LECTURE 3 CHI SQUARED SIG TESTING Flashcards
What are inferential statistics?
Statistical methods that allow us to make inferences about a population based on a sample.
What is the null hypothesis (H₀)?
A hypothesis stating there is no difference or association.
What is the alternative hypothesis (H₁)?
A hypothesis predicting a difference or association exists.
What is Null Hypothesis Significance Testing (NHST)?
A process estimating the probability of a result occurring by chance if the null hypothesis is true.
What is a p-value?
The probability that the observed result (or one more extreme) occurred by chance, assuming the null hypothesis is true.
What is the typical alpha level (α) for statistical significance?
0.05 or 5%.
What does p < 0.05 indicate?
The result is statistically significant, and we reject the null hypothesis.
What does p > 0.05 indicate?
The result is not statistically significant, and we fail to reject the null hypothesis.
What is a directional (one-tailed) hypothesis?
A hypothesis predicting the effect in a specific direction.
What is a non-directional (two-tailed) hypothesis?
A hypothesis predicting a difference or association without specifying the direction.
What are effect sizes?
Measures indicating the magnitude or strength of a difference or association.
What is Cohen’s d?
A popular effect size metric for comparing two groups.
What are the thresholds for Cohen’s d?
Small: 0.2, Medium: 0.5, Large: 0.8.
How do p-values differ from effect sizes?
P-values indicate significance; effect sizes indicate magnitude.
What is the purpose of Chi-square tests?
To examine relationships between two categorical variables.
What type of data is Chi-square used for?
Nominal or sometimes ordinal data.
What are the assumptions of Chi-square tests?
Independent groups and expected frequencies greater than 5 in each cell.
What is a 2x2 Chi-square?
A Chi-square test with two rows and two columns (e.g., binary variables).
What is an observed frequency?
The actual count of cases in each category.
What is an expected frequency?
The count we expect in each category if there is no association between variables.
How do we calculate expected frequencies?
E= RowTotal×ColumnTotal / grand total
What does a significant Chi-square result indicate?
An association between the variables.
What is Cramer’s V?
An effect size measure for Chi-square tests.
What are the thresholds for Cramer’s V?
Small: 0.1, Medium: 0.3, Large: 0.5 (for df = 1).
What are the degrees of freedom (df) for Chi-square?
df=(r−1)(c−1), where r is rows and
c is columns.
What is dummy coding?
Arbitrarily assigning numerical values to nominal data for analysis.
What type of statistic is used for within-subjects ordinal data?
Wilcoxon Signed-Ranks test.
What is the main difference between parametric and non-parametric tests?
Parametric tests assume normal distribution; non-parametric tests do not.
What happens when assumptions of Chi-square are violated?
Results are less valid, requiring alternative analyses or adjustments.
What is the role of significance testing?
To determine if the observed results are unlikely under the null hypothesis.
Why are statistical tests like Chi-square important?
They provide a method to test hypotheses and draw conclusions about data.
What does the p-value of 0.012 in the Zoella example indicate?
A 1.2% chance the results occurred by random chance, leading to rejection of the null hypothesis.
What is the relationship between sample size and significance?
Larger samples reduce variability but may also make small effects significant.
How are nominal level data presented?
As frequencies and percentages.
Why are p-values controversial?
They are often misinterpreted as providing the probability of the hypothesis being true.
