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3rd Year Stats Exam
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Questions in this quiz (80)
1What is the purpose of performing a linear regression analysis?
- ATo identify potential outliers in the data
- BTo fit the data to a model that defines y as a function or 2 or more variables
- CTo determine the dependence of a dependent variable on a predictor/independent variable
- DTo perform multiple comparisons whilst controlling overall type 1 error rate
- ETo derive robust confidence intervals
2Which axis does the dependent variable go on?
- Ay
- Bx
3What does the mean of the x and y values give you in a linear regression analysis?
- AThe size of the force which the points exert on the line of best fit
- BThe leverage of those data points
- CThe fit and slope of the model
- DThe centre of gravity and pivot point of the data
4What does the R-squared value represent?
- AHow well the model fits the data (0 - 1)
- BThe slope coefficient
- CThe distribution of the residuals
- DThe level of multicolinearity in the model
5What does an R-squared value of 0.068 and a slope coefficient (b1) value of 0.12 mean?
- AThe model can explain 68% of the data and for every unit of independent variable, the dependent variable goes up 12 units
- BThe fit of the model to the data is 0.12% and the influence that the data points have on the model is 0.68%
- CThe data points have an influence of 68% on the model and 12% on the outcome
- DThe model can explain 6.8% of the data and for every unit of independent variable, the dependent variable goes up 0.12 units
6In order to identify potential outliers:
- AStandardised residual >2 is worth checking, if more than 5% of the residuals >2 may indicate model is a poor fit
- BStandardised residual >3 is worth checking, if more than 5% of the residuals >2 may indicate that the model is a poor fit
- CStandardised residual >2.5 is worth checking, if more than 5% of the residuals >2 may indicate that the model is a poor fit
- DStandardised residual >3 is worth checking, if more than 10% of the residuals >2 may indicate that the model is a poor fit
7What does Cook's distance tell us when performing model diagnostics to see if the regression model is stable or biased by a few cases?
- Ainfluence of data point on predicted values (0 = no influence, 1 = complete influence)
- Bstandardised measures of how much each element of the model would change if data point was removed (values >1 = substantial influence)
- Chow susceptible the mean is to being biased by the outliers present in the data
- Dmeasure of overall influence of each individual data point on the overall model (>1 = concern)
8What does the Leverage value tell us when performing model diagnostics to see if the regression model is stable or biased by a few cases?
- Ainfluence of data point on predicted values (0 = no influence, 1 = complete influence)
- Bstandardised measures of how much each element of the model would change if data point was removed (values > 1 = substantial influence)
- Cmeasure of overall influence of each individual data point on the overall model (> 1 = concern)
- Dprecisely how large the standardised residuals are
9With regard to model diagnostics, what do the DFFit and DFBeta values tell us about the data model?
- Athey are standardised measures of how much each element of the model would change if that data point was removed (values > 1 = substantial influence)
- Bthey indicate the influence of that data point on predicted values (0 = no influence, 1 = complete influence)
- Cwhether or not the standardised residuals are worth checking and if they indicate that the model is a poor fit
- Dthey summarise the equation: 2(k+1)/n where k = number of predictors and n = number of data points
10With regard to the model diagnostic called the Leverage value, what defines whether or not the data point is worth investigating?
- Aif >2(k+1)/n where k = number of predictors (2 for simple linear regression) and n = number of data points
- Bif >2(k+1)/n where k = number of predictors (1 for simple linear regression) and n = number of data points
- Cif >2(K+1)/n where k = number of data points and n = number of predictors (1 for simple linear regression)
- Dif >n(k+1)/2 where k = number of predictors (1 for simple linear regression) and n = number of data points
- Eif >2(n+1)/k where k = number of predictors (1 for simple linear regression) and n = number of data points
11Multiple linear regression does what?
- Afits the data to a model that defines y as a function of 2 or more variables - determines the effect of an independent variable on the dependent variable taking account of other variables
- Bprovides an analysis of variance and determines if an interaction is present in the data
- Cdetermines the dependence of a dependent variable on a predictor/independent variable and allows outliers to be identified from x, y plot or from standardised residual plot
12With regard to multiple linear regression, what is the correct form of the equation for the model which is fitted? (all of the numbers are technically subscript)
- Ay = b0 + b1x2 + b2x1
- By = b0 + b1x1 + b2x2 +....
- Cy = b0 + b1 + b2x
- Dy = b0 + b1x1 + b2x2
13What does the F-ratio represent?
- Athe average variability due to the model divided by the average variability due to the residuals
- Bthe unexplained variability divided by the variability due to the model
- Cthe signal to noise ratio multiplied by the number of data points
- Dthe variance in the model divided by the R-squared value
14With regard to multiple linear regression, whenever you fit a predictor variable, that takes up...
- Aone slope parameter
- Btwo degrees of freedom
- Cone degree of freedom
- Done R-squared value
15As colinearity increases what effect does this have?
- Astandard errors of b coefficients decrease therefore confidence increases
- Blimits F-ratio value and variance inflation factor
- Ccoefficients become stable
- Dstandard errors of b coefficients increase and therefore confidence decreases
16How do you interpret the variance inflation factor (VIF) when assessing multicolinearity?
- AA VIF > 5 or an avereage VIF > 2 is problematic
- BA VIF > 10 or an average VIF > 1 is problematic
- CA VIF > 2 or an average VIF > 1 is problematic
- DA VIF > 10 or an average VIF > 2 is problematic
17How do you interpret the tolerance factor when assessing multicolinearity?
- A< 5 is problematic
- B< 10 is problematic
- C< 2 is problematic
- D< 0.1 is problematic
- E< 1 is problematic
18When does multicolinearity truly pose a problem?
- Awhen predicting y using the multiple regression equation
- Bwhen you want to look inside the model at the effect of individual predictors
- Cwhen you want to perform separate correlations for each x variable
- Dwhen you want to quantify the relationship between an independent and dependent variable
19How do you help solve the problem of multicolinearity?
- Aalways take a colinear variable out
- Bcombine predictors into a single predictor (as long as it makes biological sense)
- Crely on automatic variable selection
- Dremove all outliers
20With regard to hierarchical multiple regression, what value do you use when comparing new model to previous model?
- AF-ratio
- BCook's distance
- CR-squared
- Dvariance inflation factor
- Etolerance factor
21For multiple linear regression assumptions, what must the variables be?
- Adependent variables = quantitative or categorical
predictor variable = qualitative and continuous - Bdependent variables = qualitative
predictor variable = continuous - Cdependent variables = qualitative and continuous
predictor variable = quantitative or categorical - Ddependent variables = continuous or categorical
predictor variable = quantitative or categorical
- Adependent variables = quantitative or categorical
22When considering multiple linear regression assumptions, how do you assess the independence of the residuals?
- Aassess the DFFit and DFBeta values
- Buse the Welch's test
- Cuse Gabriel's test
- Duse the Durbin-Watson test
23For multiple linear regression, how large should the sample size be?
- A10 times the number of predictors tested
- B5 times the number of predictors tested
- Cat least 30
- Dat least 40
24What would an interaction among predictors look like in the form of an equation?
- Aeffect of height + effect of weight = overall effect on SBP
- Beffect of height + overall effect on SBP = effect of weight
- Ceffect of height x effect of weight = overall effect on SBP
25What is simple linear regression equal to?
- Apaired t-test
- Bunpaired t-test
- Cunpaired, two-tailed t-test
- Dpaired, one-tailed t-test
26A one-way anova is the same as what?
- Aunpaired t-test
- Bpaired t-test
- Csimple linear regression
- Dmultiple regression
27What does a one-way ANOVA do?
- Aanalyses how much of the overall variance can be explained by variation between group means compared to the unexplained variation within a group
- Bfits data to a model that defines y as a function of 2 or more variables
- Cperforms separate correlations for each x variable
- Ddetermines the dependence of a dependent variable on a predictor/independent variable
28What does the total variability equal?
- Atotal squares divided by the degrees of freedom
- Bthe F-ratio
- Cthe difference between each individual data point and the overall mean
- Derror mean squares divided by degrees of freedom
29The F-ratio is:
- Ahigher the larger the difference of the group means from the overall mean and smaller the amount of random variability
- Blower the larger the difference of the group means from the overall mean and smaller the amount of random variability
- Chigher the larger the difference of the group means from the overall mean and larger the amount of random variability
- Dhigher the smaller the difference of the group means from the overall mean and smaller the amount of random variability
30When is the ANOVA most robust to deviations from normality and equality of variance?
- Awhen effect size is large
- Bwhen the F-ratio is high
- Cwhen the degrees of freedom are greater than 10
- Dwhen the group sizes are equal
31If group sizes are unequal and equality of variance is not met then which correction do you use?
- AGames-Howell's
- BDurbin-Watson's
- CGabriel's
- DTukey's
- EWelch's
32What are post-hoc tests used for?
- Aperforming multiple comparisons whilst controlling overall type 2 error rate
- Bperforming multiple comparisons whilst controlling overall type 1 error rate
- Cwhen there is a specific hypothesis to be tested
- Dwhen group size is not equal
33You use Tukey's test when which of the following is true? (multiple correct answers)
- Asample sizes are unequal
- Bsample sizes are equal
- Cyou require good trade-off between type 1 and type 2 errors
- Dyou are interested in comparing all groups vs a single control group
- Eyou wish to cut down on the number of comparisons that you make
34When would you use Bonferroni as a post-hoc test? (multiple correct answers)
- Awhen you don't need a high level of confidence
- Bwhen you aren't performing multiple comparisons
- Cwhen you require a conservative test
- Dwhen you need a high level of confidence
- Ewhen sample sizes are equal
35When would you use Dunnet's as a post-hoc test? (multiple correct answers)
- Awhen interested in comparing all groups versus a single control group
- Bwhen sample sizes are equal
- Cwhen you want to cut down comparisons
- Dwhen you want a good trade-off between type 1 and type 2 errors
36Separate, unpaired t-tests to do comparisons will increase your chance of getting what?
- Aa false -ve
- Ba type 2 error
- Ca false +ve
- Dbiased data
37If you have a sample which has an n number of 10 and a sample with an n number of 12, which post hoc test should you use?
- AGabriel's
- BHochberg's GT2
- CGames-Howell
- DTukey
38If there is any doubt about equality of variance then which post-hoc test should you use?
- AGabriel's
- BHochberg's GT2
- CGames-Howell
- DSidak
39Complete this statement relating to planned contrasts:
Always _________________________ than number of groups- Aten times the number of contrasts
- Bmore contrasts
- Cone more contrast
- Dtwo times the number of contrasts
- Eone fewer contrast
40When doing orthogonal contrasts, the contrasts are independent so you can... (multiple correct answers)
- Aenter weights for most of the variables
- Btrust p-values as you aren't inflating the type 1 error rate
- Cignore the F-ratio value and R-squared value
- Dnot worry about doing any corrections for multiple comparisons
41"tests for trends in the data, which cannot be obtained directly using post-hoc tests, when there is a logical order to the groups entered"
To what is this statement referring to?- APlanned contrasts
- BOrthogonal contrasts
- CPolynomial contrasts
42An independent factorial ANOVA does what?
- Aeach level of one factor is tested against at least one level of the other
- Bperforms multiple comparisons whilst controlling overall type 1 error rate
- Cdivides total variability in the data set into different sources
- Deach level of one factor is tested at each level of the other
43Sidak is the best correction for what?
- Aindependent ANOVA
- Bone-way ANOVA
- Crepeated measures ANOVA
- Dmultiple linear regression
44Standard contrasts and post hoc tests are only available to examine main effects and are therefore most useful when:
- Athere is no unnecessary variability in the data
- Bthere is no interaction
- Cthe sphericity assumption is met
- Dgroup sizes are equal
45A p value of less than 0.5 means that....
- Athere is a less than 0.5% chance of committing a type 1error
- Bthere is a less than 5% chance of committing a type 2 error
- Cthere is a less than 5% chance of committing a type 1 error
- Dthere is a less than 0.5% chance of committing a type 2 error
46Standard error the proportion equals....
- A
- B
- C
- A
47Power =
- A1 - type 1 error rate
- B1 - type 2 error rate
- C1 - (type 1 + type 2 error rate)
- Dtype 2 error rate - type 1 error rate
48Power can be increased by....
- Aincreasing effect size. decreasing random variation. decreasing sample size.
- Bincreasing effect size. increasing random variation. increasing sample size
- Cdecreasing effect size. increasing random variation. increasing sample size
- Dincreasing effect size. decreasing random variation. increasing sample size
49This gives you a standardised effect size for a difference between means, what is it called?
- AWelch's correction
- BCohen's d
- CGames-Howell test
- DSidak correction
- Estandard error of the proportion
50how do you calculate expected frequency?
- A(row total + column total)/overall total
- B(row total - column total)/overall total
- C(row total x column total)/overall total
51How do you calculate degrees of freedom from a contingency table?
- Adf = (rows - 1) x (columns -1)
- Bdf = (rows + 1) x (columns +1)
- Cdf = (rows - 1) / (columns -1)
- Ddf = (rows x 2) + (columns x 2)
52With regard to categorical data - what must be satisfied in order for the analysis to be reliable?
- AThe assumption that at least 50% of expected frequency must be more than or equal to 5
- BDunnet's test
- CThe assumption that at least 80% of expected frequency must be more than or equal to 5
- DThe same assumptions as multiple linear regression
53Which graph indicates an interaction?
- A
- B
- C
- D
- A
54What does simple effects analysis do? (multiple correct answers)
- Aprobes where a certain effect is happening
- Bperforms an ANOVA to allow you to reject/accept a null hypothesis
- Canalyses the differences between levels of one variable
- Dperforms multiple comparisons whilst controlling overall type 2 error rate
55Which multiple comparison correction should you choose after simple effects analysis in order to control the overall type 1 error rate?
- ABonferroni
- BLSD
- CSidak
56Repeated measures ANOVA requires the data to have/be:
- Aindependent
- Bnot independent
- Cnaturally paired
- Dsorted into even group sizes
57What is the definition of sphericity?
- A“noise” in the relationship between the independent variables and the dependent variable is the same across all values of the independent variables
- Bequality of differences between linked values in each group
- Cwell-modeled by a normal distribution and likely for a random variable underlying the data set to be normally distributed
- Dresiduals are (roughly) normal and (approximately) independently distributed with a mean of 0 and some constant variance
58Which test provides a fix for sphericity?
- AWelch's correction
- BGames-Howell test
- CGabriel's test
- DMauchy's test
59How can we adjust the degrees of freedom and change the significance level associated with the F-statistic?
- AMauchy's test
- BWelch's correction
- CGreen House-Geisser correction
- DGabriel's test
60Which post hoc test is most robust and most conservative for a repeated measures ANOVA?
- ASidak
- BTukey
- CDunnets
- DBonferroni
61If parametric assumptions are in doubt, we must use the non-parametric equivalent of a single factor repeated measures ANOVA which is:
- ADurbin-Watson test
- BFriedman test
- CGabriel's test
- DHochberg's GT2 test
62For which analysis do BOTH the equality of variance assumption and sphericity assumption apply?
- ANon-linear regression
- BTwo-way ANOVA
- CIndependent ANOVA
- DMixed model ANOVA
- ERepeated measures ANOVA
63In terms of polynomial regression, what happens if you add further terms to the polynomial? (multiple correct answers)
- Athe fit will automatically improve
- Bthere is a risk of over-fitting the model
- Cthe significance level associated with the F-statistic changes
- Dthe R-squared value will increase
64In terms of nonlinear regression, why would you want to try multiple starting parameters?
- Ato ensure that the interaction between the variables is taken into account
- Bto ensure that the computer has found the global minimum
- Cto ensure that the computer has found the local minimum
- Dto ensure that an accurate scientific relationship is found
65How would you calculate the Sum of Squares (SS)?
- Aadd all the standard deviations together and square that value
- Bsquare the mean from each sample and add those together
- Csquare each standard deviation and add them all together
- Dsquare each standard deviation and add this to the variance
66Variance is calculated by doing what?
- Adividing the standard deviations by the degrees of freedom
- Bdividing the sum of squares by the degrees of freedom
- Cmultiplying the degrees of freedom by the mean
- Dmultiplying the standard deviations by the sum of squares
67How do we define the normal distribution curve?
- Athe population mean is the height and the sum of squares is the distance from the midline of the curve to the edge
- Bthe variance is the height and the population mean is the distance from the midline of the curve to the edge
- Cthe population standard deviation is the height and the population mean is the distance from the midline of the curve to the edge
- Dthe population mean is the height and the population standard deviation is the distance from the midline of the curve to the edge
68How do you calculate a z-score?
- A(x - mean) /sd
- B(x - sd)/mean
- C(mean-x)/sd
- D(x + mean)/sd
69Choose all of the correct statements
- Aapproximately 99% of normally-distributed values lie between +- 2 sds from the mean
- Bapproximately 95% of normally-distributed values lie between +-2 sds from the mean
- Capproximately 99.9% of normally-distributed values lie between +- 2.6 sds from the mean
- Dapproximately 99% of normally-distributed values lie between +- 2.6 sds from the mean
- Eapproximately 99.9% of normally-distributed values lie between +- 3 sds from the mean
- Fapproximately 95% of normally-distributed values lie between +- 3 sds from the mean
70How do you calculate SEM and therefore, confidence intervals?
- ASEM = sd x square root of n and therefore a 95% CI would be +- 1.96 x SEM
- BSEM = sd/square root of n and therefore a 95% CI would be +- 3 x SEM
- CSEM = sd x square root of n and therefore a 95% CI would be +- 2.6 x SEM
- DSEM = sd/square root of n and therefore a 95% CI would be +- 1.96 x SEM
71Which statement is true?
- AP < 0.05 means that 5% of the results arose by chance if the null hypothesis is true
- BP < 0.05 means <5% probability of the results arising by chance if the null hypothesis is true
- CP < 0.05 means <0.05% probability of the results arising by chance if the null hypothesis is true
- DP < 0.05 means that <0.5% probability of the results arising by chance if the null hypothesis is true
72Choose the correct statements
- Atype 1 error rate is conventionally set to 5% ( P < 0.05)
- Btype 2 error rate is conventionally set to 5% ( P < 0.05)
- Ctype 1 error rate = 1 - power
- Dtype 2 error rate = 1 - power
- Eif you accept a statistical power of 80% it will mean that you have a type 2 error rate of 20%
- Fif you accept a statistical power of 80% it will mean that you have a type 1 error rate of 20%
73What happens if you design an experiment with 3 groups and are tempted to test for differences between the means using 3 separate t-tests? (multiple correct answers)
- Ayou will increase the chance of making a type 2 error
- Byou will increase the chance of making a type 1 error
- Cyou will inflate your p-value
- Dyou will decrease your p-value
74Which statements are correct regarding the Pearson Correlation Coefficient?
- A+- 0.5 is a large effect
- B+- 0.1 is a small effect
- C+- 1 is a small effect
- Dit measures how close the data points are to a straight line that best describes the linear relationship
- Er = +0.1 refers to a perfect straight line with a positive slope
- Fr = -1 refers to a perfect straight line with a negative slope
75How is the line of best fit created in simple linear regression?
- Aby minimising the total sum of squares
- Bby minimising the sum of squares of the residuals
- Cby creating an equation which fits the model best
- Dby entering the data into the computer in Hierarchical form
76How do you calculate R squared?
- A1 - (SS of the residuals/total SS)
- B1 + (SS of the residuals/total SS)
- C1 - (total SS/SS of the residuals)
- D1 + (total SS/SS of the residuals)
77Shapiro Wilk's test is used to...
- Acheck for sphericity
- Bcorrect degrees of freedom
- Cascertain that residuals are random and normally distributed
- Dminimise the sum of squares of the residuals
78When entering more than 2 categories as dummy variables... (multiple correct answers)
- Athe thing that you're comparing the baseline to gets a 1
- Bthe thing that you're comparing the baseline to gets a 0.1
- C1 fewer dummy variables than number of categories
- Dbaseline condition gets a value of 0
- Ebaseline condition gets a value of 1.5
79Bonferroni test on its own - the p-values need to be less than what to claim significance?
- A0.05/number of categories
- B0.05/n
- C0.05/number of comparisons
- D0.05/variance
80Normally distributed variables X and Y are significantly correlated with a p level of 0.006 and a Pearson’s correlation coefficient of 0.468. Approximately how much of the variability in X and Y can be explained by this correlation?
- A32%
- B47%
- C22%
- D13%
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- University Statistics Quiz on 3rd Year Stats Exam, created by Jessica Whittick on 04/01/2017.
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- Jessica Whittick
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