Statistics Lecture 1 & 2: Fundamentals
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Questions and Answers

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?

    <p>Reduced probability of getting a significant result</p> Signup and view all the answers

    What is the definition of a type I error?

    <p>Rejecting the null hypothesis when it is true</p> Signup and view all the answers

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

    <p>As power decreases, p-value increases</p> Signup and view all the answers

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

    <p>Power</p> Signup and view all the answers

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

    <p>It decreases the probability of a type II error</p> Signup and view all the answers

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

    <p>It reduces the probability of a significant result</p> Signup and view all the answers

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

    <p>Within-subjects design</p> Signup and view all the answers

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

    <p>The test is significant</p> Signup and view all the answers

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

    <p>The confidence interval provides a range of values within which the population mean lies</p> Signup and view all the answers

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

    <p>It allows for the estimation of interactions between factors</p> Signup and view all the answers

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

    <p>It makes the confidence interval wider</p> Signup and view all the answers

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

    <p>The effect size is too small</p> Signup and view all the answers

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

    <p>The probability of a significant result decreases</p> Signup and view all the answers

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

    <p>To estimate the population mean with a 2.5% margin of error</p> Signup and view all the answers

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

    <p>It controls for sequencing effects</p> Signup and view all the answers

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

    <p>A p-value below the alpha level indicates a significant result</p> Signup and view all the answers

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

    <p>It increases the power of the test</p> Signup and view all the answers

    What is the purpose of a factorial design?

    <p>To test the interaction between two or more factors</p> Signup and view all the answers

    What is the implication of a narrow confidence interval?

    <p>The population mean is likely to be closer to the sample mean</p> Signup and view all the answers

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

    <p>To reject the null hypothesis 80% of the time when it is false</p> Signup and view all the answers

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

    <p>It increases the margin of error</p> Signup and view all the answers

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

    <p>It reduces the probability of a significant result</p> Signup and view all the answers

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

    <p>To provide a range of values within which the population mean is likely to lie</p> Signup and view all the answers

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

    <p>It is more efficient in terms of sample size</p> Signup and view all the answers

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

    <p>A p-value below the alpha level indicates a significant result</p> 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?

    <p>Fidelity</p> Signup and view all the answers

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

    <p>The model becomes less accurate</p> Signup and view all the answers

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

    <p>To minimize the sum of the squared errors</p> Signup and view all the answers

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

    <p>Normality</p> Signup and view all the answers

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

    <p>To make the interpretation of the moderation effect easier</p> Signup and view all the answers

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

    <p>A person's expected score if X = 0, which will vary with different values of the moderator</p> Signup and view all the answers

    What is the formula for a simple linear regression model?

    <p>Y = β0 + β1X + ε</p> 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?

    <p>Linearity</p> Signup and view all the answers

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

    <p>To identify the point at which the moderation effect is no longer significant</p> Signup and view all the answers

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

    <p>A new interaction term is created</p> Signup and view all the answers

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

    <p>There is a predictor within the errors</p> Signup and view all the answers

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

    <p>To make inferences about the value of Y</p> Signup and view all the answers

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

    <p>They are easy to interpret</p> Signup and view all the answers

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

    <p>The slope of the regression line for a particular value of the moderator</p> 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?

    <p>The results are subject to confounding</p> Signup and view all the answers

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

    <p>To change the slope and intercept of the regression line</p> Signup and view all the answers

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

    <p>To minimise the residuals of the model to the data</p> Signup and view all the answers

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

    <p>It acts on another variable through the intervening variable</p> Signup and view all the answers

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

    <p>It has low power and assumes normal distribution of a*b</p> Signup and view all the answers

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

    <p>To calculate the indirect effect of each bootstrapped sample</p> Signup and view all the answers

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

    <p>c is significant, a is significant, and b is significant, and c’ is smaller than c</p> Signup and view all the answers

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

    <p>It multiplies the chance of a test giving an erroneous result</p> 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?

    <p>To determine if the indirect effect is significantly different from 0</p> Signup and view all the answers

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

    <p>It has low power and assumes normal distribution of a*b</p> 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?

    <p>Representativeness</p> Signup and view all the answers

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

    <p>It invalidates the use of Ordinary Least Squares analysis</p> Signup and view all the answers

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

    <p>To increase the accuracy of the model</p> Signup and view all the answers

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

    <p>It violates the assumption of normality of errors</p> Signup and view all the answers

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

    <p>Fidelity</p> Signup and view all the answers

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

    <p>It invalidates the use of Ordinary Least Squares analysis</p> Signup and view all the answers

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

    <p>Linearity</p> Signup and view all the answers

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

    <p>It violates the assumption of independence of errors</p> Signup and view all the answers

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

    <p>It assumes normal distribution of the product of a and b</p> Signup and view all the answers

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

    <p>To estimate the indirect effect and create a confidence interval</p> Signup and view all the answers

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

    <p>a is significant and c' is smaller than c</p> Signup and view all the answers

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

    <p>It has low power to detect indirect effects</p> Signup and view all the answers

    What is the purpose of the Causal Steps approach?

    <p>To test the null model and identify the mediation effect</p> Signup and view all the answers

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

    <p>It does not assume normal distribution of the product of a and b</p> Signup and view all the answers

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

    <p>It acts as a mediator between the independent and dependent variables</p> Signup and view all the answers

    What is the limitation of the Hayes Process method?

    <p>It requires a large sample size to produce accurate results</p> 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?

    <p>To manage the confounding effect of the 3rd variable</p> Signup and view all the answers

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

    <p>The moderation effect will be obscured</p> Signup and view all the answers

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

    <p>It identifies the point at which the moderation effect is no longer significant</p> Signup and view all the answers

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

    <p>The confidence interval will be wider</p> Signup and view all the answers

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

    <p>To facilitate the interpretation of the interaction term</p> Signup and view all the answers

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

    <p>The standard error of the regression coefficients will be biased</p> Signup and view all the answers

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

    <p>It allows for the interpretation of the moderation effect at specific points</p> Signup and view all the answers

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

    <p>The true value of the moderation effect is more precise</p> Signup and view all the answers

    What is the primary objective of exploratory factor analysis?

    <p>To identify the underlying factors that explain the relationships between variables</p> Signup and view all the answers

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

    <p>To display the coefficients for a regression in which components predict observed variables</p> Signup and view all the answers

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

    <p>The data must be at least on an interval scale</p> Signup and view all the answers

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

    <p>To assess the quality of the correlation matrix</p> Signup and view all the answers

    What is the primary purpose of exploratory factor analysis?

    <p>To identify the underlying factors and their relationships with the variables</p> Signup and view all the answers

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

    <p>It is more robust to outliers and non-normality</p> Signup and view all the answers

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

    <p>PCA is used for dimension reduction, while EFA is used for theory testing</p> Signup and view all the answers

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

    <p>The correlations between the variables are not well-explained by the factors</p> Signup and view all the answers

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

    <p>They only test average fit and don't identify where in the model fit is not good</p> Signup and view all the answers

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

    <p>The factor loadings of the existing factors will change</p> Signup and view all the answers

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

    <p>It is more theory-driven and can test a pre-conceived theory</p> Signup and view all the answers

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

    <p>To assess the absolute fit of the model</p> Signup and view all the answers

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

    <p>It is used to extract the factors from the data</p> 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?

    <p>The CFI compares the model fit with a baseline model</p> Signup and view all the answers

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

    <p>To identify areas of misfit in the model</p> Signup and view all the answers

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

    <p>The component is unreliable and should be discarded</p> Signup and view all the answers

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

    <p>It is sensitive to sample size</p> Signup and view all the answers

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

    <p>To standardise the RMR for model comparison</p> Signup and view all the answers

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

    <p>CFA is more flexible and allows for the restriction of factor loadings to certain values.</p> Signup and view all the answers

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

    <p>The sample size required depends on the factor loadings, communalities, and other model parameters.</p> 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)?

    <p>To identify the model and set the scale of the latent variables.</p> Signup and view all the answers

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

    <p>CFA allows for the testing of complex hypotheses about the relationships between the variables.</p> 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)?

    <p>Larger sample sizes increase the power of the significance tests, but may lead to overfitting.</p> Signup and view all the answers

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

    <p>The observed variables must be multivariately normally distributed.</p> Signup and view all the answers

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

    <p>To generate bootstrap samples from a transformed sample to assess overall fit</p> Signup and view all the answers

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

    <p>The goodness of fit of the model</p> Signup and view all the answers

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

    <p>When the error terms are theoretically expected to be correlated</p> Signup and view all the answers

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

    <p>They allow for the comparison of the strength of relationships between different variables</p> Signup and view all the answers

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

    <p>The Chi2 statistic may be inaccurate and may incorrectly reject the model</p> Signup and view all the answers

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

    <p>To generate standard errors and confidence intervals around the standardized estimates</p> Signup and view all the answers

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

    <p>To evaluate the plausibility of the variance-covariance matrix implied by the model</p> Signup and view all the answers

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

    <p>The presence of feedback loops</p> Signup and view all the answers

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

    <p>Recursive</p> Signup and view all the answers

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

    <p>SEM can include correlated independent variables</p> Signup and view all the answers

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

    <p>To evaluate the overall fit of the model</p> Signup and view all the answers

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

    <p>They do not account for model complexity</p> Signup and view all the answers

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

    <p>Bi-directional paths</p> 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?

    <p>The type of relationships</p> Signup and view all the answers

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

    <p>To evaluate the plausibility of the model</p> Signup and view all the answers

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

    <p>It allows for correlated independent variables</p> Signup and view all the answers

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

    <p>To identify the underlying mechanisms of a phenomenon</p> Signup and view all the answers

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

    <p>X → M → Y</p> Signup and view all the answers

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

    <p>The sum of the direct and indirect effects of X on Y</p> Signup and view all the answers

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

    <p>To test the significance of the mediation effect</p> Signup and view all the answers

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

    <p>It provides a more nuanced understanding of the relationships between variables</p> Signup and view all the answers

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

    <p>c = a*b + c'</p> Signup and view all the answers

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

    <p>The effect of X is reduced or eliminated</p> Signup and view all the answers

    What is the focus of newer approach to mediation analysis?

    <p>Testing the indirect effect of X on Y through M</p> Signup and view all the answers

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

    <p>To test the significance of the indirect effect of X on Y through M</p> Signup and view all the answers

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

    <p>c = a*b + c'</p> Signup and view all the answers

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

    <p>There is a partial mediation effect</p> Signup and view all the answers

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

    <p>0.3059</p> Signup and view all the answers

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

    <p>-4.1311</p> Signup and view all the answers

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

    <p>0.0000</p> Signup and view all the answers

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

    <p>0.0141</p> Signup and view all the answers

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

    <p>0.0348</p> 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?

    <p>0.4646</p> Signup and view all the answers

    What is a necessary condition for full mediation to occur?

    <p>The effect of X on Y is eliminated</p> Signup and view all the answers

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

    <p>To establish a causal relationship between X and Y</p> Signup and view all the answers

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

    <p>There is partial mediation</p> Signup and view all the answers

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

    <p>It represents the reduced effect of X on Y when controlling for M</p> Signup and view all the answers

    What is the necessary condition for partial mediation to occur?

    <p>The effect of X on Y is reduced</p> Signup and view all the answers

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

    <p>Run a script of syntax unchanged, then SPSS will recognize the syntax command 'process' for the rest of that session</p> Signup and view all the answers

    What is the purpose of the PROCESS script in SPSS?

    <p>To enable complex mediation and moderation models</p> Signup and view all the answers

    What is the output of the PROCESS procedure in SPSS?

    <p>Multiple s output for mediation analysis</p> Signup and view all the answers

    What is the role of the 'model' command in the PROCESS syntax?

    <p>To specify the DV and IV variables</p> Signup and view all the answers

    What is the purpose of the Sobel test in the PROCESS procedure?

    <p>To estimate the mediation effect</p> Signup and view all the answers

    What is the default number of bootstrap samples in the PROCESS procedure?

    <p>10,000</p> Signup and view all the answers

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