Quantitative Revision

Question 1

In what circumstances would you perform a simple linear regression test?

Answer 1

To determine if there are linear relationships/associations between ratio/interval variables i.e. X and Y

Enable prediction of the values of Y (DV) from the values of X (IV)

Question 2

What assumptions must be met in order for you to use the simple linear regression test with your data?

Answer 2

Ratio/interval data

Linear relationship between X and Y

Data are randomly sampled

No outliers amongst data

Residuals must be approximately normally distributed

Question 3

What would be an appropriate null and alternative hypotheses for the simple linear regression test?

Non-directional (two-tailed)
Directional (one-tailed)

Answer 3

H0: There is no linear relationship between X and Y.
H1: There is a linear relationship between X and Y.

H0: There is no positive linear relationship between X and Y.
H1: There is a positive linear relationship between X and Y.

Question 4

Describe what the results mean for a simple linear regression test./
Interpret the results
Write-up of conclusion and results

Answer 4

Standardized coefficient
r: strength of the relationship between X and Y (with 1 being the strongest)
Beta: predictedeffectonYif X increases by 1 SD –> When X increasesby1SD,Yispredictedtoincreaseby.85SDs UsefulwheretherearemultipleIVs(inmultipleregression)

r^2: represents the variability in Y that can be explained by X

Unstandardized coefficient

b: For every increase in 1 unit of X, Y increases by b units
a: only interpret this if it makes sense/there is meaning/it is useful in knowing the value of Y when X = 0

significance (sig.) (i.e.p-value).: tells us the significance of
association between X and Y
effect of X on Y
The statistical significance associated with height matters
IGNORE the statistical significance associated with the constant

Be sure to answer in terms of the question and its scenario

Question 5

In what circumstances would you perform a Pearson’s (r) correlation test?

Answer 5

To determine the (strength and direction of an) association between 2 variables i.e. X and Y, where neither is categorical, but instead continuous outcome:
ratio/interval(parametric) e.g. weight (kg)
ordinalscale(non‐parametricequivalent) e.g. world ranking No.1, No.5 etc.

Parametric data

Question 6

What assumptions must be met in order for you to use the Pearson’s (r) correlation test with your data?

Answer 6

X and Ymustberatio/interval

Linearassociation between X and Y(scatterplot)

Theassociationmustshowhomogeneity of variance(scatterplot), wherethedatapointsareevenly distributedalongtheregressionline

Data for X and Y should follow a normal distribution (histogram, box plot, normal probability Q-Q plot, skewness and kurtosis z-scores, mean = median)

No outliers (scatter plot, box plot)

Ideally,shouldonlybeused withasampleofn>=100
[Forsmallersamplesizes,thereisariskthatoneortwo extremedatapoints‘drive’theassociation]

Question 7

What would be an appropriate null and alternative hypotheses for the Pearson’s (r) correlation test?

Non-directional (two-tailed)
Directional (one-tailed)

Answer 7

H0: There is no association between X and Y.
HA: There is an association between X and Y.

H0: There is no positive association between X and Y.
H1: There is a positive association between X and Y.

Question 8

Describe what the results mean for a Pearson’s (r) correlation test./
Interpret the results
Write-up of conclusion and results

Answer 8

The results show a significant/non-significant (significance) weak/strong (strength) negative/positive (direction) correlation between X and Y

r: represents the strength of the relationship/association between X and Y

sig (i.e.p-value).: tells us the significance of the association between X and Y

r^2: represents the variability in Y that can be explained by X

Question 9

In what circumstances would you perform a Spearman’s (rho) test?

Spearman’s rho calculates the ranked scores for each variable and considers the association between the ranks

Answer 9

To determine the (strength and direction of an) association between the ranks of X and Y, where X and Y are both non-categorical (i.e. not ordinal)

Non-parametric data i.e. parametric assumptions have been violated/breached

Question 10

What assumptions must be met in order for you to use the Spearman’s (rho) test with your data?

Answer 10

X and Ymustberatio/interval

Association between the ranks of X and Y does not need to be linear but it must be monotonic (i.e. does not change direction) (scatterplot)

Theassociationmustshowhomogeneity of variance(scatterplot), wherethedatapointsareevenly distributedalongtheregressionline

Onlyappropriatewheren (samplesize) is at least 20 or more

Question 11

What would be an appropriate null and alternative hypotheses for the Spearman’s (rho) test?

Answer 11

H0: There is no association between the ranks of X and Y.
H1: There is an association between the ranks of X and Y.

H0: There is no positive association between the ranks of X and Y.
H1: There is a positive association between the ranks of X and Y.

Question 12

Describe what the results mean for a Spearman’s (rho) test.

Answer 12

The results show a significant strong positive correlation between the ranks of X and Y

Question 13

In what circumstances would you perform a Kendall’s (tau) test?

Answer 13

To determine the (strength and direction of an) association between the ranks of X and Y, where X and Y are both non-categorical (i.e. not ordinal)

Non-parametric data (data is not normally distributed) i.e. parametric assumptions have been violated/breached

Useful with small data set n < 20

Can deal with a large number of tied ranks in the data

Question 14

What assumptions must be met in order for you to use the Kendall’s (tau) test with your data?

Answer 14

Bothvariablesmustberatio/interval

Association between the ranks of X and Y does not need to be linear but it must be monotonic (i.e. does not change direction) (scatterplot)

Theassociationmustshowhomogeneity of variance(scatterplot), wherethedatapointsareevenly distributedalongtheregressionline

Onlyusefulwheren < 20

Question 15

What would be an appropriate null and alternative hypotheses for the Kendall’s (tau) test?

Answer 15

H0: There is no association between the ranks of X and Y.
H1: There is an association between the ranks of X and Y.

H0: There is no positive association between the ranks of X and Y.
H1: There is a positive association between the ranks of X and Y.

Question 16

Describe what the results mean for a Kendall’s (tau) test.

Answer 16

The results show a non-significant weak negative correlation between the ranks of X and Y

Question 17

In what circumstances would you perform a multidimensional Chi-Square test?

Answer 17

Relationship/association between variables (Test of association)

Variables are both categorical i.e. nominal

Independent research design (No subjects/participants appears in > one group)

[Compare the observed and expected counts i.e. Test for differences where samples are independent]

Question 18

What assumptions must be met in order for you to use the multidimensional Chi-Square test with your data?

Answer 18

Randomly sampled

Variables must be categorical i.e. nominal

Independentmeasures

Counts(actualnumbers), notpercentages

No calculatedexpected value < 1

No > 20% of expected values < 5

Solution=collect more data, collapse categories, or use an exact test (SPSS)

Question 19

What would be an appropriate null and alternative hypotheses for the multidimensional Chi-Square test?

ResearchQuestion: Does the proportion of athletes who are normal weight or overweight differ by sport?

Answer 19

(H0):Inthepopulation,thethreesportsdo not differ in the proportions who are normal and overweight.

(H1):Inthepopulation,thethreesportsdo differ in the proportions who are normal and overweight.

Question 20

Describe what the results mean for a multidimensional Chi-Square test./
Interpret the results
Write-up of conclusion and results

Answer 20

Method
A Chi-square test was performed to test the H0 that the 3 sports do not differ in the proportions who are normal and overweight

Results
There was a difference between the proportion of those athletes who are normal and those who are overweight in the 3 sports (Field, Netball and Rowing), Chi-Square statistic = … (df = …, n = …), p = …

Basically:
Method: Test was performed to test the H0
Results: 
Conclusion/result
Chi-Square statistic
df
n
p-value

Question 21

In what circumstances would you perform a McNemar’s (Chi-Square) test?

Answer 21

Relationship/association between variables (Test of association)

Variables are both nominal

Repeatedmeasuresdesignwithtwo dichotomous variables

[Test for differences where samples are paired]

Question 22

What assumptions must be met in order for you to use the McNemar’s test with your data?

Answer 22

Randomly sampled

Dependent/repeated measures

DV and IV must be
dichotomous
of only 2 categories each

Variables must be categorical i.e. nominal

Counts(actualnumbers), notpercentages

No calculatedexpected value < 1

No > 20% of expected values < 5

Solution=collect more data, collapse categories, or use an exact test (SPSS)

Question 23

What would be an appropriate null and alternative hypotheses for the McNemar’s test?

Research question: To investigate the number of correct identifications of the writer’s sex by their handwriting style

49Psychologystudentswereaskedtowriteusingtheir normal handwritingandthenaskedtowriteimitatingthe handwritingoftheopposite sex
Students recruited a participant to judge the handwriting of both samples and identify the sex (repeatedmeasures)

IV: handwritingstyle
DV:participant’sjudgementof handwriter’ssex

Answer 23

H0: There will be no difference in the number of correct identifications of the writer’s sex from the 2 handwriting samples.

H1: There will be a difference in the number of correct identifications of the writer’s sex from the two handwriting samples.

Question 24

Describe what the results mean for a McNemar’s test.

Answer 24

Method
A McNemar’s Chi-Square test was performed to test the H0 that there will be no difference in the number of correct identifications of the writer’s sex from the two handwriting samples

Results
There is a significant difference in the number of correct judgements between the two conditions of handwriting style (n = …, exact p = …)
Of the 49 participants, ‘..’ correctly identified the handwriter’s sex for normal writing. Of the ‘…’ who were incorrect for the normal handwriting, ‘…’ of them correctly identified the handwriter’s opposite handwriting

Question 25

In what circumstances would you perform an independent samples design t-test?

Answer 25

Parametric data Independent (i.e. different) data/groups/samples To compare means - compare sample mean to another sample mean i.e. to compare differences between groups (mean) e.g. Intervention and control group --> study participant is in one group only [independent data: data that comes from different (independent) groups of people]

Question 26

What assumptions must be met in order for you to use the independent t-test with your data?

Answer 26

Dependent Variable is ratio/interval Measurements in condition 1 are independent of  measurements in condition 2 For n < or equal to 30 --> distribution of DV data for each group (X and Y) should not be badly skewed i.e. should follow a normal distribution (Can use CLT to help explain, if we still remember) Homogeneity of variance: The variance of the DV data for the two groups should not be very different A problematic difference in variances is indicated by a significant Levene’s Test If significant, interpret the p-value associated with ‘equal  variances not assumed’ If non‐significant, interpret p-value associated with ‘equal  variances assumed’

Question 27

What would be an appropriate null and alternative hypotheses for the independent t- test? two-tailed one-tailed

Answer 27

H0: There is no difference between the population means of X and Y. H1: There is a difference between the population means of X and Y. H0: The population mean of X not > population mean of Y. H1: The population mean of X > population mean of Y.

Question 28

Describe what the results mean for an independent t-test.

Answer 28

p < or equal to 0.05 or 0.01 --> There is a significant difference between the population means of X and Y or The population mean of X is significantly > population mean of Y

Question 29

In what circumstances would you perform a paired design t-test?

Answer 29

Parametric data Dependent/paired (i.e. same) data/groups/samples To compare means - compare sample mean to another sample mean i.e. to compare differences within groups (mean) e.g. pre-test post-test study Data collected from an/the same individual at different points in time/under different conditions Compare differences in outcome between time 1 & 2 or condition 1 & 2 (mean) [dependent/paired data: data that comes from one group of individuals]

Question 30

What assumptions must be met in order for you to use the paired t-test with your data?

Answer 30

Dependent Variable is ratio/interval Observations not independent Each measurement in Condition/TIme 1 has a match in  Condition/Time 2 For n < or equal to 30 --> distribution of differences between X and Y (i.e. X - Y) should not be badly skewed i.e. should follow a normal distribution (Can use CLT to help explain, if we still remember) Homogeneity of variance

Question 31

What would be an appropriate null and alternative hypotheses for the paired t-test? two-tailed one-tailed

Answer 31

H0: No difference in the means before and after. H1: A difference in the means before and after. H0: Mean after < or equal to mean before. H1: Mean after > mean before. or H0: Mean difference = 0. H1: Mean difference is not = 0. H0: Mean difference is not positive. H1: Mean difference is positive.

Question 32

Describe what the results mean for a paired t-test.

Answer 32

p < or equal to 0.05 or 0.01 --> Significant difference between the means before and after or Mean after is significantly > mean before

Question 33

In what circumstances would you perform a Mann Whitney U test?

Answer 33

Non-parametric data: Ordinal scale DV Ratio/interval DV that does not meet parametric assumptions (Sample sizes are small and normality is questionable Data contain outliers that because of  their magnitude distort the mean values and affect the outcome of the comparison) Independent (i.e. different) data/groups/samples To compare mean ranks/medians - compare sample medians to another sample median i.e. to compare differences between groups (median) e.g. Intervention and control group --> study participant is in one group only [To test the H0 that  2 samples come from the same population (i.e. have the same median) observations in one sample > than observations in the other]

Question 34

What assumptions must be met in order for you to use the MWU test with your data?

Answer 34

Independent data/samples Data distributions of X and Y are the same shape Not too many ties in ranks of data [Data values are assigned ranks relative to both samples  combined]

Question 35

What would be an appropriate null and alternative hypotheses for the MWU test? Two-tailed One-tailed

Answer 35

H0: There is no difference between the population medians of X and Y. H1: There is a difference between the population medians of X and Y. H0: The population median of X not > population median of Y. H1: The population median of X > population median of Y.

Question 36

Describe what the results mean for a MWU test.

Answer 36

p < or equal to 0.05 or 0.01 --> There is a significant difference between the population medians of X and Y or The population median of X is significantly > population median of Y

Question 37

In what circumstances would you perform a Wilcoxon signed rank test? [A Wilcoxon signed rank test: Measures the differences between each variable Compares paired data Is used when you cannot justify a  normality  assumption  for the differences Very simple --> counts the number of differences that are positive (+) and those that are negative (‐) and makes a decision based on these counts]

Answer 37

Non-parametric data Dependent/paired (i.e. same) data/groups/samples To compare medians - compare sample medians to another sample median i.e. to compare differences within groups (median) e.g. pre-test post-test study Data collected from an/the same individual at different points in time/under different conditions Compare differences in the ranks of the outcome between time 1 & 2 or condition 1 & 2 (median)

Question 38

What assumptions must be met in order for you to use Wilcoxon test with your data?

Answer 38

Paired/dependent data/samples Non-categorical data

Question 39

What would be an appropriate null and alternative hypotheses for the Wilcoxon test?

Answer 39

H0: No difference in the medians before and after. H1: A difference in the medians before and after. H0: Median after < or equal to median before. H1: Median after > median before. or H0: Median difference = 0. H1: Median difference is not = 0. H0: Median difference is not positive. H1: Median difference is positive.

Question 40

Describe what the results mean for a Wilcoxon test.

Answer 40

p < or equal to 0.05 or 0.01 --> Significant difference between the medians before and after or Median after is significantly > median before

Question 41

What is a type I error?

Answer 41

False positive Incorrectly rejecting the H0 when it is actually true Saying that there is a difference when in reality/actually there is no difference e.g. Telling a man that he is pregnant

Question 42

What is a type II error?

Answer 42

False negative Incorrectly failing to reject i.e. accepting the H0 when it is actually wrong Saying that there is no difference when in reality/actually there is a difference e.g. Telling a pregnant women that she is not pregnant (when it is so obvious that she is!)

Question 43

What is the common structure of all statistical tests?/What are the 7 steps of hypothesis testing?

Answer 43

Set H0 and H1 Establish alpha i.e. level of significance Determine p-value Accept or reject H0 OR Define study question and choose an inferential test Set hypotheses Select/establish level of significane i.e. alpha = 0.05 EDA and assess test assumptions to see if they are met/satisfied Go ahead and run the test Obtain p-value Decide whether to reject or accept H0 + conclusion, interpretation and write-up of results

Question 44

What is the benefit of using a paired t-test over an independent t-test?

Answer 44

Independent t-test gives rise to more random error because the control group might, by chance, be very different from the treatment group Variation is limited in paired t-test as each person is their own control

Question 45

What are residuals?

Answer 45

= Predicted - actual value of y Difference between the predicted value of Y (line) and the actual value of Y (points) An observable estimate of the unobservable statistical error

Question 46

What is the simple linear regression equation?

Answer 46

Y = a + bX i.e. DV = constant +  coefficient x (IV) a: constant or intercept b: coefficient or slope of the line associated with this independent variable As X increases by 1 unit, Y increases by b unit

Question 47

What does r^2 = 0.8 mean?

Answer 47

80% of variability in Y is explained by X *Note: In an exam, interpret the Adjusted R Square (if it is given) as it is more accurate

Question 48

What is the assumption that all inferential tests make about the sample?

Answer 48

The sample is randomly sampled from the population

Question 49

What is heteroscedasticity?

Answer 49

No linearity Data points fan out, does not go along regression line (evenly)

Question 50

How do we obtain the p-value for one-tailed test (directional) from the p-value of/for two-tailed test (non-directional)?

Answer 50

p-value for one-tailed test = Half the p-value for two-tailed test

Question 51

What is the difference between one-tailed and two-tailed tests with regard to rejecting the H0?

Answer 51

Two-tailed tests are non-directional. We would reject H0 if we found a positive or negative association or difference etc. One-tailed tests are directional. We only reject H0 if the association or difference etc. is in the direction that we specified/expected

Question 52

What does the multidimensional Chi-Square test compare?

Answer 52

Compares observed frequencies in our sample with the frequencies we would expect if there were no relationship at all between the two variables in the population that the sample was drawn from

Question 53

What is the formula for Chi-square?/How do we obtain a Chi-square statistic?

Answer 53

Chi-Square = SUM((O‐E)^2/E) O: observed count E: expected count For each cell, apply the formula (O-E)^2/E Then sum up all the cells to get the Chi-Square statistic

Question 54

What is (the concept of) degrees of freedom? How do we calculate it?

Answer 54

The more categories there are in the IV and DV, the more chance there is of the analysis being affected by sampling error (No. of categories in the row variable minus 1) x (No. of categories in the column variable minus 1) i.e. (rows-1)(columns-1) EXCLUDE marginal cells!

Question 55

From the study done by Chris Gratton and Ian Jones on Research methods for Sports Studies (2008), what are the 4 purposes of data analysis?

Answer 55

Describe Compare Examine similarities Examine differences

Question 56

What are the aims of Descriptive statistics?

Answer 56

Check for errors and outliers Describe and summarise the data Spread of the data Ensure appropriate analysis Data parametric or non-parametric?

Question 57

Ways of summarising interval/ratio data

Answer 57

Measure of Central Tendency mean median mode Measure of Dispersion range SD variance Normal curve, skewness, kurtosis

Question 58

What do parametric tests assume about the characteristics of the sample in terms of its distribution?

Answer 58

Data is drawn from a normally distributed population (i.e. data is not skewed) Have the same variance or spread on the variables being measured

Question 59

What assumptions do non-parametric tests make about the characteristics of the sample in terms of its distribution?

Answer 59

Do not make any assumption

Question 60

What is p-value?

Answer 60

Exact probability that H0 is true Probability that the difference found occurred by chance

Question 61

When do we use non-parametric tests?

Answer 61

When assumptions of parametric tests are not met (i.e. breached) level of measurement (e.g.,interval or ratio data) normal distribution homogeneity of variances across groups Not always possible to correct for problems with the distribution of a data set (i.e. data transformation) --> have to use non‐parametric tests: Make fewer assumptions about the type of data on which they can be used Many of these tests use “ranked” data

Question 62

What is alpha/level of significance?

Answer 62

The chance of making a Type 1 error and tolerating it Alpha level of .05 (5%), decide to reject H0 and accept HA when p-value is no more than .05 --> up to 5% chance that you are wrong in concluding that there is a difference (making a Type 1 error) when there actually isn't (false positive)