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Research Design & Statistics > Lecture 6: ANCOVA > Flashcards

Lecture 6: ANCOVA Flashcards

1
Q

What is the decision tree for choosing ANCOVA? - (5)

A

Q: What sort of measurement? A: Continuous
Q:How many predictor variables? A: Two
Q: What type of predictor variable? A: Both Categorical and Continuous
Q: How many levels of the categorical predictor? A: Two or more
Q: Same or Different participants for each predictor level? A: Assumed different

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2
Q

one-way ANOVA could be charactercised in terms of a

A

multiple regression equation that used dummy variables to code group memberships

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3
Q

regression equation which includes a lot of predictor variables for ANOVA can extended to include one or more

A

continous variables that predict outcome/DV

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4
Q

regression equation for ANOVA
can be extended to include one or more continuous variables that predict the outcome (or dependent variable).

these continous variables are not

A

part of the main experimental manipulation but have an influence on the dependent variable, are known as covariates and they can be included
in an ANOVA analysis.

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5
Q

What does ANCOVA involve?

A

When we measure covariates and include them in an
analysis of variance

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6
Q

Continuous variables, that are not part of the main experimental manipulation (don’t want to study them) but have an influence on the dependent variable, are known as

A

covariates

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7
Q

What does ANCOVA stand for?

A

Analysis of covariance

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8
Q

From what we know from hierarchical regression model, if we enter covariate into regression model first then dummy variables representing exp manipulation after… - (2)

A

then we can see what effect an IV has after the effect of covariate

We partial out the effect of covariate

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9
Q

What are the two reasons for including covariates in ANOVA? - (2)

A
  • To reduce within-group error variance = if we can explain unexplained variance , SSR, in terms of other variables (covariates)then reduce SSR to accurately assess effects of SSM
  • Elimination of confoundd = remove bias of unmeasured variables that confound results and influence DV
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10
Q

ANCOVOA has same assumptions of ANOVA, e.g., normality and homogenity of variance (Levene’s test) expect has two more important assumptions which are… - (2)

A
  • Independence of the covariate and treatment effect
  • Homogeneity of regression slopes
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11
Q

For ANCOVA to reduce within-group variance by allowing the covariate to explain some of the error variance the covariate must be

A

independent from the experimental/treatment effect - (IVs - categorical predictors) ( ANCOVA assumption)

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12
Q

People should no use ANCOVA when the effect of covariate overlaps with the experimental effect as it means the

A

experimental effect is confounded with the effect of covariate = interpretation of ANCOVA is compromised

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13
Q

In ANCOVA, the effect of the covariate should be independent of the

A

experimental effect

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14
Q

When an ANCOVA is conducted we look at the overall relationship between DV and covariate meaning we fit a regression line to

A

entire dataset and ignore which groups pps fit in

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15
Q

In ANCOVA, we fit an overall regression line to the entire data set, ignoring to which group a person belongs.

In fitting this overall model we, therefore, assume that this

A

overall relationship is true for all grps of pps (e.g., if there is a positive relation between covariate and outcome in one group assume positive relation in all grps) - homogenity of regression slopes

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16
Q

When is homogenity of regression slope is not satisifed in ANCOVA?

A

the relationship between the
outcome (dependent variable) and covariate differs across the groups then the overall regression model is inaccurate (it does not represent all of the groups).

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17
Q

What is best way to test homeogenity of regression slopes assumption in ANCOVA?

A

imagine plotting a scatterplot for each experimental condition with the covariate on one axis and the outcome on the other and calculate its regression line

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18
Q

Diagram of regression slopes satisfying homogenity of regression slopes

A
  • exhibits the same slopes
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19
Q

Diagram of a regression slopes not satisfying homogenity of regression slopes

A
  • 30 minutes of therapy exhibts a different slope compared to others
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20
Q

What is design, variables and test would you use to test this researh scenario? - (5)

A
  • ANCOVA
  • Independent samples-design
  • One IV , two conditions, interval regime and steady state
  • One covariate (age in years)
  • One DV (Race time)
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21
Q

What does SPSS output show? - (3)

A
  • Interval group has race time of 57 minutes
  • Steady state has race time of 62.97 minutes
  • Levene’s test shows we have equal variances since we have a non-significant p-value (p = 0.934)
22
Q

What does this ANCOVA output show? - (2)

A
  • Age F(1,27) = 5.36, p = 0.028, partial eta-squared = 0.17 (large and sig main effect)
  • Regime F(1,27) = 4.28, p = 0.048, partial eta-squared = 0.14 (large and sig main effect)
23
Q

What DF do you report from this ANCOVA table for age for example…

A

DF for age and DF for error

24
Q

Guidelines for interpreting partial eta-squared - (3)

A

η2 = 0.01 indicates a small effect.
η2 = 0.06 indicates a medium effect.
η2 = 0.14 indicates a large effect

25
Q

What does this SPSS output for ANCOVA show? - (3)

A
  • Interval has a marginal mean of race times of 56.57
  • Steady state has a marginal mean of race times 62.97
  • Estimated marginal means partialled out the effects of age and view mean scores of race times in interval and steady state if mean age scores (30.07) across two groups was held constant
26
Q

What does this output show in terms of homogenity of regression slopes?

age is covariate and regime is IV and DV is race times - (2)

A
  • Interaction effect of regime * age has a p-value of 0.980
  • Since p-value is not significant the assumption of homogeneity of regression slopes has been met
27
Q

What happens if the interaction effect of IV and covariate is significant in testing homogenity of regression slopes

A

relationship between covariate and DV differ significantly between two groups or many groups you got and assumption is not satisfied

28
Q

For testing assumption of independence of covariate and experimental effect (IV) in SPSS, we need to add

A

IV (e.g., regime) and covariate (e.g., age) in DV instead of covariate box

29
Q

What does this SPSS output show in terms of independence of covariate and exp effect (IV)?

age is covariate (treated as DV) , regime is IV - (2)

A
  • P-value is not signifcant (p=0.528) so effect of variable age is not sig difference of age across training regime
  • and so independent variable are assumed to be independent.
30
Q

We can look at parameter estimates table in ANCOVA to

A

interpret the covariate

31
Q

What does positive and negative b-value for covariates in ANCOVA parameter estimate box indicate? - (2)

A

f the b-value for the covariate is positive then it means that the covariate and the outcome variable have a positive relationship

If the b-value is negative it means the opposite: that the covariate and the outcome variable have a negative relationship

32
Q

What does this table of parameter estimates show for ANCOVA where..

DV = Libido, IV = Dose of Viagara, Covariate is Libido - (3)

A
  • b for covariate is 0.416
  • Besides other things being equal, if a a partner’s libido increases by one unit, then the person’s libido should
    increase by just 0.416 units
  • Since b is positive then partner’s libido ahs pos relation with pps’s libido
33
Q

How is DF calculated for these t-tests in ANCOVA table? - (2)

A

N - p -1
N is total sample size, p is number of predictors (2 dummy variables and covariate )

34
Q

What post-hoc tests can you do with ANCOVA? - (3)

A
  • Tukey LSD with no adjustments (not reccomended)
  • Bonferroni correction (reccomended)
  • Sidak correction
35
Q

The sidak correction is similar to what correction?

A

Bonferroni correction

36
Q

Sidak correction is less conserative than

A

Bonferroni correction

37
Q

The Sidak correction should be selected if you are concerned about

A

loss of power associated with Bonferroni corrected values.

38
Q

What does these planned contrast results show in ANCOVA?

DV = Libido, IV = Dose of Viagara, Covariate is Libido -

IV Dose: Level 3 = high dose, level 2 = low dose, level 1 = placebo

(3)

A
  • Contrast 1 of comparing level 2 (low dose) against level 1 (placebo) is significant (p = 0.045)
  • Contrast 2 of comparing level 3 (high dose) with level 1 (placebo) is significant (p - 0.010)
39
Q

What does this Sidak correction post-hoc comparison in ANCOVA output show?

DV = Libido, IV = Dose of Viagara, Covariate is Libido -

IV Dose: Level 3 = high dose, level 2 = low dose, level 1 = placebo

    • (3)
A
  • The significant difference between the high-dose and placebo groups remains (p = .030)
  • high-dose and low-dose groups do not significantly differ (p = .93)
  • Low dose and placebo groups do not significantly differ (p value = 0.130)
40
Q

What do these scatterplot of regression lines show in terms of homogenity of regression slopes?

DV = Libido, IV = Dose of Viagara, Covariate is Libido -

IV Dose: Level 3 = high dose, level 2 = low dose, level 1 = placebo

(3)

A

For placebo and low dose there appears to be a positive relationship between pp’s libido and that of their partner

However, in the high-dose condition there appears to be no relationship at all between participant’s libido and that of their partner - shows negative relationship

Doubts whether homogenity of regression slopes is satisfied as not all the slopes are the same (go same direction)

41
Q

What effect sizes can we use for ANCOVA/ANOVA? - (4)

A
  • eta-squared
  • partial-eta squared (ANCOVA)
  • omega squared = used when equal numbe of pps in each grp
  • r
42
Q

How is eta-squared calcuated?

A

Dividing the effect of interest SSM by total variance in the data SST

43
Q

How is partial eta-squared calculated?

A

SS Effect/ SS Effect + SS Residual

44
Q

What is the difference between partial and eta-squared?

A

This differs from eta squared in that it looks
not at the proportion of total variance that a variable explains, but at the proportion of variance that a variable explains that is not explained by other variables in the analysis

45
Q

What test is used to investigate this question and how is it conducted?

We want to know whether or not studying technique (3 levels) has an impact on exam scores,but we want to account for the grade that the student already has in the class.

A
  • ANCOVA
  • ANCOVA is conducted to determine i f there is a statistically significant difference between different studying techniques (IV) on exam score (DV) after controlling for current grade (covariate)
46
Q

In ANCOVA, we partion the totasl variance into

A

IV, DV and covariate

47
Q

In ANCOVA, examine influence of categorical IVs on DV while removing the effect of

A

covariate factor(s)

48
Q

In ANCOVA, the covariate correlates with the … but not the ..

A

correlates with outcome DV but not with IV

49
Q

What is an example of covariate?

A

baseline pre-test scores can be used as a covariate to control for inital grp differences on test performance

50
Q

In ANCOVA, the IVS, Covariates and DVs are.. - (2)

A
  • IVs are categorical
  • Covariates are metric (quantiatively) independent of IV
  • DV is metric

Research Design & Statistics (19 decks)

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