Statistics And Data Analysis 21061 Flashcards
What is the difference between categorical level data and continuous data
Week 1
Catergorical data is nominal only (numbers, names gender only) whereas as continious data can be put on a continious scale
What two descriptive statistics do we typically use
Week 1
Central tendency & spread
What is the difference between how independent variables and dependent variables are measured
Week 1
The IV is ALWAYS measured on a categorical scale
The DV is IDEALLY measured on a discrete/continious scale
What is the benefit of measuring the DV on a continious scale
Week 1
So that we can use parametric statistics
What is the difference between a true-experimental vs a quasi-experimental design
Week 1
We actively manipulate the IVs in a true experimental design whereas the IVs in a quasi experimental design reflect fixed characteristics
Is handedness a quasi or true experimental IV
Week 1
Quasi - it is a fixed characteristic
What are the 3 main types of subject design
Week 1
Between subjects, within subjects, mixed design
What is a (2^ 3) mixed design
Week 1
Has two IVs, one between, one within.
Between IV has two levels, within IV has 3 levels
(e.g males and females preferences to horror, action and romance movies)
What does normally distributed data allow us to do
Week 1
Use parametric stats
What are the properties of normally distributed data
Week 1
Symmetrical about the mean
Bell shaped - mesokurtic
What is Platykurtic data
Week 1
Data which has more variations/spread than normally distributed data
(-ve kurtosis value)
What is leptokurtic data
Week 1
Data which has less variations/spread than normally disributed data (+ve kurtosis value)
What type of skew does normal data have
Week 1
normally distributed data has no skew
What is sampling error
Week 1
degree to which sample statistics differ from underlying population parameters
What are Z scores
Week 1
converted scores from normally distributed populations
What is sampling distribution
Week 1
Distribution of a stat across an infinite number of samples
What is the sampling distribution of the mean
Week 1
Distribution of all possible sample means.
What are standard error (SE) and estimated standard error (ESE)
Week 1
Standard deviation of sampling distribution
ESE is simply an estimate of the standard error based on our sample
What do we use sample statistics for
Week 1
to estimate the population parameters
What is a T-test
Week 2
Inferential statistic when we have 1 IV and 2 DVs that estimates whether population means under 2 IV levels are different
What contributes to variance between IV levels in an independent t-test
Week 2
- manipulation of IV (treatment effects)
- individual differences
- experimental error
* random error
* constant error
what contributes to variance within IV levels in an independent t-test
week 2
individual differences
random experimental error
What would happen if we continued to determine the mean of the difference for infinite samples
Week 2
it would essentially be like calculating the population mean difference
What is the null hypothesis when talking about sampling distribution of differences
Week 2
the sampling distribution of differences will have a mean of 0 as there is no difference between the sample means of 2 different samples
Why do we use estimated standard error instead of standard deviation in T-distribution
Week 2
Because it is a sampling distribution, instead of s.d we use s.e. This is because standard error is used to express the extent an individual sample mean difference deviates from 0
As we do not have all of the possible samples to calculate the standard error, we estimate the standard error , hence why we use e.s.e
What is the equation for t in an independent design
Week 2
Xd/ESEd
AKA
Mean of the difference / estimated standard error of the difference
AKA
variance between IV levels/variance within IV levels
What does the distance to 0 of the t value indicate?
Week 2
If t value is closer to 0, smaller variance between IV levels relative to within
If t value is further from 0 , large variance between IV levels relative to within IV levels
What does it mean if the null hypothesis is true for t-dist
Think CI
week 2
If the null hypothesis is true - 95% of sampled t-values will fall within the 95% bounds of the t-dist
If the null hypothesis is true, only 5% of sampled t-values will fall outside the 95% bounds
What are degrees of freedom and how are they calculated
Week 2
the differences between the number of measurements (sample size) made & number of parameters estimated (usually one, mean)
(Sample size - # of parameters)
N-2 for independent t-test
n-1 for paired t-test
What happens to the degrees of freedom value the larger they get
Week 2
They tend to 1.96, the original value
What are some of the assumptions we make for an independent t-test
Week 2
- Normality: the DV should be normally distributed under each level of the IV
- Homogeneity of variance: The variance in the DV, under each level of the IV should be reasonably equivalent
-
Equivalent sample size: sample size under each level of IV should be roughly equal ( matters more with smaller samples)
* Independence of observations: scores under each level of the IV should be independent
What test do we use when the asumptions for the independent t-test are violated
Week 2
we use the non-parametric equvalent: Mann-Whitney U test
What is Levenes test
Week 2
A test for equality of variance –> homogeneity of variances
what does levenes test tell us and what does it not tell us
Week 2
Tells us: Whether theres a diff in variances under the IV levels
doesn’t tell us:if our means are different or IV manipulation
What is the null hypothesis of levenes test
Week 2
no diff between the variance under each level of the IV (i.e homogeneity in variance)
If we reject Levene’s test, what does this mean
Week 2
There is heterogeneity in variance - the way in which the data varies under both IVs is different
What assumptions do we want when it comes to variance between IV levels?
Week 2
equal variance and homogeneity
What contributes to variance between IV levels in a paired t test
Week 2
- Manipulation of IV (treatment effects)
- Experimental error
what contributes to variance within IV levels in a paired t test
Experimental error
(RM designs - can discount the variance due to individual differences (leaving only variance due to error))
What assumptions do we make during a paired t-test
-
Normality - distribution of difference scores between the IV levels should be approximately normal
* Assume ok if n> 30 - Sample size - sample size under each IV level should be roughly equal
What do we do when our assumptions are violated during a paired t-test
Week 2
We use the non-parametric equivalent - Wilcoxon test
How do we interpret 95% Confidence intervals for repeated measure designs
Week 2
we can’t determine if result is likely to be significant by looking at 95% CI plot therefore we need to look at the influence of the IV in terms of size & consistency of effect
For a repeated measures design, what would happen if the confidence intervals cross 0 (lower value is negative and higher value is positive)
Week 2
you cannot reject the null hypothesis as you cannot conclude that the true population mean difference is different from 0
What is Cohen’s D
Week 2
The magnitude of difference between two IV level means, expressed in s.d units
I.e - a standardised value expressing the diff between the IV level means
What are the values for effect size of Cohen’s d
week 2
Effect size d
Small 0.2
Medium 0.5
Large 0.8
How does cohen’s d differ from T? Define both.
week 2
D = magnitude of difference between two IV level means, expressed in s.d units
T = magnitude of diff between two IV level means, expressed in ESE units
T takes sample size into account - qualifies the size of the effect in the context of the sample size .
When do we use a One way anova
Week 3
When we have 1 IV with more than 2 levels
What does a one way anova do?
Week 3
Estimate whether the population means under the diff the levels of the IV are different
What is an ANOVA like (think of t-tests)
Week 3
an extension of the t-test –> if you conducted a one-way anova on an IV w/ 2 levels, you’d obtain the same result (F = t^2)
Why do we use ANOVA instead of running multiple t-tests
Week 3
the more we draw from a population, the more likely we are to encounter a type I error and reject the null hyothesis, even if it true
What is the familywise error rate and what does ammedning it provide
Week 3
Probability that at least one of a ‘family’ of comparisons run on the same data, will result in a type I error
Provides a corrected significance level (a) reducing the probability of making a type I error
How do calculate the familywise error rate ?
Week 3
a’ = 1 - (1- a)^c
where c is the number of comparisons
e.g for 3 IV levels (3 comparisons) (ab ac bc)
1 - (1 - 0.05) ^3 = .143 = 14% chance of type I error
for 4 IV levels (6 comparisons (ab ac ad bc bd cd) )
1 - (1 - 0.05)^6 = .264 = 26% chance of type 1 error
Why do we use omnibus tests?
Week 3
To control familywise error rate
What is the null hypothesis of the F ratio/ANOVA?
Week 3
there is no difference between populations means under different levels of IV
H0:u1=u2=u3
what is the ratio for the F value.
Week 3
Variance between IV levels/ Variance within IV levels
What does the closeness of the F value to 0 indicate
Week 3
F value close to 0 = small variance between IV levels relative to within IV levels
F Value further from 0 = large variance between IV levels relative to within IV levels
What assumptions do we make for an independent one way ANOVA
Week 3
Same as those for independent T-test
Normality: DV should be normally distributed, under each level of the IV
Homogeneity of variance : Variance in the DV, under each level of the IV, should be (reasonably) equivalent
Equivalent sample size : sample size under each level of the IV should be roughly equal
Independence of observations : scores under each level of the IV should be independent
What do we do when the assumptions of the independent one-way anova aren’t met?
Week 3
We use the non-parametric equivalent, the Kruskal Wallis test
1.
What is the model sum of squares?
Equation
Week 3
Model Sum of Squares (SSM): sum of squared differences between IV level means and grand mean (i.e. between IV level variance)
What is the residual sum of squares?
Week 3
Residual Sum of Squares (SSR): sum of squared differences between individual values and corresponding IV level mean (i.e. within IV level variance)
What is SSt and how is it calculated
Week 3
Sum of squares total
= SSm( Sum of squares model ) + SSr (Sum of squares residual)
What is the mean square value and how is it calculated? What are the two types?
Week 3
MS = SS/df (Sum of squares/ degrees of freedom)
MSm = model Mean square value
MSr = residual mean square value
What do we use mean square values for?
Week 3
To calculate the F statistic
How do we calculate the F statistic
mean square values
Week 3
MSm/MSr
aka
model mean square value / residual mean square value
What do we do when the assumption of homogeneity is violated in an independent 1-way ANOVA
Week 3
We report Welch’s F instead of ANOVA F
What happens to the degrees of freedom when we use Welch’s F?
Week 3
The degrees of freedom are adjusted (to make the test more conservative)
How is the ANOVA F value reported
Week 3
F(dfm,dfr)=F-value, p =p-value
How do we calculate degrees of freedom for an independent 1 way ANOVA
Week 3
find the difference between the number of measurements and the number of parameters estimated
i.e. no. of measurements – no. parameters estimated
How do we calculate df for between IV level (model) variance where N is total sample size and k is number of IV levels
Week 3
K-1
How do we calculate df for within IV level (residual) variance where N is total sample size and k is number of IV levels
Week 3
N-k
What are post hoc tests
Week 3
Secondary analyses used to assess which IV level mean pairs differ
When do we use post-hoc tests
Week 3
only when the F-value is significant
How do we run post-hoc tests?
Week 3
As t-tests, but we include correction for multiple comparisons
what are the 3 type of post-hoc test
Week 3
- Bonferroni
- least significant difference (LSD)
- Tukey honestly significant difference (HSD)
Which post hoc test has a very low Type I error risk, very high type II error risk and is classified as ‘very conservative’
week 3
Bonferroni
Which post-hoc test has a high type I error risk, a low type II error risk and is classified as ‘liberal’
Least significant difference (LSD)
Which post-hoc test has a low type I error risk , a high type II error risk and is classified as ‘reasonably conservative’
week 3
Tukey Honestly significant difference (HSD)
What are the three levels of effect size for partial eta^2 for ANOVA
week 3
> 0.01 is small
0.06 is medium
0.14 is large
what is effect size measured in for ANOVA
calculated in 2 ways, cohens d and partial eta squared
How do you calculate partial eta squared
week 3
Model sum of squares/ (model sum of squares + residual sum of squares)
In a repeated measures design for a one way ANOVA, what contributes to variance between IV levels
Week 4
- Manipulation of IV (treatment effects)
- Experimental error (random & potentially constant error
In a repeated measures design for one way ANOVA, what contributes to variance within IV levels
Week 4
Experimental error (random error)
**
how do we calculate total variance?
Week 4
Model variance(variance between IV levels)/ residual variance (variance within IV levels) -
Individual differences (in independent designs)
what is the t/F ratio and how do we calculate it?
Week 4
variance between IV levels/ variance within IV levels (excluding variance due to individual diffs WHEN IN RM design)
how is the F ratio calcated in terms of Mean square values
Week 4
Mean sum of squares model/ mean sum of squares residual
What are the 3 assumptions made in a repeated measures 1-way ANOVA
Week 4
- Normality - distribution of difference scores under each IV level pair should be normally distributed
- Sphericity (homogeneity of covariance) - the variance in difference scores under each IV level pair should be reasonably equivalent
- Unique to RM 1-way anova
- Equivalent sample size: sample size under each level of the IV should be roughly the same
What corrects for the sphericity assumption.
Week 4
Greenhouse-geisser
What test do we do to check for sphericity and what is its respective value?
Week 4
Mauchly’s test & the W value
What is the null hypothesis of the assumption of sphericity in the repeated measures ANOVA
Week 4
There is no difference between the covariances under each IV level pair (i.e homogeneity)
If p ≤ .05 we reject null hypothesis (i.e heterogeneity)
What do we do if our data seriously violates the assumptions of a repeated measures One-way ANOVA
Week 4
we should use the non-parametric equivalent - Friedman test
If Mauchlys is significant, what do we use in SPSS output
Week 4
The row that labelled Greenhouse-geisser as sphericity cannot be assumed
If Mauchlys is not significant, which row do we use in SPSS output?
Week 4
The row labelled sphericity assumed
**
How do we report the F statistic in repeated measures ANOVA
Week 4
F(dfM,dfR) =F-value p = p value (greenhouse-geisser/sphericity assumed)
How do we calculate the degrees of freedom for RM 1-way anova
for model and residual
week 4
dfM = K -1(where K number of IV levels/ parameters)
dfR = dfM x (n-1) (where n = number of participants)
Which post Hoc test do we use for RM 1 way anova
week 4
bonferroni
why is recruitment an advantage of repeated measures designs
Week 4
needs fewer p’s to gain same number of measurements
How does the model of repeated measures design cause error variance to be reduced and why is this advantageous
Week 4
Remove variance due to individual differences from error variances –> leading to less variance within IV levels
Apart from recruitment and reduction in error variance,what is another advantage of repeated measures designs
There is more power with the same amount of participants
* its easier to find a significant difference ( and avoid type II error)
what are order effects and what effect can they have on repeated measure designs
Week 4
They are the effects of having the participants go through the same thing in different conditions and becoming habituated to it in a variety of different ways.
They introduce confines - error introduced systematically between IV levels
What are the 4 types of order effects
Week 4
- Practice effets
- fatigue
- sensitisation
- carry-over effects
What are practice effects in terms of order effects
Week 4
P’s get better at the task which positively skews how they do in subsequent IV levels
What is fatigue in terms of order effects
Week 4
Participants get bored/ tired of engaging which negatively skews how they do in subsequent tasks
What is sensitisation in terms of order effects
Week 4
P’s start behaving in a particular way to please or annoy the experimenter due to understanding IV manipulation
What are carry over effects in terms of order effects
Week 4
- effect of taking part in one IV level effects how one acts on subsequent IV levels
What is counterbalancing and how is it used to minimise order effects
Week 4
counterbalancing what order people undergo the IV levels go through must be done to ensure as much randomness as possible, this does not get rid of order effects, but spreads their impact
What are alternatives for each type of order effect when counterbalancing is not possible (4)
week 4
– Practice - extensive pre-study practise
– Fatigue - short experiments
– Sensitisation - intervals between exposure to IV levels
– Carry-over effects - include a control group
When do we use factorial ANOVAs
Week 5
to test for differences when we have more than one IV with at least 2 levels
What are the 3 broad factorial ANOVA designs
Week 5
- all IVs are between-subjects (independent)
- all IVs are within-subjects (repeated measures)
- a mixture of between-subjects and within-subjects IVs (mixed)
what would a 2 * 2 ANOVA mean
Week 5
2 IVs/factors, each with 2 levels
what would a 2 * 4 ANOVA mean
week 5
2 IVs/factors, one with 2 levels and one with 4 levels
What are the three type of main effects we would be looking for in a 2 * 3ANOVA design if the primary IV is gender (male female) and the secondary IV is colour (red, white and blue)
- is there a significant main effect of gender
- is there a significant main effect of colour
- is there an significant main interaction between gender and colour?
If we are doing a study to try and see whether there is a difference between how much men and women like chocolate, and we are also looking to see whether the texture of the chocolate (chunks vs tablets) has an effect, what is the primary IV, what is the secondary IV, why are they respectivley so andwhat do these terms mean?
Week 5
The primary IV is gender, the secondary IV is texture. Gender is the primary IV as it is the IV main IV we are looking for an effect for. Texture is the secondary IV as we are looking to see if the addition of this variable also creates an effect, hence it being secondary because it is not the focus.
In a between subjects 2 * 3 ANOVA, how many possible conditions are there?
Week 5
6
What is the null hypothesis for Factorial ANOVAand how many are there?
Week 5
There is one per IV and one for each possible interaction IV pair.
e.g in 2 * 2 ANOVA , there is a null hypothesis of no difference in means for IV one, one for IV two and one for the interaction between IV one and IV two
What does a significant interaction indicate in ANOVA?
Week 5
that the effect of manipulating one IV depends on the level of the other IV
What is an interaction in terms of ANOVA.
Week 5
The combined effects of multiple IVs/factors on the DV
What are Marginal means used for in ANOVA
Week 5
to determine if there is significant effect for either IV
In an ANOVA line chart, what does it mean if the lines for the IVs are parallel
Week 5
There is no interaction of the two IVs
What does it mean if the marginal mean of one of the IVs is at roughly the same level as the means for both populations
Week 5
there is no main effect
What are the assumptions made in an independent factorial (two way) ANOVA (5)
Week 5
Normality: DV should be normally distributed, under each level of the IV
Homogeneity of variance : Variance in the DV, under each level of the IV, should be (reasonably) equivalent
Levennes - DON’T want a significant result
NO correction
Equivalent sample size : sample size under each level of the IV should be roughly equal
Independence of observations : scores under each level of the IV should be independent
What is the non-parametric equivalent for the Independent factorial ANOVA
Week 5
There is no non-parametric equivalent for factorial ANOVA
If our data seriously violate these assumptions we can attempt a ‘fix’ or we can simplify the design
How many F statistics do we report in factorial ANOVA
Week 5
one for each IV i.e the main effect for each IV
What is the difference between classical eta squared and partial eta squared
Week 5
Classical eta^2 : proportion of total variance attributable to factor
Partial eta^2: Only takes into account variance from one IV at a time
(Proportion of total variance attributable to the factor, partialling out/excluding variance due to other factors)
when do we use Post Hoc tests
Week 5
If the main effect of at least one of the IVs is significant, then we reject the null hypothesis
**Only relevant when **
* main effect of IV is significant & IV hs more than 2 levels
For one-way ANOVA what do we report alongside post hoc results
Week 5
Cohens D
For factorial ANOVA what do we report alongside post hoc results
Week 5
nothing, we dont report Cohens d
What are simple effects in terms of interaction effects and how do we check them
Week 5
effect of an IV at a single level of another IV
* * do compairsosn of cell mean conditions (i.e t-tests)
For an IV with a between subjects design, how do we check for simple effects
Week 5
we do independent t-test for each comparison
What is the bonferroni correction and what is it the calculation is performs?
Week 5
a correction that divides the required alpha level by the number of comparions (e.g for 6 comparisons , .05/6 = .008)
How can ANOVAs in general be described as
Week 7
a flexible and powerful technique appropriate for many experimental designs
What questions are necessary to ask before collecting any data and performing an ANOVA
Week 7
*Do I have a clear research question?
*Do I know what analyses I will need to conduct to answer this?
*Will I be able to carry out and interpret the results of these analyses?
*Have I considered and controlled for potential confounds?
*Will I understand the answer I get?
What does our choice of statistical test depend on
Week 1
- Scale of measurement
-
Research aim
*
*
* -
Experimental design
*
*Number of IV’s
* -
Properties of dependent/outcome variable
*Normally distributed: parametric
*
What do descriptive statistics not allow us to do
Week 1
Make predictions or infer causality
What does a 95% confidence interval mean
Week 1
95% of all sampled means will fall within the 95% bound of the population mean
When writing proportions (such as partial eta squared) what is the correct notation for them?
General
you drop the leading zero and report it to 3dp
What can relationships vary in
Week 8
Form, Direction ,Magnitude/strength
What are the two types of form a relationship can take
Week 8
linear or curvilinear
What are the two directions a relationship can go in
week 8
positive or negative
What is the magnitude/strength of a relationship measured in
Week 8
The R value
What R values are indicative of a perfect positive relationshp, a perfect negative relationship and no relationship
Week 8
1, -1 & 0
The dots are random and there is no systematic relationship
What are the values for weak, moderate and strong correlation
Week 8
± 0.1 - 0.39 = weak correlation
± 0.4 - 0.69 = moderation correlation
± 0.7 - 0.99 = strong correlation
What is meant by non-linear correlation?
Week 8
The idea that some DV’s peak at a certain point of an IV
(e.g confidence in ability to pass course, too low = do worse, too high = do worse, at optimum = do best)
what does bivariate linear correlation involve
Week 8
Linear correlation involves measuring relationship between 2 variables measured in a sample
We use sample stats to estimate population parameters -whole logic of inferential statistical testing
What is the null hypothesis when doing a bivariate linear correlation?
Week 8
no relationship between population variables
What parametric assumptions do we have when doing a bivariate linear correlation? (4)
Week 8
- Both variables should be continious
- Related pairs: each P (or observation) should have a pair of values (one for each axis/IV)
- absence of outliers: outliers skew results, we can usually just remove them
- linearity: points in scatterplot should be best explained w/ a straight line
Apart from the parametric assumptions, what other things are important to consider in regards to Correlation and correlation coefficients
Week 8
they are sensitive to range restrictions
* E.g floor and ceiling effects - floor effect, clustering of scores at bottom of scale, ceiling effect = clustering at top of scale
* Can be hard to see relationship between variables as you dont see how far they stretch due to cap
There is debate over likert scales,
if you have 6-7 points, can get away with parametric, if you have less, best to use non-parametric
What happens if our data seriously violates our parametric assumptions for a correlation coefficient test?
Week 8
use non-parametric equivalent **Spearman’s rho (or kendall’s Tau if fewer than 20 cases)
What does Pearson’s correlation coefficient do, and what does it’s outcome show?
Week 8
- Investigates relationship between 2 quantitative continuous variables
- Resulting correlation coefficient ( r ) is a measure of strength of association between the two variable
What is covariance
Wee k 8
Variance between the x and Y variable
How do you calculate Covariance? (we will never have to do this by hand but good practice to know)
The process
Week 8
- For each datapoint, calculate diff from mean of X and difference from mean of Y
- Multiply the differences
- Sum the multiplied differences
- Divide by N-1
What does the correlation coefficient of pearson’s provide us with and what actually is it?
Week 8
a measure of variance shared between our X and Y variables
it is a ratio of covariance (the shared variance) to separate variances
What does the distance of the r value in relation to 0 mean in regression?
Covariance and variances
Week 8
If covariance is large relative to separate variances - r will be further from 0
If covariance is small relative to the separate variances - r will be closer to 0
If the things (variables) tend to go up and down together a lot (large covariance), the correlation (r) will be far from 0, indicating a strong relationship.
If the things don’t move together much (small covariance), the correlation will be closer to 0, indicating a weaker relationship.
What does R tell us in terms of a scatter graph? - How does the spread of the data points relate to R?
Week 8
how well a straight line fits the data points (i.e strength of correlation → strength is about how tightly your data points fit on the straight line )
If data points cluster closely around the line, r will be further from 0
If data points are scattered some distance from the line, r will be closer to 0
What difference reflects sampling error?
Week 8
The fact that if you took two samples from the same populations you’re likely to get two different R values.
If we did the sampling distribution of correlation coefficients what would the null hypothesis be
Week 8
if we plotted the R values, the majority would cluster around a common point,the true populaion mean.
What would the null hypothesis be for the sampling distribution of correlation coefficients
Week 8
The mean would be 0 thus most R values would cluster close to 0
What is the r-distribution, what does it tell us and what is its mean value?
Week 8
- It is the extent to which an individual sampled correlation coefficient (r) deviates from 0 which can be expressed in standard error units
- we can determine the probability of obtaining an r-value of a given magnitude when the null hypothesis is true (p-value)
- the mean is 0
What is the relationship between the R-value and the population
Week 8
the obtained r-value is a point estimate of the underlying population r-value
When is linear regression used, and what is it’s purpose?
Week 9
- Similarly to linear correlation, it is used when the relationship between variables x & y can be described with a straight line
- by proposing a model of the relationship between x & y, regression allows us to estimate how much y will change as a result of given change in x
What is the Y variable in linear regression?
Week 9
The variable that is being predicted –> the outcome variable
What is variable X in linear regression and what is special about it
The variable that is being used to predict –> The predictor variable
**can have Multiple predictor variables **
What is regression used for? (3)
Week 9
- Investigating strength of effect x has on y
- Estimating how much y will change as a result of a given change in x
- Predicting a value of y, based on a known value of x
What assumption is made in regression that is not done in correlation and what does this mean in regards to what evidence can be obtained from regression?
Week 9
Regression assumes that Y (to some extent) is dependent on X, this dependence may or may not reflect causal dependency.
This therefore means regression does not provide direct evidence of causality
Does a significiant regression infer causality?
Week 9
No, other factors other than our used predictor variables may come in to effect, thus can’t suggest causality.
What are the 3 stages of performing a linear regression?
Week 9
- analysing the relationship between variables
- proposing a model to explain the relationship
- evaluating the model
What does ‘ analysing the relationship between variables’ mean as a stage during linear regression?
Week 9
Determining the strength & direction of the relationship
What kind of model is being proposed in linear regression and what is expected of this model?
Week 9
a line of best fit where the distance between the line and the individual datapoints is minimised as much as possible
Ideally, for a line of best fit, where should the datapoints be relative to it
Week 9
- half above, half below line
- clustered as close as possible to line (signifies strong relationship)
- distance is minimised as much as possible
What are the 2 properties of a regression line?
Week 9
- The intercept: value of y when x is 0 (typically the baseline) (a value)
- The slope: how much y changes as a result of a 1 Unit increase in x (the gradient) (b value)
When ‘evaluating the model’ , what are we doing and how do we do this
Week 9
Assessing the goodness of fit of our model (best model/line of best fit) vs the simplest model (b=0, comparing data points to the mean of y)
What is the simplest model?
Week 9
- Using the average Y value (mean) to estimate what Y might be
- **assumes no relationship between x and y (b=0) **
What is the ‘best model’? (What is it based on, what functions can it serve?)
Week 9
- based on the relationship between x & y
- uses regression line & line of best fit to determine what a value of Y would be at a particular value of X
- allows for better predicition
When calculating the goodness of fit your model, what is the first thing you do? What does this provide?
Week 9
first check how much variance remains when checking the simplest model (mean of y) to predict Y.
This provides the sum of squares total (diff between each data point & mean value, & squaring it and summing them )
How do you calculate the variance not explained by the regression line and what does this give you?
calculate difference between each data point and point on the line it matches up to (score that would be predicted), square these differences and then add them together
This gives you the sum of square of the residuals
What does more clustering around the regression line indicate for the model?
Week 9
The model is providing a better model, meaning there is smaller error variance, and that the model is more accurate (about variance due to the variable in question).
What is the sum of squares total in relation to regression?
Week 9
*the difference between the observed values of y and the mean of y
i.e. the variance in y not explained by the simplest model (b = 0)* ‘
What best matches the description ‘the difference between the observed values of y and those predicted by the regression line
i.e. the variance in y not explained by the regression model ‘
Week 9
Sum of squares residual
What is reflective of the improvement in prediction using the regression model when compared to the simplest model?
Week 9
The difference between Sum of squares total and and sum of squares residual , in other words **the model sum of squares **
**SST - SSR = SSM **
What does a large sum of squares value indicate in regression?
Week 9
a large(er) improvement in the prediction using the regression model over the simplest model
What can we use F tests (what we call an ANOVA in cases of regression to avoid confusion) to evaluate and what is this reported as?
Week 9
the improvement due to the model (SSM) relative to the variance the model does not explain ( SSR)
It is reported as the F-ratio
What does the F ratio do in goodness of fit tests and how do you calculate it?
Week 9
- provides a measure of how much the model has improved the prediction of y, relative to level of inaccuracy of the model
- F = Model mean squares / residual mean squares
What would you expect to see in terms of model mean squares (MSM) and residual means squares (MSR) if the regression model is good at predicting y?
Week 9
the improvement in prediction due to the model (MSM) will be large, while the level of inaccuracy of the model (MSR ) will be small
What are the assumptions we make for simple linear regression? (5)
Week 9
- Linearity: x and y must be linearly related
- Absence of outliers
- Normality
- homoscedasticity
- Independence of residuals
How do we check for the assumption of normality in regression models and what would we expect to see (idk if this’ll be on the exam but just know it init)
Week 9
Using a normal P-P plot of regression standardised residual
* Ideally data points will lie in a reasonably straight diagonal line from bottom left to top right - this would suggest no major deviations from normality
How do we check for the assumption of Homoscedasticity in regression models and what would we expect to see
Using the scatterplot of regresssion standardised residual
* Ideally, residuals will be roughly, rectangularly distributed, with most scores concentrated in the centre (0)
What do the values of R, R^2 and adjusated R^2 each tell you about regression in the SPSS output
Week 9
- R - strength of relationship between x and Y
- R^2- proportion of variance explained by the model
- Adjusted R^2 - R^2 adjusted to account for the degrees of freedom (number of participants and number of parameters being estimated)
Why would we use adjusted R^2
Week 9
-If we wanted to use the regression model to generalise the results of our sample to the population, R2 is too optimistic
What are the key values identifying when evaluating the regression model and what do they mean? (3 values)
Week 9
- a - constant, also the intercept where the line intersects Y
- b - gradient of slope
- beta - slope converted to a standardised score
If there is only one predictor variable, what does this mean for the beta coefficient?
Week 9
Beta coefficient and R are the same value
Why would we use a T-test in a regression model
Week 9
- t-value: equivalent to √F when we only have 1 predictor variable)
- *i.e.** it does the same job as the F-test when we have just one predictor variable**
What additional info do we have regarding the b value in regression models?
Week 9
The b value has 95% confidence intervals
What else can R^2 be interpreted as
Week 9
the amount of variance in y explained by the model (SSM), relative to the total variance in y (SST)
In what ways can we express R^2
Week 9
as a proportion or as a percentage
What is the fundamental difference between correlation and regression
Week 9
Correlation shows what variance is shared,Regression explains the variance by showing that a certain amount of the variance can be explained by the mode
What does multiple regression allow us to do
Week 9
to assess the influence of several predictor variables (e.g. x1, x2, x3 etc…) on the outcome variable (y)
How does multiple regression work (basic description)/what do you need to do in order to conduct it?
Week 9
Need to combine both predictor variables to see the joint effect on the outcome variable
Why do we have to use a plane of best fit when proposing a model in multiple regression
Week 9
Because you’re looking at 3 things; outcome variable & predictor variables one and two , thus it will be best model in 3 dimensions instead of two, thats why we look at a plane instead of a line
What are some of the assumptions being made multiple regression? (4)
- Sufficient sample size
- Linearity - Predictor variables should be linearly related to the outcome variable
- Absence of outliers
- Multicollinearity - *Ideally, predictor variables will be correlated with the outcome variable but not with one another
What does a violaition of the assumption of multicollinearity mean? What is a way to tell if this has be violated?
Week 9
- There is some overlap in the variables you are measuring for (the predictor variables might be one thing in two different terms - e.g., confidence and self-esteem are basically the same)
- Predictor variables which are highly correlated with one another (r = .9 and above) are measuring much the same thing
if a multiple regression model is significant what does this mean
Week 9
- The regression model provides a better fit (explains more variance) than the simplest model
* I.e at least one of the slopes is not 0 (without specifying which)
What does hierarchical regression involve and what does this allow us to see?
Week 10
Hierarchical regression involves entering predictor variables in a specified order of ‘steps’ based on theoretical grounds.
This allows us to see the relative contribution of each ‘step’ (set of predictor variables) in making the prediction stronger.
Why do we use hierarchical regression
Week 10
- Examine influence of predictor variable(s) on an outcome variable after ‘controlling for’ (i.e partialling out) the influence of other variables
When doing a hierarchical regression what is the difference between step one and two.
Step 1 (what you want to partial out)
Step 2 (what you want to measure) = optimism
When looking at hierarchical regression in SPSS, what are we looking at?
Week 11
The row labelled Model 2. Particularly the R square change, F Change and Sig F change values. (Check SPSS, this will make sense)
What does the sig f change column tell us in Hierarchical regression?
Week 11
Whether this predictor variable alone explains a significant proportion of the variance of the outcome variable
What type of non-parametric tests are there and what are their parametric equivalents
Week 11
- Between P’s - Independent T-test → Mann-whitney U Test
- Within P’s - Paired T-test → Wilcoxon test
- Between P’s - 1 way independent ANOVA - Kruskal Wallis test
- Within P’s - 1 way Repeated measures ANOVA → Friedman test
What are the non parametric tests for factorial Designs
Week 11
Factorial designs do not have a non parametric equivalent and either need to have a simplified design or have adjustments made
What is the non parametric equivalent of pearsons correlation coefficient when N>20
Week 11
Spearmans rho
What is the non parametric equivalent of pearsons correlation coefficient when N<20?
week11
Kendall’s tau
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What types of nonparametric test exist for tests of relationships? (2)
week 11
Spearmans rho and Kendallls tau are both non parametric equivalents of pearsons correlation coefficient
What is the non parametric equivalent of partial correlation
week 11
Partial correlation has no non-parametric equivalent
what is the non parametric equivalent for regression
Regression has no non-parametric equivalent
What types of test do we use when analysing categorical data
Week 11
Chi-square (one variable or test of independence)
What type of test is a chi-square test
Week 11
non-parametric
What are the parametric equvalents of One-variable Chi-Square (a.k.a. Goodness of Fit Test) and
Chi-Square Test of Independence (two variables)
neither of them have parametric equivlaents, they are non-parametric only
What is an example of an Omnibus test?
Week 3
An ANOVA (because they control for familywise error rate)
How do you calculate the number of comparisons for an IV with n levels
Week 3
n x (n-1/2)
e.g N = 3
3((3-1)/2) = 3(2) / 2 = =6/2 = 3
e.g N = 6
6((6-1)/2) = 6((5)/2) = 30/2 = 15
