Statistics Lecture 1 & 2: Fundamentals

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What is the primary purpose of a confidence interval?

To test the null hypothesis
To calculate the effect size
To provide a range of values within which the population mean is likely to lie (correct)
To determine the probability of getting a significant result

What is the main factor that affects the power of a statistical test?

The effect size
The type of statistical test used
The sample size (correct)
The alpha level

What is the purpose of a randomized controlled trial (RCT) design?

To establish cause-and-effect relationships
To reduce the number of observations needed
To ensure equivalence of groups (correct)
To control for sequencing effects

What is the consequence of having a small sample size in a statistical test?

Reduced probability of getting a significant result (A) Signup and view all the answers

What is the definition of a type I error?

Rejecting the null hypothesis when it is true (C) Signup and view all the answers

What is the relationship between the p-value and the power of a statistical test?

As power decreases, p-value increases (B) Signup and view all the answers

Which statistical concept is directly related to the amount of observations?

Power (C) Signup and view all the answers

What is the implication of having high power in a statistical test?

It decreases the probability of a type II error (C) Signup and view all the answers

What is the effect of having an unequal number of observations in different groups in a logistic regression?

It reduces the probability of a significant result (A) Signup and view all the answers

Which design controls for sequencing effects by making sure all sequences are trialled?

Within-subjects design (C) Signup and view all the answers

What is the interpretation of a p-value below the alpha level?

The test is significant (C) Signup and view all the answers

What is the relationship between the confidence interval and the population mean?

The confidence interval provides a range of values within which the population mean lies (B) Signup and view all the answers

What is the advantage of a factorial design over a single-factor design?

It allows for the estimation of interactions between factors (A) Signup and view all the answers

What is the consequence of a high margin of error in a confidence interval?

It makes the confidence interval wider (A) Signup and view all the answers

What is the primary reason for a statistical test to have a low power?

The effect size is too small (B) Signup and view all the answers

In a logistic regression, what happens when the number of observations is unequal in different groups?

The probability of a significant result decreases (B) Signup and view all the answers

What is the purpose of a confidence interval with a 95% confidence level?

To estimate the population mean with a 2.5% margin of error (A) Signup and view all the answers

What is the advantage of a within-subjects design over a between-subjects design?

It controls for sequencing effects (C) Signup and view all the answers

What is the relationship between the p-value and the significance of a result?

A p-value below the alpha level indicates a significant result (A) Signup and view all the answers

What is the effect of increasing the sample size on the power of a statistical test?

It increases the power of the test (B) Signup and view all the answers

What is the purpose of a factorial design?

To test the interaction between two or more factors (C) Signup and view all the answers

What is the implication of a narrow confidence interval?

The population mean is likely to be closer to the sample mean (D) Signup and view all the answers

What is the primary purpose of a statistical test with 80% power?

To reject the null hypothesis 80% of the time when it is false (C) Signup and view all the answers

What is the effect of a small sample size on the confidence interval?

It increases the margin of error (C) Signup and view all the answers

What is the main limitation of a logistic regression with unequal observations in different groups?

It reduces the probability of a significant result (B) Signup and view all the answers

What is the purpose of a confidence interval with a 95% confidence level?

To provide a range of values within which the population mean is likely to lie (D) Signup and view all the answers

What is the advantage of a between-subjects design over a within-subjects design?

It is more efficient in terms of sample size (C) Signup and view all the answers

What is the relationship between the p-value and the significance of a result?

A p-value below the alpha level indicates a significant result (B) Signup and view all the answers

What is the primary assumption of linear models that is related to the accuracy of the model in representing the observations?

Fidelity (C) Signup and view all the answers

What is the consequence of violating the assumption of homoscedasticity in linear models?

The model becomes less accurate (C) Signup and view all the answers

What is the primary purpose of the Ordinary Least Squares (OLS) analysis in linear models?

To minimize the sum of the squared errors (D) Signup and view all the answers

What is the assumption of linear models that is related to the distribution of the errors?

Normality (A) Signup and view all the answers

What is the primary purpose of standardizing variables in moderation analysis?

To make the interpretation of the moderation effect easier (C) Signup and view all the answers

What is the interpretation of the simple intercept in a moderation analysis?

A person's expected score if X = 0, which will vary with different values of the moderator (D) Signup and view all the answers

What is the formula for a simple linear regression model?

Y = β0 + β1X + ε (C) Signup and view all the answers

What is the assumption of linear models that is related to the relationship between the predictor variables and the outcome variable?

Linearity (D) Signup and view all the answers

What is the purpose of the Johnson-Neyman Technique in moderation analysis?

To identify the point at which the moderation effect is no longer significant (A) Signup and view all the answers

What is the result of rearranging the equation in moderation analysis?

A new interaction term is created (B) Signup and view all the answers

What is the consequence of violating the assumption of independence of errors in linear models?

There is a predictor within the errors (A) Signup and view all the answers

What is the purpose of the pick-a-point approach in moderation analysis?

To make inferences about the value of Y (A) Signup and view all the answers

What is the primary reason why linear models are often used in statistical analysis?

They are easy to interpret (C) Signup and view all the answers

What is the interpretation of the simple slope in a moderation analysis?

The slope of the regression line for a particular value of the moderator (B) Signup and view all the answers

What is the consequence of not considering a 3rd variable that intervenes between two variables and the mediator in mediation analysis?

The results are subject to confounding (D) Signup and view all the answers

What is the purpose of moderating a variable in moderation analysis?

To change the slope and intercept of the regression line (B) Signup and view all the answers

What is the primary objective of using Ordinary Least Squares in regression analysis?

To minimise the residuals of the model to the data (A) Signup and view all the answers

In mediation analysis, what is the role of the intervening variable?

It acts on another variable through the intervening variable (D) Signup and view all the answers

What is the limitation of the Baron and Kenny approach to testing mediation?

It has low power and assumes normal distribution of a*b (B) Signup and view all the answers

What is the purpose of bootstrapped sampling in the Hayes Process method?

To calculate the indirect effect of each bootstrapped sample (C) Signup and view all the answers

What is the condition for partial or full mediation in the Hayes Process method?

c is significant, a is significant, and b is significant, and c’ is smaller than c (D) Signup and view all the answers

What is the problem with the Causal Steps approach to testing mediation?

It multiplies the chance of a test giving an erroneous result (B) Signup and view all the answers

What is the purpose of creating a confidence interval around the bootstrap sampling distribution in the Hayes Process method?

To determine if the indirect effect is significantly different from 0 (D) Signup and view all the answers

What is the limitation of the Sobel test in estimating mediation effects?

It has low power and assumes normal distribution of a*b (C) Signup and view all the answers

What is the primary assumption of linear models that ensures the model's ability to make generalizations beyond the sample data?

Representativeness (C) Signup and view all the answers

What is the effect of violating the assumption of homogeneity of errors in linear models?

It invalidates the use of Ordinary Least Squares analysis (C) Signup and view all the answers

What is the purpose of including all relevant predictors in a linear model?

To increase the accuracy of the model (B) Signup and view all the answers

What is the implication of having a non-normal distribution of errors in linear models?

It violates the assumption of normality of errors (D) Signup and view all the answers

What is the assumption of linear models that ensures the model's ability to accurately represent the observations?

Fidelity (C) Signup and view all the answers

What is the effect of having a large variance of errors in linear models?

It invalidates the use of Ordinary Least Squares analysis (D) Signup and view all the answers

What is the primary assumption of linear models that ensures the model's ability to make accurate predictions?

Linearity (D) Signup and view all the answers

What is the implication of having a non-independent distribution of errors in linear models?

It violates the assumption of independence of errors (B) Signup and view all the answers

What is the primary limitation of the Baron and Kenny approach to testing mediation?

It assumes normal distribution of the product of a and b (A) Signup and view all the answers

What is the purpose of bootstrapping in the Hayes Process method?

To estimate the indirect effect and create a confidence interval (A) Signup and view all the answers

What is the condition for partial or full mediation in the Baron and Kenny approach?

a is significant and c' is smaller than c (D) Signup and view all the answers

What is the problem with the Sobel test in estimating mediation effects?

It has low power to detect indirect effects (D) Signup and view all the answers

What is the purpose of the Causal Steps approach?

To test the null model and identify the mediation effect (D) Signup and view all the answers

What is the advantage of the Hayes Process method over the Baron and Kenny approach?

It does not assume normal distribution of the product of a and b (B) Signup and view all the answers

What is the role of the intervening variable in mediation analysis?

It acts as a mediator between the independent and dependent variables (B) Signup and view all the answers

What is the limitation of the Hayes Process method?

It requires a large sample size to produce accurate results (A) Signup and view all the answers

What is the primary purpose of considering a 3rd variable that intervenes between two variables and the mediator in mediation analysis?

To manage the confounding effect of the 3rd variable (D) Signup and view all the answers

What is the result of not standardizing the variables in moderation analysis?

The moderation effect will be obscured (A) Signup and view all the answers

What is the primary advantage of using the Johnson-Neyman Technique in moderation analysis?

It identifies the point at which the moderation effect is no longer significant (D) Signup and view all the answers

What is the implication of having a high margin of error in a confidence interval in moderation analysis?

The confidence interval will be wider (A) Signup and view all the answers

What is the primary purpose of centring the variables on a mean of 0 in moderation analysis?

To facilitate the interpretation of the interaction term (B) Signup and view all the answers

What is the consequence of violating the assumption of homoscedasticity in moderation analysis?

The standard error of the regression coefficients will be biased (A) Signup and view all the answers

What is the primary advantage of using the pick-a-point approach in moderation analysis?

It allows for the interpretation of the moderation effect at specific points (D) Signup and view all the answers

What is the implication of having a narrow confidence interval in moderation analysis?

The true value of the moderation effect is more precise (A) Signup and view all the answers

What is the primary objective of exploratory factor analysis?

To identify the underlying factors that explain the relationships between variables (A) Signup and view all the answers

What is the purpose of the pattern matrix in oblique rotation?

To display the coefficients for a regression in which components predict observed variables (A) Signup and view all the answers

What is the assumption of exploratory factor analysis regarding the data scale?

The data must be at least on an interval scale (C) Signup and view all the answers

What is the purpose of the anti-image correlation matrix in exploratory factor analysis?

To assess the quality of the correlation matrix (D) Signup and view all the answers

What is the primary purpose of exploratory factor analysis?

To identify the underlying factors and their relationships with the variables (A) Signup and view all the answers

What is the primary advantage of using principal axis factoring in exploratory factor analysis?

It is more robust to outliers and non-normality (B) Signup and view all the answers

What is the key difference between principal component analysis and exploratory factor analysis?

PCA is used for dimension reduction, while EFA is used for theory testing (D) Signup and view all the answers

What is the consequence of having low partial correlations in exploratory factor analysis?

The correlations between the variables are not well-explained by the factors (A) Signup and view all the answers

What is the main limitation of global fit indices in structural equation modeling?

They only test average fit and don't identify where in the model fit is not good (A) Signup and view all the answers

What is the implication of adding another factor in exploratory factor analysis?

The factor loadings of the existing factors will change (B) Signup and view all the answers

What is the primary advantage of using confirmatory factor analysis over exploratory factor analysis?

It is more theory-driven and can test a pre-conceived theory (A) Signup and view all the answers

What is the purpose of the Root Mean-Square Residual (RMR) in structural equation modeling?

To assess the absolute fit of the model (A) Signup and view all the answers

What is the role of canonical algorithm in exploratory factor analysis?

It is used to extract the factors from the data (B) Signup and view all the answers

What is the advantage of using the Comparative Fit Index (CFI) over the Root Mean-Square Error of Approximation (RMSEA) in structural equation modeling?

The CFI compares the model fit with a baseline model (A) Signup and view all the answers

What is the primary purpose of modification indices in structural equation modeling?

To identify areas of misfit in the model (D) Signup and view all the answers

What is the implication of having eigenvalues less than 1 in principal component analysis?

The component is unreliable and should be discarded (B) Signup and view all the answers

What is the primary limitation of the Root Mean-Square Error of Approximation (RMSEA) in structural equation modeling?

It is sensitive to sample size (A) Signup and view all the answers

What is the purpose of the Standardised Root Mean-Square Residual (SRMR) in structural equation modeling?

To standardise the RMR for model comparison (D) Signup and view all the answers

What is the primary advantage of Confirmatory Factor Analysis (CFA) over Exploratory Factor Analysis (EFA)?

CFA is more flexible and allows for the restriction of factor loadings to certain values. (C) Signup and view all the answers

What is the primary issue with regards to sample size in Confirmatory Factor Analysis (CFA)?

The sample size required depends on the factor loadings, communalities, and other model parameters. (A) Signup and view all the answers

What is the purpose of setting one of the factor loadings to a non-zero value in Confirmatory Factor Analysis (CFA)?

To identify the model and set the scale of the latent variables. (B) Signup and view all the answers

What is the primary advantage of using Confirmatory Factor Analysis (CFA) over other multivariate techniques?

CFA allows for the testing of complex hypotheses about the relationships between the variables. (A) Signup and view all the answers

What is the implication of having a large sample size on the significance testing in Confirmatory Factor Analysis (CFA)?

Larger sample sizes increase the power of the significance tests, but may lead to overfitting. (A) Signup and view all the answers

What is the primary assumption of Confirmatory Factor Analysis (CFA) regarding the distribution of the observed variables?

The observed variables must be multivariately normally distributed. (A) Signup and view all the answers

What is the primary reason for using Bollen-Stine bootstrapping in Structural Equation Modeling (SEM)?

To generate bootstrap samples from a transformed sample to assess overall fit (D) Signup and view all the answers

In a SEM model, what does the Chi2 statistic primarily indicate?

The goodness of fit of the model (B) Signup and view all the answers

When is it justified to allow errors to correlate in a SEM model?

When the error terms are theoretically expected to be correlated (D) Signup and view all the answers

What is the primary advantage of using standardized estimates in a SEM model?

They allow for the comparison of the strength of relationships between different variables (B) Signup and view all the answers

What is the consequence of violating the assumption of normality in a SEM model?

The Chi2 statistic may be inaccurate and may incorrectly reject the model (A) Signup and view all the answers

What is the purpose of using naïve ML bootstrapping in a SEM model?

To generate standard errors and confidence intervals around the standardized estimates (D) Signup and view all the answers

What is the main purpose of assessing the overall fit of a path model in structural equation modeling?

To evaluate the plausibility of the variance-covariance matrix implied by the model (D) Signup and view all the answers

What is the key difference between recursive and non-recursive path models?

The presence of feedback loops (B) Signup and view all the answers

Which type of path model is typically tested using regression analysis?

Recursive (A) Signup and view all the answers

What is the main advantage of using structural equation modeling over regression analysis?

SEM can include correlated independent variables (A) Signup and view all the answers

What is the purpose of the Chi-Square test in structural equation modeling?

To evaluate the overall fit of the model (C) Signup and view all the answers

What is the main limitation of using global fit indices in structural equation modeling?

They do not account for model complexity (A) Signup and view all the answers

Which of the following is a characteristic of non-recursive path models?

Bi-directional paths (A) Signup and view all the answers

What is the main difference between a recursive and non-recursive path model in terms of the relationships between variables?

The type of relationships (B) Signup and view all the answers

What is the purpose of assessing the fit of a path model in structural equation modeling?

To evaluate the plausibility of the model (A) Signup and view all the answers

Which of the following is a characteristic of structural equation modeling?

It allows for correlated independent variables (A) Signup and view all the answers

What is the primary goal of mediation analysis in psychological studies?

To identify the underlying mechanisms of a phenomenon (D) Signup and view all the answers

What is the simplest mediation model in the context of the Theory of Reasoned Action?

X → M → Y (C) Signup and view all the answers

What is the total effect of X on Y in a mediation model?

The sum of the direct and indirect effects of X on Y (C) Signup and view all the answers

What is the purpose of the Baron and Kenny approach to testing mediation?

To test the significance of the mediation effect (D) Signup and view all the answers

What is the primary advantage of using mediation analysis in psychological studies?

It provides a more nuanced understanding of the relationships between variables (C) Signup and view all the answers

What is the formula for the total effect of X on Y in a mediation model?

c = a*b + c' (B) Signup and view all the answers

What happens to the effect of X when both X and M predict the Y?

The effect of X is reduced or eliminated (B) Signup and view all the answers

What is the focus of newer approach to mediation analysis?

Testing the indirect effect of X on Y through M (D) Signup and view all the answers

What is the purpose of the Sobel test in mediation analysis?

To test the significance of the indirect effect of X on Y through M (D) Signup and view all the answers

What is the equation for the total effect of X on Y in mediation analysis?

c = a*b + c' (B) Signup and view all the answers

What is the implication of finding a significant indirect effect in mediation analysis?

There is a partial mediation effect (B) Signup and view all the answers

What is the R-squared value for the model where the outcome variable is na?

0.3059 (B) Signup and view all the answers

What is the coefficient of the constant in the model where the outcome variable is psych6?

-4.1311 (B) Signup and view all the answers

What is the p-value for the total effect of X on Y?

0.0000 (B) Signup and view all the answers

What is the bootstrapped standard error for the indirect effect of X on Y?

0.0141 (D) Signup and view all the answers

What is the lower limit of the 95% confidence interval for the indirect effect of X on Y?

0.0348 (A) Signup and view all the answers

What is the proportion of the variance in the outcome variable psych6 that is predictable from the independent variables?

0.4646 (C) Signup and view all the answers

What is a necessary condition for full mediation to occur?

The effect of X on Y is eliminated (A) Signup and view all the answers

What is the purpose of the four sequential requirements in the Baron and Kenny (1986) causal steps approach?

To establish a causal relationship between X and Y (D) Signup and view all the answers

What is the consequence of X directly predicting Y and M directly predicting Y?

There is partial mediation (D) Signup and view all the answers

What is the role of the coefficient c′ in the mediation analysis?

It represents the reduced effect of X on Y when controlling for M (A) Signup and view all the answers

What is the necessary condition for partial mediation to occur?

The effect of X on Y is reduced (B) Signup and view all the answers

What is the necessary step in SPSS before running the PROCESS script?

Run a script of syntax unchanged, then SPSS will recognize the syntax command 'process' for the rest of that session (A) Signup and view all the answers

What is the purpose of the PROCESS script in SPSS?

To enable complex mediation and moderation models (D) Signup and view all the answers

What is the output of the PROCESS procedure in SPSS?

Multiple s output for mediation analysis (D) Signup and view all the answers

Statistics Lecture 1 & 2: Fundamentals

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Questions and Answers

What is the primary purpose of a confidence interval?

What is the main factor that affects the power of a statistical test?

What is the purpose of a randomized controlled trial (RCT) design?

What is the consequence of having a small sample size in a statistical test?

What is the definition of a type I error?

What is the relationship between the p-value and the power of a statistical test?

Which statistical concept is directly related to the amount of observations?

What is the implication of having high power in a statistical test?

What is the effect of having an unequal number of observations in different groups in a logistic regression?

Which design controls for sequencing effects by making sure all sequences are trialled?

What is the interpretation of a p-value below the alpha level?

What is the relationship between the confidence interval and the population mean?

What is the advantage of a factorial design over a single-factor design?

What is the consequence of a high margin of error in a confidence interval?

What is the primary reason for a statistical test to have a low power?

In a logistic regression, what happens when the number of observations is unequal in different groups?

What is the purpose of a confidence interval with a 95% confidence level?

What is the advantage of a within-subjects design over a between-subjects design?

What is the relationship between the p-value and the significance of a result?

What is the effect of increasing the sample size on the power of a statistical test?

What is the purpose of a factorial design?

What is the implication of a narrow confidence interval?

What is the primary purpose of a statistical test with 80% power?

What is the effect of a small sample size on the confidence interval?

What is the main limitation of a logistic regression with unequal observations in different groups?

What is the purpose of a confidence interval with a 95% confidence level?

What is the advantage of a between-subjects design over a within-subjects design?

What is the relationship between the p-value and the significance of a result?

What is the primary assumption of linear models that is related to the accuracy of the model in representing the observations?

What is the consequence of violating the assumption of homoscedasticity in linear models?

What is the primary purpose of the Ordinary Least Squares (OLS) analysis in linear models?

What is the assumption of linear models that is related to the distribution of the errors?

What is the primary purpose of standardizing variables in moderation analysis?

What is the interpretation of the simple intercept in a moderation analysis?

What is the formula for a simple linear regression model?

What is the assumption of linear models that is related to the relationship between the predictor variables and the outcome variable?

What is the purpose of the Johnson-Neyman Technique in moderation analysis?

What is the result of rearranging the equation in moderation analysis?

What is the consequence of violating the assumption of independence of errors in linear models?

What is the purpose of the pick-a-point approach in moderation analysis?

What is the primary reason why linear models are often used in statistical analysis?

What is the interpretation of the simple slope in a moderation analysis?

What is the consequence of not considering a 3rd variable that intervenes between two variables and the mediator in mediation analysis?

What is the purpose of moderating a variable in moderation analysis?

What is the primary objective of using Ordinary Least Squares in regression analysis?

In mediation analysis, what is the role of the intervening variable?

What is the limitation of the Baron and Kenny approach to testing mediation?

What is the purpose of bootstrapped sampling in the Hayes Process method?

What is the condition for partial or full mediation in the Hayes Process method?

What is the problem with the Causal Steps approach to testing mediation?

What is the purpose of creating a confidence interval around the bootstrap sampling distribution in the Hayes Process method?

What is the limitation of the Sobel test in estimating mediation effects?

What is the primary assumption of linear models that ensures the model's ability to make generalizations beyond the sample data?

What is the effect of violating the assumption of homogeneity of errors in linear models?

What is the purpose of including all relevant predictors in a linear model?

What is the implication of having a non-normal distribution of errors in linear models?

What is the assumption of linear models that ensures the model's ability to accurately represent the observations?

What is the effect of having a large variance of errors in linear models?

What is the primary assumption of linear models that ensures the model's ability to make accurate predictions?

What is the implication of having a non-independent distribution of errors in linear models?

What is the primary limitation of the Baron and Kenny approach to testing mediation?

What is the purpose of bootstrapping in the Hayes Process method?

What is the condition for partial or full mediation in the Baron and Kenny approach?

What is the problem with the Sobel test in estimating mediation effects?

What is the purpose of the Causal Steps approach?

What is the advantage of the Hayes Process method over the Baron and Kenny approach?

What is the role of the intervening variable in mediation analysis?

What is the limitation of the Hayes Process method?

What is the primary purpose of considering a 3rd variable that intervenes between two variables and the mediator in mediation analysis?

What is the result of not standardizing the variables in moderation analysis?

What is the primary advantage of using the Johnson-Neyman Technique in moderation analysis?

What is the implication of having a high margin of error in a confidence interval in moderation analysis?

What is the primary purpose of centring the variables on a mean of 0 in moderation analysis?

What is the consequence of violating the assumption of homoscedasticity in moderation analysis?

What is the primary advantage of using the pick-a-point approach in moderation analysis?

What is the implication of having a narrow confidence interval in moderation analysis?