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51 Cards in this Set
- Front
- Back
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Minimizing Individual Differences |
- In basic between-subject designs, can randomise (does little), standardise, practice before real trials (exp. control) to reduce IDs Other options: Between (independent) subjects design - Analysis of Covariance (between subs design), statistically removes some (not all) individual differences - Within (repeated measures) subject design (removesinitial group non-equivalence as a confound by putting the same people in everygroups) |
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Repeated Measures ANOVA [Repeated Measures Design) |
By having the same people in each condition in arepeated measures design we effectively eliminate group non‐equivalence as aconfound, eliminate it as a plausible rival explanation for any changes weobserve in our IV - BUT [putting the same people in every condition]we introduce time related threats to internal validity (confoundingvariables) -E.g. History, maturation, regression to the mean |
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Individual Differences in an Independent Groups [Between Subjects] Design |
The problems of individual differences: * Group non-equivalence contributing to between groups variance - Randomisation attempt to equate IDs, groups still differ on average * Inflated Within Groups Variance - Can be reduced by proper controls/standardisation - Individual differences remain a major source of error variance in independent group designs |
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Removing Individual Differences [Independent Groups Design] [Between Subjects Design] |
If removed, design much more powerful - Can be removed as a source of error variance by adopting a repeated measures design/analysis - Removes both within/between ID by placing the same participants in all conditions - E.g. Duration of headaches after _ week(s) of meditation, end up with a piece of data for each participant each week (over the five weeks) - ID can no longer explain the differences between conditions because the same people are in each condition |
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Repeated Measures ANOVA: Terminology Change |
Independent ANOVA: Between Groups, Within Groups Repeated Measures ANOVA: NOW Between Levels, Within Levels - Only one group |
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Between Levels Variance |
Due to: Errors in control Errors in measurement Effects of IV But not individual differences - as same participants in each condition |
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Within Levels Variance |
E.g. Headache/Meditation: Why do the scores in the week one condition differ from eachother, week 2 differ from each other etc.? - Errors in control, measurement, effects of IV, individual diff (primary) Having the same participants perform in allconditions removes individual differences from between levels but not fromwithin levels variance. Cannot be due to the IV as it is a measure of variability in each condition |
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F-Ratio Still Suited? [No] |
No, thisis because removing individual differences from between levels variance leadsus to have something unworkable - To restore balance we must remove ID from within levels variance as well - Need to partition within-level variance |
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The Partition of Within Levels Variance |
Within Levels SS --> Between Subjects SS (ID) --> Error SS (Error) Component 1: Between Subjects SS (ID part) Component 2: Error SS (within levels variance minus individual differences) |
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F-Ratio [Repeated Measures ANOVA] |
- F = Between Levels Variance / Error Variance F = MeasErr+ControlErr+EffectsOfIV / MeasErr+ControlErr - Within Levels Variance minus individual differences F-ratio larger than 1 indicatesa treatment effect (H1), an F-ratio around 1 does not (H0) |
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Assumptions of Repeated Measures ANOVA [One more added, Sphericity] |
Independence Scale data Normality Homogeneity of Variance Sphericity |
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Sphericity [Repeated Measures ANOVA] |
[The variance of the different scores between any two conditions] is the same as [the variance of the different scores between any two other conditions] - Difference scores: Cond 1 - Cond 2, Cond 2 - Cond 3, Cond 1 - Cond 3 - Can calculate a different pair of scores foreach condition - The sphericity assumption says that should beroughly the same amount of variability in all three sets of different scores - Basically homogeneity of variance but instead of raw scores, diff scores |
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Test For Sphericity [Repeated Measures ANOVA] |
Tested using Mauchly's W test - If significant (p < .05), then the data departs from sphericity - Repeated Measures ANOVA verysensitive to departures from sphericity, if violated we need to make acorrection |
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If Mauchly's W is Not Significant... |
If not sig., we read the top row (Sphericity Assumed, SPSS) - Then take df, F-ratio and sig. - F= Between Levels Variance / Error Variance - BLV located in sphericity assumed (sum of squares) - Error variance (SS) located in sphericity assumed, error section - Each figure divided by own df = meansquare, then divided again to get F - E.g. F(4,16) = 47.94, p < .001 (Significant, reject H0) |
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If Mauchly's W is Significant... [Repeated Measures ANOVA] |
If Mauchly’s W is significant, the sphericityassumption has been violated, repeated measures ANOVA very sensitive to this An epsilon based correction is recommended |
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Epsilon Based Correction (Huyn-Feldt value) [If Mauchly is Violated] |
If Mauchly is violated, an adjustment (Epsilon Based Adjustment) is made to the degrees of freedom in whichsignificance is evaluated to ensure that the type one error rate does notexceed 5% .05 - Assumptionviolations inflate type-1 error rates - Multiply the df (E.g., 4, 16) by the epsilon (Huyn-Feldt) - E.g. 4 x .761 = 3.04; 16 x .761 - Provides critical F in which to compare our calculated F |
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If Mauchly's W is Significant: Results [Repeated Measures ANOVA] |
Must make sure we readHuynh-Feldt rows instead of sphericity assumed |
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Follow-Ups and Effect Sizes [Repeated Measures ANOVA] |
As ourANOVA was statistically significant and because the IV has more than twolevels the outcome is ambiguous, we do not specifically know which levels ofthe IV differ from each other, to follow up from this we should - Post-Hoc/Planned Comparisons - η2 as a measure of variance in DV explained by IV |
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Evaluation of Repeated Measures Designs [Between Levels] |
- Effectively removed individual differences - Introduces new systematic confounds, order effects - Normallywe introduce counterbalancing techniques, randomising the order in whichparticipants are exposed to a level of the IV - Counterbalancing is only effective when the order effects aresymmetrical, exposure to level 2 has the same effects on the experience oflevel 1 as exposure to level 1 has on level 2 |
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Order Effects |
Order effects occur when exposures to some levels of the IV influencehow participants respond to other levels (practice effect, fatigue) |
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Evaluation of Repeated Measures Designs [Within Levels] |
- By design, individual differences are eliminated from between-levelsvariance and within-levels from statistics - Repeated measures ANOVA test removes the largestsource of error variance (individual differences) - Repeated measures designs are more powerful, need less subjects |
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More Sensitive Tests Lead to More Complex Assumptions... |
- Complex assumptions are hard tomeet. - The riskof a Type 1 error is raised - Our sphericity assumptions arelikely to be violated - Attempts to minimise these T1 risks by making an Epsilonadjustments = less power - Power gained from RM ANOVA lost due to violations of assumptions |
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Recap: Individual Differences, Repeated Measure Designs, |
- Repeated measures designs canbe used to reduce the influences of individual differences in experimentalresearch, same participants placed in every condition, cannot always be employed - Cannot perform surgery 1, undo it, perform surgery 2 - For practical reasons researchers often opt for an independent groupsdesign, whilst still wanting the power associated with a repeated measuresdesign, this is where an ANCOVA come into play
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ANCOVA (One Way Analysis of Covariance) |
- Allowsus to account for and reduce the effects of individual differences in anindependent groups context, statistically rather than methodo. - Equates everyone in the sample on key individualdifferences, once done it becomes easier to see the effect of the IV - In equating everyone in the sample based on the individual differencesfactors, it removes them as a source of error variance in the experiment – Removing them as a source of between-groups variance and also as a source ofwithin-groups variance |
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F-Ratio Recap |
F = BGV / WGV Between Groups Variance: The means differ acrossconditions Within Groups Variance: Individual scores differ(difference) withineach condition We must address individual differences in boththese sources of variance |
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Minimising Individual Differences: BGV |
Good at minimising IDs, - In repeated measuresdesign we put the same participants in each condition guaranteeing that IDs are not causing the diff. weobserve between treatment means |
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Minimising Individual Differences: WGV |
Inan independent-groups ANOVA, we randomise and hope that that equates to thethree groups. Moredifficult to minimise the amount of ID in within-groups variance Done statistically in RM design, can be done statistically with ANCOVA |
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Minimising Individual Differences: Independent Groups Design |
- Random allocation (not guaranteed) - Match Groups (Recruiting pairs/trios of similar participants then randomising them, very hard) |
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Minimising Individual Differences: Repeated Measures Design |
- Same participants in each condition (introduces order effects) - Great at eliminating IDs as a source of between levels variance, done by puttingthe same participants in every condition - Canend up with order effects – practice/fatigue - Not always possible |
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Minimising Individual Differences: Interdependent Groups Design |
- Standardise procedures (practice, telling participants what is expected of them) - Swamped in error - Willstill be individual differences, as the participants are different people |
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Minimising Individual Differences: Repeated Measures Design |
- Individual differences are subtractedstatistically - Ableto split the within levels variance and remove the bits associated withindividual differences = more power |
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Removing Individual Differences from Independent Groups Designs? |
- Make use of a technique that is used by thoseseeking to explain individual differences (prior to running an experiment) - Regression (partialling) |
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Regression (Partialling) |
Theability to statistically control or hold things constant - Partialling enables you to do things you cannot do in an experimental situation- Technique used: ANCOVA |
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ANCOVA |
- Techniquefor dealing with individual differences - Allowsus to account for individual differences as a source of bgv and wgv in an independent groups design - Does not remove all ID, just what is able to be measured Statistically removing IDs will make participants more similar statistically - ANCOVA is a procedure by whichwe directly measure specific individual differences we consider to beresponsible for the variability in our DV, overshadowing the effects of the IV, then remove them |
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ANCOVA: Example |
- 3 different teaching methods, DV is spellingability - Does teaching method effect spelling ability - Do the three means presented differ by more thanwhat would be expected by chance alone - Focused on the typical person, how does someonetypically perform after being exposed to the three teaching methods |
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Explanation of Statistical Non-Significance [ANCOVA] |
Assuming no confounds: - Manipulation of IV ineffective- Not enough power (ind diff.) (indep swamped) - ANCOVA is a procedure by whichwe directly measure specific individual differences we consider to beresponsible for the variability in our DV, overshadowing the effects of the IV, then remove them |
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The Covariate [ANCOVA] |
The individual differencesthat we wish to remove mathematically from both the between/with groupsvariance estimates are referred to as covariates - It must be an individual difference that iscorrelated to the DV |
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The Covariate: Example [ANCOVA] |
If DV: Spelling Score, Covariate: Verbal IQ (related to spelling ability) - Statistically equating all of our variance on verbal IQ,to make it as though they all have the same verbal IQs If all individuals the same in terms of verbal IQ (statistically), thegroups will no longer differ in terms of verbal IQ (and can thus no longer influenceresults) - If we can statistically account for the proportion of variability inspelling that is due to differences in verbal IQ, we will reduce the overallwithin-groups variance – subsequently making the effects of teaching method (IV)easier to detect |
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Performing the ANCOVA [Boxplot] |
Now each participant has two bits of data (VIQ, Spelling Score) 1. Arrange participant scores (low/high) 2. See how far each point deviates from group mean (P1: -1p above mean, P2: +7p above mean) 3. Scatterplot DV(Y Axis), Covariate (X Axis), plot participant scores with a mean line, then add line of best fit (does not fit perfect but can account for some variability, not all.) Line reaching from mean to (DV), tells us total variability. |
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Performing the ANCOVA: Cont. [Boxplot] |
New line spanning from mean line to line of regression tells us for participant x, taking VIQ into account, the best guess of their spelling score (DV) will be x. - Regression line does not fully account for variability, e.g. score above far above the line of regression, other IDs are an explanation for this - But variability from regression line is much less than total variability |
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Performing the ANCOVA: Cont. [Boxplot] |
- Scatterof scores around the regression line is referred to as adjusted within-groupsvariance,it is the within-groups variability that cannot be accounted for by verbal IQ - Scatterof points around the mean is referred to as unadjusted within-groups variance Summary: Theaverage deviation of scores from the regression line is less than the averagedeviation of scores from the group mean, the larger amount of within-groupsvariance we had initially has been made much smaller by taking verbal IQ intoaccount |
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Adjusted Within-Groups Variance [ANCOVA] |
Scatter of scores around the regression line, it is the within-groups variability that cannot be accounted for by the covariate (verbal IQ) |
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F-Ratio [ANCOVA] |
The within groups variancewe are now using in the F ratio will be the adjusted within-groups variance, wehave made the denominator smaller – making it easier to see any treatmenteffect - Shrinking the amount of variance due to IDs makes the test more sensitive to seeing the effects of the IV |
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Performing the ANCOVA (Cannot be used in non-exp research) |
1. Measure participant on the covariate (needs tooccur first) 2. Randomly allocate participants to the experimentalgroups (if possible) (Important) 3. Measure participants on the DV followingadministration of their treatment - Similar to ANOVA but BEFORE the experimentthe participant is also measured on covariate |
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ANCOVA Output: SPSS |
* IQ row tells you relationship between DV and covariate (want this to be sig., no point selecting a covariate that is not correlated) * Method row: theeffects of the independent variable - Is spelling ability influenced by a teaching method after controllingfor verbal IQ, it is as (p = .018) * Error Row: within-groups error variance * Stat sentence: F(2, 20) = 4.96, p = .018
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ANCOVA/ANOVA Contrast |
- Both interested in the effects of teachingmethod (IV) - Both based on same spelling data, yet the ANCOVAis significant and the ANOVA is not - Because the ANOVA is swamped in errorvariance, IV masked - ANCOVA has mopped up most of this variance byaccounting for verbal IQ, making it easier to see the effects of the experiment(test is more powerful) - The interpretation is: Yes, the teaching methodsdid have a statistically significant effect on spelling ability AFTERcontrolling for verbal IQ |
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ANCOVA: Follow Up Tests and Effect Sizes |
- Results are ambiguous (do not know therelationships between each IV, differ) - Ambiguous omnibus F can be followed by post-hoc tests/planned comparisons - Need measure of effect size (η2) - η2 = SS[For Method] / SS[Corrected Total] |
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Evaluation of ANCOVA [Between Groups Variance] |
- Between Groups Variance equates (all) groups on covariate - If randomised, the impact of doing this onbetween-groups variance should be relatively small, groupshould look more or less the same anyway |
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Evaluation of ANCOVA [Within Groups Variance] |
- Reducesto a much greater extent than what it reduces in between-groups variance, thisis because it takes out any within-groups variability that can be contributedto the covariate - Thesmaller the within-groups variance is relative to between-groups variance, thegreater the size of F (sig. increases) |
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Evaluation of ANCOVA: Assumptions |
- More complex and difficult to meet. - More sophisticated and powerful the technique,the more harder it is to meet the assumptions |
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ANCOVA WARNINGS |
- Never ever do if covariate is not correlated, makes test less sensitive than independent groups ANOVA - Always measure covariate before administration of treatments - If the covariate becomes correlated with the treatment, then when weremove the variance attributable to the covariate from the DV, we will also endup removing variance attributable to the treatment |
