct choice)
a. Proportion of explained variation b. Proportion of unexplained variation (i.e. residual) c. Proportion of mean variation d. Proportion of variance variation e. Proportion of points on the line
Robin beaumont C:\web_sites_mine\HIcourseweb new\stats\basics\MCQS_statistics_course1_student_ver.docx
- There is a special variety of the correlation coefficient used in the situation where the x and y values are interchangeable such as when comparing two measures, this intraclass correlation can be calculated easily by? (one correct choice)
a. Appending the y scores to the x scores and then performing a standard correlation. b. Appending the y scores to the x scores and then performing a rank correlation a. Appending the y scores to the x scores and appending the x scores to the y ones then performing a standard correlation. b. Appending the y scores to the x scores and appending the x scores to the y ones then performing a rank correlation. c. Appending the y scores to the x scores and appending the x scores to the y ones then performing a paired t statistic.
- Which is the most important assumption that is relaxed when considering Rank correlation compared to those for the Pearson correlation coefficient? (one correct choice)
a. Linear relationship b. Normal distribution c. Observation pairs are independent d. Sample is randomly selected e. Data cannot be nominal
- Which of the following statements concerning the correlation coefficient is not correct? (one correct choice)
a. Correlation does not imply causation b. Usual correlation techniques only consider monotonic/linear associations c. Non-homogenous groups can affect the correlation d. A significant p value provides evidence that the population correlation is equal to that observed e. Correlation was originally developed by Sir Francis Galton
- Which of the following provides the most accurate interpretation of a Pearson correlation coefficient of. (p=.0001)? (one correct choice)
a. We are likely to observe a correlation of .733 given that the population correlation is equal to. around once in ten thousand times on average in the long run. b. We are likely to observe a correlation of .733 or one more extreme given that the population correlation is not equal to zero around once in ten thousand times on average in the long run. c. We are likely to observe a correlation of .733 or one more extreme given that the population correlation is equal to zero around once in a hundred times on average in the long run. d. We are likely to observe a correlation of .0001 or one more extreme given that the population correlation is equal to .733 in the long run. e. We are likely to observe a correlation of .733 or one more extreme given that the population correlation is equal to zero around once in ten thousand times on average in the long run.
