W3

Question 1

Why do we describe data?

Answer 1

Datasets are often large and complex, so summaries help give insights and make the data easier to process.

Question 2

What types of summaries can we use to describe data?

Answer 2

Numerical and visual summaries.

Question 3

What are frequency distributions?

Answer 3

They count the number of responses for each value of a variable and show it as a percentage.

Question 4

What numerical and visual summaries suit nominal data?

Answer 4

Numerical: Frequency table, mode, Visual: Bar chart, pie chart

Question 5

What numerical and visual summaries suit ordinal data?

Answer 5

Numerical: Frequency table, percentiles, median, Visual: Bar chart, pie chart

Question 6

What numerical and visual summaries suit interval and ratio data?

Answer 6

Numerical: Average, standard deviation, min, max, percentiles, Visual: Histogram, scatter plot, box plot

Question 7

What are the three types of descriptive statistics?

Answer 7

Measures of shape: Skewness, kurtosis, Measures of location: Mean, mode, median, - Measures of variability: Range, interquartile range, variance, standard deviation

Question 8

What is the limitation of descriptive statistics?

Answer 8

They only give an impression and aren’t enough for conclusions — you need to run tests for that.

Question 9

Why do we do hypothesis testing?

Answer 9

We want to know about a big population but only have a sample, so we use it to test assumptions about the population.

Question 10

How does a good sample help in hypothesis testing?

Answer 10

If your sample is representative, you can generalize findings to the full population.

Question 11

What does inferential statistics try to do?

Answer 11

It tries to find the true value in the population using sample statistics.

Question 12

What is a hypothesis in statistics?

Answer 12

It’s an educated guess about a population, stated as H0 (null) and H1 (alternative), and they must be mutually exclusive.

Question 13

What are the steps of hypothesis testing?

Answer 13

1. State the hypothesis 2. Define the method & gather data 3. Make a decision using statistics and thresholds

Question 14

What is the P-value used for?

Answer 14

It’s used to help decide whether to reject the null hypothesis based on the likelihood of the observed result.

Question 15

What is a P-value?

Answer 15

It’s the probability of getting your result (or something more extreme) if the null hypothesis is true.

Question 16

What does a low P-value mean?

Answer 16

The result is unlikely under the null hypothesis, so we may reject H0 and consider H1 instead.

Question 17

How do we interpret the P-value in a distribution?

Answer 17

If your result falls in the middle, it likely has no effect. If it’s in the tail, it might be significant.

Question 18

What determines statistical significance?

Answer 18

Whether the P-value is smaller than the chosen level of significance (e.g., 0.05).

Question 19

What are the two types of hypothesis tests?

Answer 19

1. Two-tailed (two-sided) 2. One-tailed (one-sided)

Question 20

What is a two-tailed test?

Answer 20

You test whether there’s any difference — e.g., men and women have different Instagram followers (without saying who has more).

Question 21

What is a one-tailed test?

Answer 21

You test for a specific direction — e.g., women have more Instagram followers than men.

Question 22

What is the main difference between one-sided and two-sided tests?

Answer 22

Two-sided tests check for any difference. One-sided tests check for a difference in a specific direction.

Question 23

What are one-sided tests used for?

Answer 23

Only for t-tests. They cannot be used for ANOVA, regression, or chi-squared tests.

Question 24

What does R do by default for p-values?

Answer 24

R gives the p-value for a two-sided test. For a one-sided test, divide the p-value by 2 or indicate it directly.

Question 25

What test do you use when the dependent variable is metric and you compare one sample with a population value?

Answer 25

One sample t-test.

Question 26

What test do you use for two dependent samples with a metric variable?

Answer 26

Paired t-test.

Question 27

What test do you use for two independent samples with a metric variable?

Answer 27

Independent samples t-test.

Question 28

What test do you use for more than two independent samples with a metric variable?

Answer 28

One-way ANOVA.

Question 29

What test do you use for non-metric dependent variables?

Answer 29

Chi-square test — goodness-of-fit for 1 sample, and test of independence for 2+ samples.

Question 30

What do you use when independent variables are metric?

Answer 30

Correlation (1 variable) or regression (2+ variables).

Question 31

What is a chi-square goodness-of-fit test used for?

Answer 31

Comparing one sample's distribution with a known or expected distribution using proportions.

Question 32

What does a chi-square test help determine?

Answer 32

Whether the distribution of responses in categories is statistically different from what we expected.

Question 33

What are the assumptions for the chi-square test?

Answer 33

You need at least 5 observations per group and mutually exclusive categories.

Question 34

What is the null hypothesis (H0) in a chi-square test?

Answer 34

The proportions of cases in the groups are equal.

Question 35

What is the alternative hypothesis (H1) in a chi-square test?

Answer 35

The proportions of cases in the groups are not equal.

Question 36

What R code is used to run a chi-square test with equal expected proportions?

Answer 36

chisq.test(table(df$var), p = rep(1/3,3))

Question 37

What does a p-value < 0.05 mean in a chi-square test?

Answer 37

The result is statistically significant — we reject H0 and conclude the observed distribution is not equal.

Question 38

Can you test with unequal expected proportions in a chi-square test?

Answer 38

Yes! You use chisq.test(table(df$string), p = c(0.35, 0.25, 0.40)) to test based on specific expectations.

Question 39

What does it mean if the observed values differ from expected with low p-value?

Answer 39

It means there's a significant difference between what we expected and what actually happened.

Question 40

What kind of plots help visualize chi-square results in R?

Answer 40

Bar plots of observed vs. expected frequencies.

Question 41

What is the chi-squared test for independence used for?

Answer 41

It’s used when we have 2 or more different samples and want to test if there is a relationship between them. Each sample has 2+ categories.

Question 42

What are the assumptions for the chi-squared test for independence?

Answer 42

Each group needs at least 5 expected frequencies and categories must be mutually exclusive.

Question 43

What is the null hypothesis (H0) in a chi-squared test for independence?

Answer 43

There is NO relationship between the two variables.

Question 44

In the chi-square test for independence, what is the alternative hypothesis (H1)?

Answer 44

There IS a relationship between the two variables.

Question 45

Give a real-life example of the chi-squared test for independence.

Answer 45

Testing if gender (male/female) is related to learning medium preference (e-book, video, book).

Question 46

What does the R code chisq.test(df$Gender, df$StudyMethod) do?

Answer 46

It performs a chi-square test to see if gender and study method are related.

Question 47

How are expected values calculated in chi-square independence?

Answer 47

Automatically based on the assumption of independence.

Question 48

What does it mean if the observed values differ a lot from expected values in a chi-square test?

Answer 48

There may be a relationship between the two variables, and we can reject the null hypothesis.

Question 49

What is a 1 sample t-test used for?

Answer 49

Comparing the sample mean with a population mean to see if they are significantly different.

Question 50

What kind of variable is needed for a 1 sample t-test?

Answer 50

A metric variable (ratio, interval, or continuous), assumed to be normally distributed.

Question 51

What are the hypotheses in a 1 sample t-test?

Answer 51

H0: Sample mean = / ≤ / ≥ population mean, H1: Sample mean ≠ / < / > population mean

Question 52

Give an example scenario for a 1 sample t-test.

Answer 52

A researcher tests if a sample's depression scores differ from the population value of 4.0.

Question 53

What R code is used for a 1 sample t-test?

Answer 53

t.test(df$depression_score, mu=4)

Question 54

What does it mean if the sample mean falls outside the confidence interval?

Answer 54

The difference is statistically significant and you can reject the null hypothesis.

Question 55

What if the p-value is less than 0.05?

Answer 55

It shows significance — you reject the null hypothesis.

Question 56

How can you visualise the data before doing a t-test?

Answer 56

Use mean(), sd(), and boxplot() in R to get an idea of the data's distribution.

Question 57

What is a paired sample t-test used for?

Answer 57

Comparing the mean scores of two sets of observations from the same people (e.g., before and after measurements).

Question 58

What is the hypothesis for a paired sample t-test?

Answer 58

H0: Mean difference = 0, H1: Mean difference ≠ 0

Question 59

What does the null hypothesis (H0) mean in the paird t-test test?

Answer 59

The average difference between the two scores is zero — no significant change.

Question 60

Give an example of when to use a paired t-test.

Answer 60

A company measures employee satisfaction in 2022 and again in 2023 using the same survey.