LECTURE 3 CHI SQUARED SIG TESTING

Question 1

What are inferential statistics?

Answer 1

Statistical methods that allow us to make inferences about a population based on a sample.

Question 2

What is the null hypothesis (H₀)?

Answer 2

A hypothesis stating there is no difference or association.

Question 3

What is the alternative hypothesis (H₁)?

Answer 3

A hypothesis predicting a difference or association exists.

Question 4

What is Null Hypothesis Significance Testing (NHST)?

Answer 4

A process estimating the probability of a result occurring by chance if the null hypothesis is true.

Question 5

What is a p-value?

Answer 5

The probability that the observed result (or one more extreme) occurred by chance, assuming the null hypothesis is true.

Question 6

What is the typical alpha level (α) for statistical significance?

Answer 6

0.05 or 5%.

Question 7

What does p < 0.05 indicate?

Answer 7

The result is statistically significant, and we reject the null hypothesis.

Question 8

What does p > 0.05 indicate?

Answer 8

The result is not statistically significant, and we fail to reject the null hypothesis.

Question 9

What is a directional (one-tailed) hypothesis?

Answer 9

A hypothesis predicting the effect in a specific direction.

Question 10

What is a non-directional (two-tailed) hypothesis?

Answer 10

A hypothesis predicting a difference or association without specifying the direction.

Question 11

What are effect sizes?

Answer 11

Measures indicating the magnitude or strength of a difference or association.

Question 12

What is Cohen’s d?

Answer 12

A popular effect size metric for comparing two groups.

Question 13

What are the thresholds for Cohen’s d?

Answer 13

Small: 0.2, Medium: 0.5, Large: 0.8.

Question 14

How do p-values differ from effect sizes?

Answer 14

P-values indicate significance; effect sizes indicate magnitude.

Question 15

What is the purpose of Chi-square tests?

Answer 15

To examine relationships between two categorical variables.

Question 16

What type of data is Chi-square used for?

Answer 16

Nominal or sometimes ordinal data.

Question 17

What are the assumptions of Chi-square tests?

Answer 17

Independent groups and expected frequencies greater than 5 in each cell.

Question 18

What is a 2x2 Chi-square?

Answer 18

A Chi-square test with two rows and two columns (e.g., binary variables).

Question 19

What is an observed frequency?

Answer 19

The actual count of cases in each category.

Question 20

What is an expected frequency?

Answer 20

The count we expect in each category if there is no association between variables.

Question 21

How do we calculate expected frequencies?

Answer 21

E= RowTotal×ColumnTotal / grand total
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Question 22

What does a significant Chi-square result indicate?

Answer 22

An association between the variables.

Question 23

What is Cramer’s V?

Answer 23

An effect size measure for Chi-square tests.

Question 24

What are the thresholds for Cramer’s V?

Answer 24

Small: 0.1, Medium: 0.3, Large: 0.5 (for df = 1).

Question 25

What are the degrees of freedom (df) for Chi-square?

Answer 25

df=(r−1)(c−1), where r is rows and c is columns.

Question 26

What is dummy coding?

Answer 26

Arbitrarily assigning numerical values to nominal data for analysis.

Question 27

What type of statistic is used for within-subjects ordinal data?

Answer 27

Wilcoxon Signed-Ranks test.

Question 28

What is the main difference between parametric and non-parametric tests?

Answer 28

Parametric tests assume normal distribution; non-parametric tests do not.

Question 29

What happens when assumptions of Chi-square are violated?

Answer 29

Results are less valid, requiring alternative analyses or adjustments.

Question 30

What is the role of significance testing?

Answer 30

To determine if the observed results are unlikely under the null hypothesis.

Question 31

Why are statistical tests like Chi-square important?

Answer 31

They provide a method to test hypotheses and draw conclusions about data.

Question 32

What does the p-value of 0.012 in the Zoella example indicate?

Answer 32

A 1.2% chance the results occurred by random chance, leading to rejection of the null hypothesis.

Question 33

What is the relationship between sample size and significance?

Answer 33

Larger samples reduce variability but may also make small effects significant.

Question 34

How are nominal level data presented?

Answer 34

As frequencies and percentages.

Question 35

Why are p-values controversial?

Answer 35

They are often misinterpreted as providing the probability of the hypothesis being true.