Data Analysis Lecture 3 & 4

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Questions and Answers

What is the value of the correlation coefficient indicating the relationship between English and Maths marks?

  • 0.569
  • 0.869
  • 0.669 (correct)
  • 0.769

Which statistical test can be run if the assumptions for Pearson's correlation are not met?

  • ANOVA
  • Wilcoxon Signed-Rank Test
  • Regression Analysis
  • Spearman Rho (correct)

What is a requirement for conducting a Chi-squared test related to expected counts?

  • All cells should have an expected count of at least 1.
  • The sample size must be fewer than 30 participants.
  • No more than 20% of cells should have an expected count less than 5. (correct)
  • No more than 10% of cells should have an expected count less than 5.

Given a p-value of .001 in relation to a hypothesis test, what conclusion can be drawn?

<p>There is a significant link between the variables. (C)</p> Signup and view all the answers

Which test is appropriate when comparing two groups of participants regarding one interval-ratio variable?

<p>Independent Sample t-test (D)</p> Signup and view all the answers

What does a p-value of .057 indicate regarding the null hypothesis for syntactic complexity?

<p>The null hypothesis is accepted, indicating no significant differences exist. (D)</p> Signup and view all the answers

Which finding was revealed by the Tukey HSD test regarding the pre-task planning group?

<p>The pre-task planning group produced significantly more syllables than the no planning group. (B)</p> Signup and view all the answers

What is the minimum size of a sample suggested when conducting EFA per item?

<p>5 to 10 (D)</p> Signup and view all the answers

Which statistical test is used to ensure the adequacy of sampling in EFA?

<p>Bartlett's test of sphericity (C)</p> Signup and view all the answers

What is the goal of using Multivariate Analysis methods like EFA and PCA?

<p>To reduce a large number of items into smaller dimensions for simpler analysis. (D)</p> Signup and view all the answers

What does a Cronbach's alpha value of 0.82 indicate about the reliability of a test?

<p>High reliability (B)</p> Signup and view all the answers

For the means of syllables, what can be concluded about the comparison between the no planning and online planning groups?

<p>No significant differences were found between the two groups. (D)</p> Signup and view all the answers

Which factor extraction criterion must be met for effective EFA?

<p>Eigenvalue greater than 1 (A)</p> Signup and view all the answers

What hypothesis is represented when stating H1 for the mean scores of syllables across the three planning groups?

<p>There are significant differences in the mean scores. (C)</p> Signup and view all the answers

Which factor rotation method is commonly used in EFA?

<p>Direct oblimin (C)</p> Signup and view all the answers

What is the mean proficiency score based on the descriptive statistics provided?

<p>69.6 (D)</p> Signup and view all the answers

What is the standard deviation of the proficiency scores?

<p>16.44342 (D)</p> Signup and view all the answers

Which method can be used to detect outliers in a dataset?

<p>Use Z scores (C)</p> Signup and view all the answers

What does the Pearson correlation coefficient indicate about the relationship between age and proficiency?

<p>Strong negative correlation (C)</p> Signup and view all the answers

What is the significance level associated with the correlation between age and proficiency?

<p>0.01 (C)</p> Signup and view all the answers

What does the coefficient of variation represent in descriptive statistics?

<p>The standard deviation relative to the mean (C)</p> Signup and view all the answers

What is the underlying principle of bivariate analysis using Pearson correlation?

<p>Assessing the relationship between two continuous variables (A)</p> Signup and view all the answers

Which of the following correctly describes the boxplot's function in data analysis?

<p>It visually displays outliers and the distribution of the dataset. (A)</p> Signup and view all the answers

What is the significance threshold for accepting a P Value in hypothesis testing?

<p>0.05 (C)</p> Signup and view all the answers

What reflects a perfect positive correlation between two variables?

<p>r = 1 (D)</p> Signup and view all the answers

Which of the following is NOT an assumption of Pearson's correlation?

<p>Variables are measured on an ordinal scale (B)</p> Signup and view all the answers

What does a Spearman correlation require regarding the relationship between variables?

<p>Monotonic relationship (B)</p> Signup and view all the answers

What would happen if the calculated P Value is 0.04 in a hypothesis test?

<p>Reject H0 (A)</p> Signup and view all the answers

What is the relationship strength indicated by r = 0.51?

<p>Moderate (D)</p> Signup and view all the answers

Which of the following is a condition that must be checked for verifying normal distribution?

<p>Skewness and kurtosis should be between -1 and 1 (B)</p> Signup and view all the answers

When deciding on a statistical test, which factor is NOT relevant?

<p>Sample size (C)</p> Signup and view all the answers

What is the effect size of the difference between early and late exposure learners?

<p>0.387 (C)</p> Signup and view all the answers

What must the dependent variable meet for a paired samples t-test?

<p>It must be measured at interval-ratio level. (C)</p> Signup and view all the answers

Which of the following indicates a null hypothesis that can be rejected?

<p>p &lt; 0.05 (D)</p> Signup and view all the answers

In a One-Way ANOVA, when would you run Welch's ANOVA?

<p>If variances are not equal. (D)</p> Signup and view all the answers

What is the significance of a Levene P value less than 0.05 in ANOVA?

<p>The groups do not have equal variances. (D)</p> Signup and view all the answers

What is the non-parametric equivalent of the paired samples t-test?

<p>Wilcoxon (B)</p> Signup and view all the answers

What is assumed about the distribution of the dependent variable in the analysis of variance?

<p>It should be approximately normal. (A)</p> Signup and view all the answers

What is the effect size indicating a significant large difference between vocabulary scores in pre-test and post-test?

<p>2.01 (D)</p> Signup and view all the answers

Flashcards

ANOVA (Analysis of Variance)

A statistical test used to determine if there is a significant difference between the means of two or more groups.

Null Hypothesis (H0)

The hypothesis that there is no significant difference between the means of two or more groups.

Alternative Hypothesis (H1)

The hypothesis that there is a significant difference between the means of two or more groups.

p-value

The probability of rejecting the null hypothesis when it is actually true.

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Tukey HSD Test

A post-hoc test used to determine which specific groups differ significantly from each other after an ANOVA has shown a significant overall difference.

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Exploratory Factor Analysis (EFA)

A statistical method used to reduce a large number of variables into a smaller set of underlying factors.

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Chi-Square Test

A statistical test that measures the relationship between two nominal variables. It determines if there's a significant association between the categories of the variables.

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Spearman Rho

A statistical test that examines the relationship between two ordinal variables. It evaluates the strength and direction of the association, indicating whether the variables tend to increase or decrease together.

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Multicollinearity

The degree to which multiple variables are linearly related. EFA requires sufficiently high correlations between variables.

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Kaiser-Meyer-Olkin (KMO) Test

A statistical test that measures the sampling adequacy for factor analysis. A value greater than 0.5 is generally acceptable.

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Independent Samples t-test

A statistical test comparing two independent groups on a continuous variable to determine if there's a significant difference between their means.

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Bartlett's Test of Sphericity

A statistical test that tests the null hypothesis that the correlation matrix is an identity matrix. If significant, it suggests there are relationships between variables suitable for EFA.

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Statistical Test Assumptions

Assumptions are specific conditions that must be met for a statistical test to be valid. If these assumptions are not met, the results might be unreliable.

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Cronbach's Alpha

A measure of internal consistency reliability for a scale. Generally, a Cronbach's Alpha value of 0.7 or higher indicates good reliability.

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Coefficient of Variation

A measurement of the spread of data points around the mean. It is calculated by dividing the standard deviation by the mean and multiplying by 100.

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Boxplot

A visual representation of data that shows the distribution of values, including the mean, quartiles, and outliers.

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Pearson Correlation

A statistical technique used to measure the strength and direction of the linear relationship between two interval-ratio variables.

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Pearson Correlation Coefficient (r)

A numerical value that represents the strength of the linear relationship between two variables. It ranges from -1 to +1, where -1 indicates a perfect negative correlation, +1 indicates a perfect positive correlation, and 0 indicates no correlation.

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Outliers

Values that lie significantly far from the rest of the data points, potentially skewing the analysis.

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Standardized Scores (Z-Scores)

A technique to transform raw scores into standardized scores, making it easier to compare data from different scales.

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Mean

The average value of a set of data points. It is often used to describe the central tendency of the data.

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Dispersion

The degree to which data points are spread out around the mean. The more spread out, the higher the spread.

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Spearman Rank Correlation

A test to determine if there is a significant relationship between two variables measured at least at the ordinal level.

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Monotonic Relationship

The assumption that the relationship between two variables is not linear, requiring a non-parametric test like Spearman.

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Scatter Plot

A visual representation of the distribution of data points in a scatter plot, showing whether the data points follow a linear trend.

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Interpreting Correlation

The relationship between two variables can be interpreted by its direction and strength.

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Paired Samples t-test

A statistical test used to compare the means of two related groups, where data is collected from the same subjects under two different conditions or at two different time points.

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Wilcoxon Signed Rank Test

A non-parametric equivalent to the paired samples t-test, used when the data doesn't meet the assumptions of a parametric test.

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One-Way ANOVA (Analysis of Variance)

A statistical test used to compare the means of two or more independent groups.

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Kruskal-Wallis Test

A statistical test used to compare the means of two or more independent groups when the assumptions of ANOVA are not met.

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Paired Samples T-Test

A statistical test used to compare the means of two related groups when data is collected from the same subjects under two different conditions or at two different time points. It is used to determine whether there is a significant difference between the two groups.

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Wilcoxon Signed Rank Test

A non-parametric test used to compare the means of two related groups when the data doesn't meet the assumptions of a parametric test. It is used to determine whether there is a significant difference between the two groups.

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One-Way ANOVA (Analysis of Variance)

A statistical test used to compare the means of two or more independent groups. This test determines whether there is a significant difference between the means of the groups.

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Kruskal-Wallis Test

A non-parametric test used to compare the means of two or more independent groups when the assumptions of ANOVA are not met. This test determines whether there is a significant difference between the means of the groups.

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Study Notes

Data Analysis - Lecture 3: Preliminary Univariate Statistics

  • Describing Nominal Data: Analyze descriptive statistics, frequencies, and missing values. Create charts like bar charts.
  • Describing Interval-Ratio Variables: Calculate the mean to describe central tendency. Identify dispersion measures, such as the coefficient of variation (standard deviation/mean * 100).
  • Detect Outliers: Create boxplots to visually identify outliers. Use the chart builder to isolate the boxplot. Drag and drop the variable for review.
  • Standardized Scores for Outlier Detection: Another numerical method to identify outliers is through standardized scores (z-scores). Items with z-scores between -3 and 3 are not considered outliers.

Data Analysis - Lecture 4: Bivariate Analysis - Pearson Correlation

  • Correlation: Variation in one variable corresponds to variation in another variable. A linear relationship between the variables is evaluated.
  • Pearson Product Moment Correlation: Measures the strength of a linear relationship between two interval-ratio variables.
  • Correlation Strength Interpretation:
    • Perfect: 1
    • Strong: 0.9-0.7
    • Moderate: 0.6-0.4
    • Weak: 0.3-0.1
    • Zero: 0
  • Significance: A p-value lower than .05 indicates a statistically significant correlation.

Data Analysis - Lecture 5: Bivariate Analysis (Spearman and Chi²)

  • Choosing the Right Test: Consider the number of variables, the objective (correlate, compare, predict), and the level of measurement (ordinal, nominal, interval-ratio).
  • Spearman Correlation: A non-parametric test used when the assumptions for Pearson correlation are not met. It evaluates both variables being at least ordinal, and a monotonic relationship. Check monotonicity with a scatterplot.

Data Analysis - Lecture 6: Bivariate Analysis 3: Comparison Tests (Independent Samples t-test + Mann Whitney U)

  • Independent Samples t-test: Used to compare two groups of participants on an interval-ratio variable. Consider Levene's Test for homogeneity of variances.
  • Mann-Whitney U test: A non-parametric alternative to the independent samples t-test when homogeneity of variances is not met. Use this test when the assumptions of a t-test are not met.

Data Analysis - Lecture 7: Test Assumptions Across Multiple Analyses

  • General Test Assumptions: A summary of sample size requirements, independence of observations, normal distribution, and homogeneity of variance criteria to determine the most appropriate test methodology.

Data Analysis - Lecture 8: Bivariate Analysis (ANOVA + Kruskal Wallis)

  • ANOVA (Analysis of Variance): Compares multiple groups (2 or more) on an interval-ratio variable. The test aims to identify if there are statistically significant mean differences between these groups.

Data Analysis - Lecture 9: Multivariate Analysis (EFA+PCA)

  • Factor/Component Analysis: Reduce the dimensionality of multiple variables into a smaller number of factors/components for later analysis. The goal of exploratory factor analysis (EFA and PCA is to uncover related items into a smaller pool of variables. This methodology can be utilized to generate a smaller pool of variables to evaluate from a larger pool.

Data Analysis - Lecture 10: Multiple Regression Analysis

  • Multiple Regression: Predicts a dependent variable (DV) based on a set of independent variables (IVs).
  • Correlation vs. Regression: Correlation measures the relationship between variables. Regression examines the effect of IVs on the DV.
  • Interpreting Regression: Assess whether the model adequately explains the variation in the DV. Evaluate the impact of each IV on the DV. The adjusted R-squared (adjusted for the number of IVs) is an insightful measure. The Beta component of each IV can be used to understand the significance each variable plays in the relationship.

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