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# Statistical Methods MCQ'S ANCOVA, MANOVA and Regression/Correlation

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- Created by: Rhys Hawkins
- Created on: 08-04-18 15:34

If the Null Hypothesis is true, then the treatment effect is equal to...

0

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If the Null Hypothesis is false, then the treatment effect is more than...

0

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What x2 sources of variability does ANOVA use as a ratio?

Between groups, Within Subjects

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ANOVA transforms deviations to what, and for what reason?

variance, to test the Null Hypothesis

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ANOVA defines variance as...

sum of Squared Deviations From the Mean/Degree's of Freedom

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Why do we use basic ratios?

To simplify the calculation of Sum of Squares

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Sum of Squares is defined as:

** Total = ** Within + ** Between

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A basic ratio is expressed as...

∑(Score or 〖Sum〗^2)/Divisor

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A researcher wants to predict the direction of Variable A on the basis of Variable B. What statistical model does this?

Regression

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A researcher wants to measure the strength of the relationship between Variable A and Variable B. What statistical model could they use?

Correlation

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What does the Y-Axis and X-Axis represent in a regression scatter-plot respectively?

Y-Axis - D.V, X-Axis I.V

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A 'predictor' variable is also known as the...

Independent Variable

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A 'criterion' variable is also known as the....

Dependent Variable

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A researcher runs a regression where they want to investigate height against age. Which technique should they use?

Spearman's

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A researcher wants to investigate the ranking of cities against ranking of tv-shows, and they use a regression analysis. Which technique should they use?

Spearman's Rho or Kendall's Tau

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An experiment looks at how opinion ratings affect the scores on a judge panel. The researchers involved decide to run a regression analysis. Which technique should they use?

Kendall's Tau or Spearman's Rho

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If a researcher uses a regression to investigate pass/fail on an exam and dog-lover yes/no, they should use....[......] to analyse this

Phi

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A researcher wants to investigate pass/fail on an exam with height. They should use what to analyse this?

Point Bi-Serial

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A venn diagram is created depicting the relationship between altruism (D.V) and Agreeableness (I.V) and Happiness (I.V). Happiness is the largest circle. What does this suggest?

It has the largest variance

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A venn diagram is created depicting the relationship between altruism (D.V) and Agreeableness (I.V) and Happiness (I.V). Agreeableness overlaps well with the D.V of Altruism. This suggests what?

The variables are well-correlated

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A multiple regression aims to.....

Predict an outcome via a linear combination of two or more predictor variables

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A partial correlation aims to....

Investigate the relationship between two variables once the effect of another variable has been removed

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The correlation of a scatter-plot depends on...

The degree with which points cluster around the regression line.

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The general equation for multiple regression is as follows...

y ̂ = b0+b1x1+b2x2+......bpxp

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The overall objective of a regression model is to...

Find the best fit with the data, and minimise the overall prediction error

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What does the term 'b1' denote in regression?

Slope of the line

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Name the three main ways to assess goodness of fit in a regression:

Multiple Correlation Co-efficients, Coefficient of determination, and F-ratio

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What does the multiple correlation coefficient look at?

The correlation between criterion (y) and the best linear combination of the predictors (y^)

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What does the coefficient of determination look at?

The proportion of the variability in the data set accounted for by the statistical model (r2)

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What does the f-ratio in regressions look at?

The improvement in the prediction of criterion compared to the inaccuracy of the model

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What is the equation for working out r-squared (Coefficient of determination)?

r-squared = SSm/SSt (Model Sum of Squares / Total Sum of Squares)

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What is the equation for working out the f-ratio for a regression?

F = MSm / MSr (Model Mean Squares/Residual Mean Squares)

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In order to work out the f-ratio for a regression, we need MSm and MSr. How do we work out MSm?

MSm = SSm/dfm (Model Sum of Squares / Degree's of Freedom Model) Remember, dam is simply the number of variables in the model.

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In order to work out the f-ratio for a regression, we need MSm and MSr. How do we work out MSr?

MSr = SSr/dfr (Residual Sum of Squares / Residual Degree's of Freedom) Remember, dfr is the number of observations - the number of parameters being estimated.

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What does a good regression do?

Leads to a large improvement in prediction due to the mode, and there is a small difference between the model and the data

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If a regression model is a good fit, we will usually note...

A large MSm (Model Mean Squares), A small MSr (Residual Mean Squares) and a large F-Ratio

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A researcher enters all I.V's into a regression at once, and there is no a-priori model. This is an example of what type of regression?

Simultaneous

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Regression models with a computer program chooses to input a certain subset of I.V's, capitalising on chance effects are known as...

Stepwise models

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A researcher enters her I'V's into a regression model in a a-priori fashion, using theory to underpin her decisions. She is using what type of regression model?

Hierarchical

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Cook's distance suggests that an outlier has a distance of what?

1 or greater

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A scatter-graph indicates that one or more variables are skewed and the relationship between them is non-linear. This indicates what about the data?

There may be a problem with heteroscedasdicity

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A researcher finds that the variable of self-esteem and self-worth are perfectly correlated with depression. This could be a problem, as it indicates what?

Singularity of the variables

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A variable comes back as being over 0.90 in it's correlation with a neighbouring variable. This suggests what exactly?

Variables are highly correlated with one another (possible multi-collinearity)

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A researcher finds singularity or multi-collinearity in his data. This could be a problem for the following reasons

He doesn't want to measure the same thing twice, and singularity prevents the division of scores

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What solutions are available to correct singularity and multi-collinearity?

High Bivariate Correlations (compute correlations amongst I.V's, then remove the appropriate I.V) and High Multi-Variate Correlations (Exam the squared multiple correlation of each I.V separately)

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In a regression, N and M denote what?

N = number of cases, M = number of predictors

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A psychologist finds in their regression that N/M is very small. Why is this a problem?

Results could be meaningless

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For a medium effect size in multiple correlations, N should be

More than 50+8xM

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For a simple linear regression medium effect size, N should be....

More than 104+M

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For a small effect size, or a skewed D.V or measurement errors, N should be...

More than (8/f2)+(m-1)

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Cohen's f is a measure of effect size in regression. How is it calculated?

r2/(1-r2)

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What are the Cohen's F scores for small, medium and large effect sizes respectively?

0.02, 0.15 and 0.35

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A regression has a larger range. This produces more what compared to a model with a much smaller ranger?

Statistical power

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'Anscombe's Quartet' reminds us to check what in terms of the distribution of variables before analysing?

Mean, Variance, Correlation, Regression line

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A researcher wants to see if caffeine consumption predicts athleticism. The best technique to us would be

Multiple Regression

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A researcher wants to explore the relationship between eating an apple and the ability to run 100 metres and/or engage in therapy well. What would be the best analytical model to use?

Multiple Correlation

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A psychologist has already ran a study on social attitudes to dog-racing, pigeon racing and horse racing. they now want to consider how horse racing attitudes effect with without the other two variables. Which would be the best model to use?

A partial correlation

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A counselling psychologist wants to see what is common between three different families of therapy modalities. What model would be best to use?

Canonical correlation

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How is a MANOVA different to an ANOVA?

It performs an analysis on several I.V's simultaneously

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What does a Discriminant Functions Analysis (DFA) look to do?

It aims to find a set of variables that predict membership of groups

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A psychologist chooses their predictor variables beforehand, and after running a MANOVA, asks 'What is the difference between the predictors that predict group membership?' To find the answer, they could run a...

Discriminant Functions Analysis (D.F.A)

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What is an ANCOVA used for?

To achieve statistical control of error when experimental control of error is not possible

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Define what a 'co-variate' is.

A variables that has a relationship with, or has the potential to be related to, the outcome variable we've measured

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A researcher collects the scores of IQ before their treatment. As this has a relationship to the outcome variable, score on a test, this could be known as a...

Co-variate

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A psychologist collects self-reported scores of depression levels after her experiment. As the scores of depression could have effected her outcome measure of skills in a stand-up comedy task, the scores could be a what?

A Co - variate

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How does an ANOVA typically partition variability?

It splits it into experimental effect, and Error (Experimental Error and Individual Differences Error)

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In ANCOVA, how is the variability partitioned?

Effect, Error and Co-Variate

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What use is a linear regression to an ANCOVA?

It uses a linear regression to estimate the treatment effect size

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Why is collecting co-variate scores before an experiment useful?

It helps us to see the differences between treatment groups that existed before the experiment was performed.

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How does an ANCOVA calculate error variability ?

Through use of a regression - it's residual sum of squares is based on the deviation of a particular score from the regression line

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ANCOVA has x2 assumptions that are specific to it when compared to an ANOVA. What are these?

Linear regression and Homogeneity of regression co-efficients

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Explain ANCOVA's assumption of linear regression.

Deviations from the regression equation across different levels of the I.V have normal distributions and Homoscedasticity

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Explain ANCOVA's assumption of homogeneity of regression co-efficients

The regression co-efficient for each of the groups in the I.V's should be the same

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Define 'Homoscedasticity'.

The spread of residuals/covariate scores

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How can Homogeneity of regression co-efficients be tested in an ANCOVA?

By taking a look at the interaction between the I.V and the Co-Variate

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## Other cards in this set

### Card 2

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If the Null Hypothesis is false, then the treatment effect is more than...

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### Card 3

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What x2 sources of variability does ANOVA use as a ratio?

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### Card 4

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ANOVA transforms deviations to what, and for what reason?

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### Card 5

#### Front

ANOVA defines variance as...

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