Statistics Chapter on Correlation and ANOVA
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Questions and Answers

In a scatter plot, which variable is placed on the horizontal axis?

  • Dependent variable
  • Neither dependent nor independent variable
  • Both dependent and independent variables
  • Independent variable (correct)

    • A correlation coefficient of -0.9 indicates a weaker correlation than a coefficient of 0.5.

    False

    What is the name of the measure of association used to determine the strength and direction of a linear relationship between two variables?

    Pearson's r

    A correlation where two variables change in the same direction is known as a _________ correlation.

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

    What does each dot represent in a scatter plot?

    <p>A case and its values for x and y</p> Signup and view all the answers

    The correlation coefficient can have a value of 1.5.

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

    What does a negative correlation indicate?

    <p>As one variable increases, the other decreases.</p> Signup and view all the answers

    Match the correlation coefficient with its corresponding strength.

    <p>r = 0.1 = Weak correlation r = 0.9 = Strong correlation r = -0.2 = Weak correlation r = -0.8 = Strong correlation</p> Signup and view all the answers

    What does 'df' represent in the formula df = N – k?

    <p>Degrees of freedom</p> Signup and view all the answers

    A one-way between-subjects ANOVA is used to compare two or more group means with the same participants in each group.

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

    What type of test is conducted after rejecting the null hypothesis (H0) in an F-test to determine which means differ significantly?

    <p>post-hoc test</p> Signup and view all the answers

    The statistic used to measure correlations is called a correlation _________.

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

    Match the following descriptions with the appropriate statistical term:

    <p>Scatter plot = Graphical display of data points (x, y) Correlation coefficient (r) = Measures the strength and direction of a linear relationship One-way ANOVA = Compares means of two or more groups with different participants in each group Post-hoc test = Determines which means differ significantly after rejecting H0 in an F-test</p> Signup and view all the answers

    What does the null hypothesis (H0) of Scheffé's test state for each pair of group means?

    <p>Their population means are equal.</p> Signup and view all the answers

    A correlation coefficient can only determine the strength, but not the direction of a linear relationship.

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

    What is the name of the graphical display of discrete data points (x, y) used to summarize the relationship between two variables?

    <p>scatter plot</p> Signup and view all the answers

    In a crosstab, how should percentages be compared to determine the relationship between variables?

    <p>Horizontally within the categories of the dependent variable</p> Signup and view all the answers

    When using SPSS to analyze a relationship between gender and health perception, you should put the independent variable (gender) in the row and the dependent variable (health perception) in the column.

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

    If the obtained test statistic is less than the critical value, what decision do you make regarding the null hypothesis?

    <p>retain the null hypothesis</p> Signup and view all the answers

    When conducting a one-sample test and the population standard deviation is unknown, you should use a one-sample ______ test.

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

    What does a 'p-value < alpha' indicate regarding the null hypothesis when conducting a t-test?

    <p>Reject the null hypothesis</p> Signup and view all the answers

    Match statistical test to the condition in which it is used:

    <p>One-sample z-test = Population SD is known One-sample t-test = Population SD is unknown Crosstabs = Relationship between two categorical variables P-value = Probability of observing results if the null hypothesis is true</p> Signup and view all the answers

    When you have a directional alternative hypothesis (H1) and you perform a t-test in SPSS, it is necessary to divide the p-value by 2 before comparing it to alpha.

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

    What is the standard default setting value for alpha when conducting a statistical test?

    <p>0.05</p> Signup and view all the answers

    What does the intercept (constant) in a regression analysis, as reported by SPSS, represent?

    <p>The predicted value of the DV when all IVs are zero.</p> Signup and view all the answers

    The standardized coefficients in regression analysis are used to compare the means of different groups.

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

    What is the null hypothesis (H0) for the F-test in a regression model?

    <p>In the population, R2 = 0</p> Signup and view all the answers

    The unstandardized coefficients represent the change in the predicted value of the dependent variable when the independent variable increases by one unit, with the effect of other IVs held ______.

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

    Match the following statistical tests with their null hypothesis:

    <p>F-test for the model = H0: In the population, R2 = 0 t-test for each individual IV = H0: In the population, the effect of the IV is zero</p> Signup and view all the answers

    What does the null hypothesis (H0) typically state in a one-sample z-test?

    <p>The population mean has a certain value.</p> Signup and view all the answers

    The F-test is used to compare the means of two groups.

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

    What test is used to determine which group means differ significantly from each other after rejecting the null hypothesis in an ANOVA?

    <p>post hoc test (Scheffe)</p> Signup and view all the answers

    In regression analysis, R² tells us the proportion of the variance in the _____ that can be explained by the model.

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

    Match the statistical tests with their primary purpose:

    <p>One-sample t-test = Compare a sample mean to a known or hypothesized population mean when population standard deviation is unknown Two-sample t-test = Compare the means of two independent groups ANOVA = Compare the means of more than two groups Chi-square test for independence = Determine if two categorical variables are related</p> Signup and view all the answers

    What happens to the F value in an ANOVA when the variance between group means is large and the variance within groups is small?

    <p>The F value becomes larger.</p> Signup and view all the answers

    In hypothesis testing, the decision is always to either accept or reject the null hypothesis.

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

    What kind of data are the independent and dependent variables in regression analysis measured on?

    <p>interval/ratio level</p> Signup and view all the answers

    The ____ test determines if there is a significant difference between the observed and expected distributions of a categorical variable.

    <p>Chi-square</p> Signup and view all the answers

    Which statistical test is used to determine whether two ordinal/nominal variables are related in a population?

    <p>Chi-square test for independence</p> Signup and view all the answers

    Which statistical test is used to assess the goodness-of-fit when comparing observed frequencies to expected frequencies?

    <p>Chi-square</p> Signup and view all the answers

    In regression analysis, the unstandardized coefficients indicate the predicted value of the dependent variable when all independent variables are zero.

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

    What does R² tell us in the context of regression analysis?

    <p>the proportion of the variance in the DV that can be explained by the model</p> Signup and view all the answers

    The assumption in regression analysis that there should be no strong linear relationship between any two independent variables is known as lack of ______.

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

    Match the statistical test with its primary purpose.

    <p>Pearson's r = Calculate the linear correlation between two variables One-sample t-test = Compare the mean of a single sample against a known or hypothesized mean Two-sample t-test = Compare the means of two independent groups ANOVA = Compare the means of two or more groups</p> Signup and view all the answers

    In ANOVA, what is the 'factor' in the analysis?

    <p>Independent variable</p> Signup and view all the answers

    Standardized coefficients in regression analysis are used to determine the direction of the relationship between an independent and dependent variable.

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

    What is the null hypothesis for the F-test in regression analysis?

    <p>in the population, the R2 = 0, the IVs are not useful predicting the DV</p> Signup and view all the answers

    Study Notes

    Analysis of Variance (ANOVA)

    • ANOVA is a statistical procedure used to test hypotheses about the means of two or more groups.
    • Used when the variance in one or more populations is unknown.
    • It's an extension of the independent samples t-test, comparing more than two groups.
    • The F-test is the main significance test in ANOVA, used when comparing two or more groups.
    • Null hypothesis (H0) in the F-test states that all group means are equal.
    • Alternative hypothesis (H1) states that at least one group mean is different from the others.
    • Between-subjects design uses independent samples, different participants observed at each level of the factor.

    Ways to Select Independent Samples

    • Select a sample from two or more populations (quasi-experimental design).
    • Select one sample from the same population and randomly assign participants to groups (experimental design).

    Sources of Variation

    • Between-groups variation = variation attributed to mean differences between groups
    • Within-groups variation = variation within each group, cannot be attributed to different groups.

    Degrees of Freedom

    • Degrees of freedom between groups (dfBG) = k − 1, where k is the number of groups
    • Degrees of freedom within groups (dfw) = N − k, where N is the total sample size and k is the number of groups.

    Post Hoc Tests

    • Used after rejecting the null hypothesis (H0) in ANOVA.
    • Determine which group means differ significantly.
    • Example: Scheffé's test.

    Correlation

    • Correlation analysis = measures the strength and direction of a linear relationship between two factors.
    • The correlation coefficient (r) ranges from -1.0 to +1.0.
    • Values closer to ±1.0 indicate a strong correlation.
    • The sign (+ or -) indicates the direction of the correlation (positive or negative).

    Scatter Plots

    • A scatter plot (scatter diagram) graphically displays the relationship between two (interval/ratio) variables in pairs of values (x, y).
    • The independent variable (x) is on the horizontal axis.
    • Each dot represents a case, and its position reflects its values for x and y.

    Pearson's Correlation Coefficient (r)

    • Describes the linear relationship (also known as Pearson's r).
    • The correlation coefficient ranges from -1.0 to +1.0, closer to -1 or 1 signifies a stronger correlation.

    Regression Line

    • Regression line = best-fitting straight line to a set of data points, minimizing the distances of all data points.

    Pearson Correlation Coefficient

    • Pearson's r formula: r = cov(X,Y)/ √[var(X) * var(Y)]

    Assumptions of Linear Correlation

    • Linearity : data can be described with a straight line.
    • Homoscedasticity: variance is similar for different values of an independent variable (x).
    • Normality: data points are normally distributed.

    Correlation and Causality

    • Correlation does not imply causality (e.g., if two factors are correlated, one does not necessarily cause the other.)

    Multiple Regression

    • This analysis = procedure used with more than one predictor variable (IV).
    • With more IVs, you can predict changes in a criterion variable (DV), better, than with simple regression.
    • Multicollinearity = a problem that occurs when strong correlations exist among independent variables.

    Bivariate Statistics

    • Bivariate statistic = analysis of the relationship between two variables.
    • Uses two variables to determine the relationship between two measured variables (e.g., x and y)(predictor and criterion or independent and dependent).
    • Contingency Tables are used to test the relationship between the two measured variables.

    Chi-Square Tests

    • Used with ordinal or nominal data to test hypotheses about the distribution of categorical variables.
    • Goodness-of-fit test: compares observed frequencies with expected frequencies for a single categorical variable (e.g., are observed results similar to the expected results in a distribution).
    • Test of Independence: used to determine whether the frequencies observed at the combination of levels of two categorical variables are similar to frequencies expected. (Are two variables related/dependent?)

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    Chapter 12 – Analysis of Variance: One-Way Between-Subjects Design PDF

    Description

    This quiz covers key concepts in statistics, focusing on correlation coefficients, scatter plots, and ANOVA tests. Test your knowledge of how to interpret variables, correlation strength, and statistical measures used in analysis. Ideal for students studying statistics or data analysis techniques.

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