RM and stats Flashcards
What does the difference between the means of 2 groups depend on?
- means, s.ds, var. and pop.
sample
What is Cohen’s D?
A measure of distance between 2 condition means which takes variability into account
How do you calculate Cohen’s D?
(m1 - m2) / meanSD
meanSD = (s1 + s2) / 2
can do same use pop. meand and s.d
for Cohen’s D:
as overlap decreases, does effect size increase or decrease?
increases
Give an example of a small, medium and large effect size
0.2, 0.5, 0.8
What are the two types of 2 sample t-tests? When are they used?
- related (paired, repeated measures) t-test - use when ppts take part in both conditions of ppt design
- independent t-test - use when ppts perform only 1 of 2 conditions between ppt design
How to calculate a related t-test for a 1 tail hypothesis?
- calculate the mean change between the 2 conditions (post - pre)
- calculate change s.d. change between 2 conditions
- assuming null is correct means pop. m = 0
- calculate ese.
- calculate t statistic and use to find p
How to calculate a related t-test for 2 tailed hypothesis?
same method as when calculating for 1 tailed but making sure to find p relating to two-tailed rather than one
What is the mean for a sampling distribution of difference?
pop. mean A - pop. mean B (= pop. mean D)
= 0 if assuming null is true
What is the s.d. for a sampling distribution of difference?
SQRT(pop. s.d. A^2/nA + pop. s.d. B^2/nB)
How do you calculate a z-score for an independent t-test?
Is this used often? Why?
z = (mA-mB) - (pop. meanA-pop. meanB) / SQRT(pop. s.d. A^2/nA +pop. s.d. B^2/nB) ~ N(0, 1)
not often used as often don’t have access to pop. s.d.
How do you calculate a t-statistic for an independent t-test?
t = (mA-mB) - (pop. meanA-pop. meanB) / SQRT(sA^2/nA + sB^2/nB)
v = nA + nB - 2
What is another way of writing SQRT(sA^2/nA + sB^2/nB)?
SQRT(e.s.e. A^2 + e.s.e. B^2)
What is covariance?
The extent to which a change in one variable is associated with predictable change in another variable
What would high and low covariance suggest?
high covariance = if scores for one variable change than the scores for the other variable also change is a predictable manner
low covariance = changes in 1 variable aren’t accompanied by a predictable change in the other variable
What does Pearson’s r determine?
If there is a linear relationship between variables
How to calculate total covariance?
TC(x, y) = SUM( (xi - mx) x (yi - my) )
xi - mx = difference between x co-ord and mean
yi - my = difference between y co-ord and mean
multiple = multiple the difference of the co-ord pairs
sum = add products of co-ord pairs
How to calculate sample co-variance?
C(x, y) = TC(x, y) / (n-1)
= (SUM((xi - mx) x (yi - my))) / n-1
What does sample covariance describe?
How much 2 variables co-vary (amount of variance they share)
What is positive, negative and zero covariance?
positive = higher than average values of 1 variable tend to be paired with higher than average values of the other variable negative = higher than average values of one variable tend to be paired with lower than average values of the other variable zero = 2 random variables are independent (note, not always independent, could instead have a non-linear relationship)
How can covariance and variance be related?
Var (x) = C (x, x)
How to calculate Pearson’s r?
r(x, y) = C(x, y) / sx x sy
sx x sy can also be written as: SQRT Var(x) x SQRT Var (y) SQRT C(x, x) x SQRT C(y, y)
What are the strength descriptors for Pearson’s r?
Perfect = +- 1 Strong = +- 0.7, 0.8, 0.9 Moderate = +- o.4, 0.5, 0.6 Weak = +- 0.1, 0.2, 0.3 Zero = 0
What is the null, 1-tail and 2-tail hypothesis for a correlation?
null = no correlation 1-tail = positive/ negative correlation 2-tail = a correlation
What is NHST framework for a correlation?
- formulate hypothesis
- collect data from study
- calculate Pearson’s r
- compare with p value to determine whether to reject or fail to reject null
- interpret in context
How do you calculate a p-value for Pearson’s r?
Use table
need number of tails and sample size
compare your value to value in table to see if it is significant or not (like in a t-test)
What do you need to remember when interpreting a hypothesis in context for a correlation?
Need to describe strength of correlation using the strength descriptors
e.g., r = 0.3 maybe be significant and you can reject null but it is only a weak positive correlation
How do you calculate shared (explained) variance?
(Pearson’s r)^2
= r^2
How do you calculate unshared (unexplained) variance?
1 - (Pearson’s r) ^2
= 1 -r^2
What are degrees of freedom?
related to sample size –> tells you which distribution you need to use
relates to how much data you have and therefore how good your sample statistics are likely to be
What are parametric tests?
Make certain assumptions about pops. from which data are sampled
What are 3 common assumptions that parametric tests make?
pops. from which samples are drawn should be normally distributed
variances of pops. should be approx. equal
no extreme scores
Why are parametric tests useful?
More powerful/sensitive than other approaches
What are non-parametric tests?
Make fewer assumptions about pops. from which data are sampled
Why are non-parametric tests useful?
The assumptions of parametric tests are sometimes violated
How do you take tied scores into account when ranking data?
Find the average of the ranking and then they all get the same rank
e.g., 1, 4, 4, 4, 5, 7 would first be ranked as 1, 2, 3, 4, 5, 6,
value 4 falls in rankings 2, 3, 4 so average = 3
new rankings become: 1, 3, 3, 3, 5, 6
What are Mann-Whitney U tests the NP alternative to?
Independent t-test
How do you calculate a Mann-Whitney U test?
rank data irrespective of which condition it falls in
Calc sum of the ranks in each condition (takes ties into account)
Consider what the smallest sum of the ranks could’ve been for each condition
Work out difference between smallest possible sum of ranks and actual sum for each condition
Mann-Whitney u stat = smallest difference out of the 2 conditions (U = x)
p-value calc by SPSS = exact sig (2-tailed) - compare to 0.05
if you have 1-tailed, divide p-value by 2 then compare
What is a Wilcoxon signed ranks test the NP alternative to?
Paired t-test
How do you conduct a Wilcoxon signed ranks test?
calc difference between 2 conditions (post - pre)
rank the non-zero difference scores (ignore signs but takes ties into account)
split ranks into negative and positive difference ranks (2 columns)
t-stat formed as sum of ranks of least occurring difference sign
use SPSS output for p-value –> Exact sig (1-t or 2-t) –> compare to 0.05
What is Spearman’s rho the NP alternative for?
Pearson’s R
How do you calculate Spearman’s rho?
- convert scores to ranks (rank x and y values separately)
- Calc difference in ranks (Rx - Ry)
- Square the differences
- Spearman’s rho –> p = 1 - ((6 x sum of squared differences) / n (n^2 - 1))
- use SPSS to find p-value
What values does Spearman’s rho fall between?
-1 and 1
When can we use this specific Spearman’s rho equation?
When there are no tied ranks
Why is a 1-variable Chi-squared test used?
to asses whether observed frequencies in categories are different from what might be expected
What is the DoF from a 1-variable chi-squared test?
n - 1 (n = number of categories)
What must the value of the 1-variable chi-squared test always be?
> 0
How do you calculate a 1-variable chi-squared test?
- calc difference between observed and expected (if null were true) values
- square differences
- divide squared differenced by expected value
- chi-squared stat = sum of values obtained from step above (Sum ((E - O)^2 / E)
- use DoF and sig. level in table to compare to p-value to determine if significant or not (similar to t-test)
What is a 2 x 2 chi squared test for?
asses whether there is a relationship between 2 categorical variables
How do you calculate a 2 x 2 chi squared test?
- (sum row x sum column) / total –> gives expected values for each category
- (E - O)^2 / E for each category
- sum these values to give chi squared stat
- use table to compare to p-value to determine if significant or not (like t-test)
what is the DoF for a 2 x 2 chi squared test?
(rows - 1 ) x (columns - 1)
What is a survey?
A collection of information from a sample of individuals through their responses to questions
What type of data do surveys collect?
Self report data
Qualitative and/or quantitative
Are surveys used across all research approaches? Give 3 examples
Yes
Experimental, correlational, qualitative
What are the 2 main types of surveys used?
questionnaires
interviews
True or false
Surveys are often used to operationalise constructs
True
What are 3 ways that questionnaires can be administered?
Postal
Online
In person
What are 2 ways that interviews can be administered?
Telephone
Face to Face
What are 2 uses of surveys?
Gather data e.g., on attitudes, behaviour, opinions etc.
Gather retrospective, present or future data
What are the purposes of surveys? Is there overlap?
Information gathering - exploratory or descriptive
Theory testing and building - explanatory or predictive
Usually some overlap between the 2
What are 3 general strengths of surveys?
- simple and straightforward
- easily adapted to different populations
- standardised
What is a general limitations of surveys?
- characteristics of ppts might affect data collected
e. g., memory, knowledge, experience, motivation, personality
What are 2 limitations of self-administered questionnaires?
- misunderstand questions
- response rate
What are 3 limitations of interviews?
- interviewer’s characteristics
- interaction between ppt and interviewer
- ppts might be less honest
What are 3 strengths of self-administered questionnaires?
- big sample = large amount of data
- efficient, fast, cheap
- anonymity
What are 2 strengths of interviews?
- question clarification
- interviewer can encourage involvement
What needs to be standardised in a survey? How can comparisons be made?
- measuring instruments
- what it is and how it is administered
normative data is often available to provide comparisons
What are psychometric tests? Give some examples
- standardised questionnaires/tests designed to measure particular traits/ abilities
e. g., personality inventories, cognitive ability tests, measures of MH status - items are published as an inventory
- norms are available allowing for the interpretation of individual ppt data (expressed as standardised scores)
- reliability is established but validity is sometimes questioned
When should a new questionnaire be developed?
when there are no existing tools to measure your area of interest
to avoid jangle - different labels for what are essentially the same thing
Why should questionnaires be piloted?
to identify problems and allow for revisions
to be able to gain feedback
What are 3 general design principles for questionnaires?
- keep it short
- make sure its readable (ppts can understand language used)
- provide appropriate response options (avoid forcing ppts to choose between more than 1 correct option or not having any correct options)
What is a response rate?
The percentage of questionnaires completed and returned
How can response rate be maximised?
- keeping questionnaires short, simple + clear
- include pre-paid envelopes for postal surveys
- send a reminder
- offer an incentive
What should the instructions in a questionnaire be? What does this ensure?
clear and standardised
Ensures we are measuring what we mean to and not the ppts understanding of the instructions
What should be considered in a survey concerning order?
Useful to divide into sections e.g., by topic or question type
screening if ppt is eligible should be at the start
start with easy and engaging questions
use funnelling/branching questions if appropriate –> ppts only answers questions relevant to them
What are demographics in relation to a survey?
The characteristics of the sample
e.g., age, gender, racial background, sexual orientation, religion
only include if relevant –> make sure response options are inclusive to all
What are the pros and cons of open questions?
pros:
- more detail, rich data, don’t impose assumptions
Cons:
- longer and more difficult to complete, difficult to analyse responses (often subjective)
What should be taken into consideration when considering using open questions in a survey?
- only use if justified
- ensure focus is clear
- decide on analysis strategy from outset
- more useful for descriptive and exploratory work
What are the pros and cons of closed questions?
pros:
- quick to complete, easy to analyse (objective), standardised responses
Cons:
- can impose assumptions , oversimplify complex issues
When should be taken into consideration when considering using closed questions in a survey?
- ensure questions are clear
- provide clear response options
- consider style of response options
- more useful for explanatory and predictive work