PS2021 stats exam Flashcards
What is Significance and how is it measured?
P value is used to denote significance
How surprising our data is
What is the null hypothesis
Suggests no effects
The hypothesis that there is no significant difference between specified populations, any observed difference being due to sampling or experimental error
What is the alternative hypothesis
Suggests there is the effect that was predicted
What is a p value, and what does a high and low one mean?
P values denote significance.
A lower p value is evidence to reject the null hypothesis
A higher p value is evidence to fail to reject the null hypothesis
What is the difference between independent and repeated designs?
Independent designs have different participants and the same participants are used in repeated.
What is a factorial design?
When there is more than one independent variable
What are the different types of factorial design and what do they consist of?
Factorial independent design
Factorial repeated design
Factorial mixed design –> both repeated and independent conditions??
What are the assumptions of a parametric analysis?
- Independence of observations
- Interval or ratio level data
- Normally distributed data
- Homogeneity of variance
What is meant by independence of observations?
One ppt cannot influence another’s data
What is meant by interval or ratio level data
Data is scored along a continuum
What is meant by homogeneity of variance?
The variance in the data set across groups/conditions should be roughly similar
How to test normality? In independent and repeated
Look at the histogram, data should cluster around the mean –> avoid skewness & kurtosis
If its independent: evaluate normality within each condition
If it’s repeated: evaluate normality of difference scores
How do you test homogeneity of variance
Levene’s statistic has to be used for independent design
The p value needs to be not significant for there to be homogeneity of variance
How do you report homogeneity of variance in apa format
F(df1, df2) = Levene’s statistic ‘based on mean’, p
How do you test normality on SPSS?
The Kolmogorov-Smirnov test
The p value needs to be not significant for normality
How do you report normality in SPSS?
D(df) = statistic, p = significance
D and p in italics!
What to do if Levene is not significant in an independent t test?
This means that the assumption has been met
Use the equal variances assumed row and continue with the parametric t test
What happens if Levene’s is significant in an independent t test
The assumption has been violated
SPSS does a correction to the df to correct and adjust the analysis slightly, if you violate the assumptions it makes it more conservative and difficult to get a significant result because you’ve violated that assumption.
What do you do if normality is skewed in certain conditions
Use a Mann Whitney U test
U = ‘Mann-Whitney U statistic’, z = ‘Z statistic’, p = ‘Asymp. Sig’
Do you measure homogeneity of variance in a repeated design?
Homogeneity of variance is not relevant for repeated designs!
Parametric assumption: Independence of observations
o One data point should not influence another
BUT – repeated measures, so can’t avoid this!
o If my memory is bad it will be bad in both conditions
In repeated designs random variance is reduced
o No individual differences between condition
In repeated designs there is a different assumption
o Sphericity
What do you do if normality is violated in a repeated t test?
Use a Wilcoxon test
(z = ‘Z statistic’, p = ‘Asymp. Sig’)
z and p in italics
What is a one sample t test?
One sample t tests compare the data from a single sample of participants to a “reference value”
What statistical test should you run when comparing more than two groups?
ANOVA
With each t test there is a 5% chance of saying there is a difference when there really isn’t a difference (p = .050)
ANOVA controls for all of that type 1 error within it, you just get 5% chance of error overall
What is Type 1 error
Falsely rejecting the null hypothesis
What is family wise error?
Inflating chance of finding something
What is experimental variance?
o Variability between conditions
o Due to experimental manipulation
What is random variance?
o Variability within conditions
o Due to measurement error
o Due to individual differences
o Due to unmeasured variables
What is the ANOVA statistic and what does it show
F ratio ≈ Experimental variance / Random variance
What does a larger F ratio show?
The larger the F ratio the greater the variance between the groups that is explained by experimental manipulation
Large F ratios = significant results
How to report a one-way independent ANOVA?
F(model df, error df) = F ratio, p = significance
F and p in italics!
What is model df?
Model df –> based on IV number of conditions minus one.
Note - it’s labelled as whatever the IV is under ‘tests of between-subjects effects’
What is error df?
Based on number of participants in each condition minus 1, summed together e.g., (10-1) + (10-1) + (10-1) + (10-1)
Note - it’s labelled as Error under ‘tests of between-subjects effects’
What are the different ways of breaking a main effect of a one-way independent ANOVA?
Bonferroni t test (old fashioned)
Planned contrasts
Post hoc contrasts
How do you break down the main effect of a one-way independent ANOVA using a Bonferroni t tests?
• Compare conditions with t test
o But we would need 6 t tests!!!
• Familywise error: 6 * 5% Type I Error
• Bonferroni correction:
o Change alpha level (criteria for significance)
o Bonferroni alpha = .050 / number of comparisons to be made
o Bonferroni alpha = .050 / 6
o Bonferroni alpha = .008
• Run all pairwise comparisons with t tests (see last week)
o BUT – t tests are only significant if p ≤ .008
Why do you have to do a Bonferroni correction and how do you do this?
A Bonferroni test compares conditions with a t test, but it would require many t tests!
This would lead to family wise error as there is a potential 5% Type 1 error for every comparison
For this reason you have to change the alpha level (criteria for significance) by the number of comparisons to be made
Then you run all pairwise comparisons with t tests
- But t tests are only significant to the new alpha level e.g., .05 divided by 6 comparisons = p < .008
The 5% error is shared across all the tests so it won’t go above this error –> the new significance level much stricter
When would use planned contrasts?
When you have a one tailed hypotheses (the direction of any significant differences is specified)
When would use post hoc contrasts?
When you have a one tailed hypotheses (a difference is predicted, but with no direction)
What are the different types of planned comparisons?
Simple - Compares the effect of each condition to the control (defined as “reference” and “first”) condition e.g., 1 v s2, 1 vs 3, 1 vs 4
Repeated - Compares the effect of each condition to the next condition e.g., 1 vs 2, 2 vs 3, 3 vs 4
Deviation - Compares the effect of each condition (except the first – defined as “reference”) to the overall effect e.g., 2 vs 1234, 3 vs 1234, 4 vs 1234
Helmert - Compares the effect of each condition to the overall effect of all following conditions e.g., 4 vs 321, 3 vs 21, 2 vs 1
What is a polynomial planned contrast?
Trend analysis: looks at patterns in the data –> can only be used in very specific designs, cannot be used with every ANOVA
- Trend analysis is only appropriate for continuous IVs
If you are running an ANOVA and the levenes test is significant (assumption violated) what test should you use?
use a Kruskal Wallis test
If you are running an ANOVA and normality test is violated what test should you use?
use a Kruskal Wallis test
How do you write up a Kruskal Wallis test
(H = ‘H statistic’, p < ‘p value’)
Break
Break
What is an independent one way ANOVA?
When you compare more than two independent groups with only one independent variable
E.g., Time of day (morning, afternoon, night) and IQ scores
What is an independent two way ANOVA
When you compare more than two independent groups with two independent variables
How do you write up an independent ANOVA?
- Which type of ANOVA did you run and why?
- -> What IV? Independent or repeated? Number of levels? What is the dependent variable?
- How do you break down the main effect?
- -> Planned or post hoc tests? Which contrast and why? Hypothesis!
- Is the assumption of homogeneity of variance met?
–> Give statistic using APA standards and interpret the finding
F (df1, df2) = F ratio, p =significance
-Was the main effect significant?
–> Give stats using APA standards and interpret the finding
F (model df, error df) = F ratio, p =significance
- Interpret the main effect
–> Use graph, descriptives and planned/post hoc contrasts
Use all their in combination to explain where differences are
When should you use planned/post hoc contrasts
If the result is not significant, give the descriptives but don’t go any further. Only use the planned/post hoc contrasts if your main effect is significant.
What is the assumption of sphericity?
Sphericity refers to the condition where the variances of the differences between all combinations of related groups are equal.
o How consistent is the manipulation across conditions?
o E.g., if we give participants an extra bar of chocolate, is the change in happiness consistent? Or inconsistent?
o Want consistent changes across conditions!
Are the changes between a participant’s scores between conditions the same as each other – are they all going up or down by the same amount?
We want to see similar variability in change scores
Why can’t Levene’s be used for a repeated design?
Variance in each population should be equal. The Independence of observations assumption is violated in repeated designs
o Variances across repeated measures conditions are likely to be similar, because they come from the same people!
o So, will have less random variance as there are no individual differences between conditions
How is sphericity measured and when is it violated?
Using Mauchly’s test of sphericity.
When Mauchly’s test of sphericity is not significant The assumption of having sphericity is met
–> this is because there’s no significant difference in the variability of the different scores
What do you do when sphericity is violated?
If assumption is violated…
SPSS provides a “correction”
o Various options available, but…
o “Greenhouse-Geisser” correction best
How does the Greenhouse-Geisser correction work?
o Calculation of variance and F ratio will remain the same
o Changes degrees of freedom: Reduced df means a bigger effect needed to achieve a significant finding
o Correction is proportional to the magnitude of violation
o SPSS will automatically give you corrections..
How do you write out Mauchly’s test in APA format?
W = ‘Mauchly’s W’, χ2 (df) = ‘Chi-Square’, p = significance
How do you report G-G corrected stats when sphericity is violated?
F (model df, error df) = ‘F statistic’, p = significance
These are all taken from the Greenhouse Geisser rows
How do you write up a repeated ANOVA?
- Which type of ANOVA did you run and why?
- -> What IV? Independent or repeated? Number of levels? What is the dependent variable?
- How do you break down the main effect?
- -> Planned or post hoc tests? Which contrast and why? Hypothesis!
- Is the assumption of sphericity met?
–> Give statistic using APA standards and interpret the finding
W = ‘Mauchly’s W’, χ2 (df) = ‘Chi-Square’, p = significance
If significant, give G-G corrected statistic using APA standards and interpret
F (model df, error df) = ‘F statistic’, p = significance
If not significant, give ‘sphericity assumed’ stats using APA standards and interpret
F (model df, error df) = ‘F statistic’, p = significance
- Interpret the main effect
–> Use graph, descriptives and planned/post hoc contrasts
Use all their in combination to explain where differences are
What are the different types of one-way ANOVA’s?
- One-way repeated (for more than 2 repeated conditions)
* One-way independent (for more than 2 independent groups).
What is a factorial ANOVA?
This is an ANOVA that includes more than one independent variable
e.g., if IV1 is handedness (left, right, ambidextrous) and IV2 is film watched (sci-fi or romcom) and DV is travel sickness
This would be analysed using a 3 x 2 independent ANOVA
3 (left, right, ambidextrous) by 2 (sci-fi, romcom)
What type of IV’s are in Factorial ANOVA’s
IVs should be categorical (conditions, groups).
What are the different types of factorial ANOVA’s?
- 2 IVs = Two-way ANOVA.
- 3 IVs = Three-way ANOVA.
You can have even more IVs, but don’t bother!
Why run a factorial ANOVA instead of separate ANOVA’s or t tests?
Multiple analyses like this increase chances of false positives
Adding a 2nd IV allows us to analyse whether the difference seen for one IV is dependent on the level of the other IV
There’s also more power
o Adding factors helps us to reduce the error term, by accounting for variance that would otherwise be unexplained.
o Reducing the unexplained/random variance in cake.
What hypotheses do you need in a factorial ANOVA?
You need a hypothesis for each independent variable and one for the interaction effect prediction
What contrasts or comparisons do you use in a factorial ANOVA?
If the hypothesis is one-tailed use planned contrasts
If the hypothesis is two-tailed then use post hoc contrasts
How do you report the three main effects in APA format?
Main effect 1 = F (df, error df) = ‘F stat’, p < significance, n^2 = ‘partial Eta squared’
Main effect 2 = F (df, error df) = ‘F stat’, p < significance, n^2 = ‘partial Eta squared’
Interaction = F (df, error df) = ‘F stat’, p < significance, n^2 = ‘partial Eta squared’
What do you do after you have a main effect for a factorial ANOVA?
Use the multiple comparisons to break down a main effect. Then report the mean and standard error to understand which condition is significantly higher/lower.
E.g., • There was a significant main effect of handedness on sickness score (F(2,24) = 17.09, p
What does an interaction effect show?
An interaction can tell you if the differences across one IV differ depending on the second IV.
How do you break down an interaction effect?
If one of the IV’s only has two conditions, we could run independent measures t-tests looking at one of the IV’s for each level of the other IV.
Report all the t tests at each level t(df) = ‘t statistic’, p = significance. Bonferroni corrections need to be applied here because SPSS does not know how many comparisons are being made (divide .05 by the number of comparisons)
When reporting the interaction, you must also report descriptive statistics.
If both IVs have more than two levels run separate one-way ANOVAs and use post-hocs to break them down. Use bonferroni when needed.