Study Unit 2 - Statistical Theory

Question 1

What is inference in research studies?

Answer 1

Inference is the act of generalizing results from a sample to the entire population.

Question 2

What is the role of a sample in research?

Answer 2

A sample* is a subset of the population on which the study is conducted. The findings are then generalized to the population.

*Ideally representative

Question 3

What is sampling error?

Answer 3

Sampling error refers to the difference in observations that occurs when a sample does not fully represent the population.

Question 4

What is null hypothesis significance testing (NHST)?

Answer 4

NHST is a statistical method used to account for sampling error. It helps determine whether an observed effect is likely due to chance or the effect of an independent variable.

Question 5

How are probabilities defined?

Express as probability of A….

Answer 5

The probability of an event, A, is the number of events classified as A divided by the total number of possible outcomes.

Question 6

What is a hypothesis in research?

Answer 6

A hypothesis is a scientific claim or proposed explanation for a phenomenon.

Question 7

What is the difference between null and alternative hypotheses?

Answer 7

The null hypothesis expects no effect if the claim is false, while the alternative hypothesis expects some effect if the claim is true.

Question 8

What is the logic behind NHST?

Answer 8

NHST starts by assuming the null hypothesis (any observed effect is due to chance) is true and only rejects it if the result is very unlikely to have occurred by chance.

Question 9

What is a p-value in statistical analysis?

Answer 9

A p-value quantifies the probability of getting a result at least as extreme as what was observed, assuming the null hypothesis is true.

Question 10

How do you decide whether to accept or reject the null hypothesis based on the p-value?

Answer 10

If the p-value is very small, it’s unlikely the result occurred by chance, so we reject the null hypothesis. If the p-value is not small, we retain the null hypothesis.

Question 11

How is NHST similar to court proceedings?

Answer 11

In both cases, the assumption (null hypothesis or innocence) is deemed true until sufficient evidence is provided against it.

Question 12

What is the effect of sampling variation in inferential statistics?

Answer 12

Sampling variation can cause the sample mean or other statistics to differ greatly from sample to sample, potentially leading to inaccurate inferences about the population.

Question 13

What does it mean for a result to occur ‘by chance’ in a study?

Answer 13

A result is said to occur ‘by chance’ if it could be explained by sampling error rather than the effect of an independent variable.

Question 14

What does P(A) denote?

Answer 14

P(A) denotes the probability of event A occurring.

Question 15

What range do probabilities fall in?

Answer 15

Probabilities always fall between 0 (0%) and 1 (100%).

Question 16

State the first two steps of the NHST procedure.

Answer 16

First step: we first assume that there is no effect (i.e., the null hypothesis is true) and any observed result is due to chance.

Second step: To quantify the likelihood of getting the observed result due to chance, resulting in the p-value.

Question 17

What does a small p-value signify in NHST?

Answer 17

A small p-value signifies that the observed result is very unlikely to have occurred by chance, suggesting that the null hypothesis can be rejected.

Question 18

What does the alternative hypothesis in NHST signify?

Answer 18

The alternative hypothesis signifies what we would expect to observe if our claim is true.

Question 19

What is a directional hypothesis?

Answer 19

A directional hypothesis states a direction to the effect (e.g., X increases Y, X decreases Y).

Question 20

What is a non-directional hypothesis?

Answer 20

A non-directional hypothesis does not state a direction to the effect (e.g., X affects Y, X is related to Y).

Question 21

What does the term ‘at least as extreme’ mean in the definition of p-value?

Answer 21

‘At least as extreme’ refers to outcomes that are as extreme or more extreme than the observed outcome in the direction of the alternative hypothesis.

Question 22

What does it mean to ‘retain the null hypothesis’?

Answer 22

Retaining the null hypothesis means that there isn’t enough evidence to reject it, so the assumption that there’s no effect remains.

Question 23

When is a p-value considered ‘small enough’ to reject the null hypothesis?

Answer 23

Generally, a p-value less than 0.05 is considered small enough to reject the null hypothesis, but the threshold can vary based on the field and the context of the study.

Question 24

What does P(A) = 0 imply?

Answer 24

If P(A) = 0, it implies that event A will definitely not occur.

Question 25

What does P(A) = 1 imply?

Answer 25

If P(A) = 1, it implies that event A will definitely occur.

Question 26

What does P(A) = 1 imply?

Answer 26

If P(A) = 1, it implies that event A will definitely occur.

Question 27

What does it mean if P(A) is between 0 and 1?

Answer 27

If P(A) is between 0 and 1, it implies that event A will sometimes occur.

Question 28

Why do researchers use two-tailed tests for both directional and non-directional hypotheses?

Answer 28

Two-tailed tests are used to account for possible effects in both directions, making them suitable for both directional and non-directional hypotheses.

Question 29

What is the aim of a scientific hypothesis?

Answer 29

The aim of a scientific hypothesis is to provide reasons or explanations for why certain phenomena have happened or are happening.

Question 30

What is the final step in the NHST procedure?

Answer 30

The final step in NHST is deciding whether to reject or retain the null hypothesis based on the calculated p-value.

Question 31

What is a sampling distribution?

Answer 31

A sampling distribution is the distribution of a statistic for all possible random samples of a given size.

Question 32

What is the sampling distribution of the mean?

Answer 32

The sampling distribution of the mean is the distribution of sample means when the null hypothesis is true, i.e., when there is no effect of the independent variable or no difference between the conditions.

Question 33

What is the Central Limit Theorem (CLT)?

Answer 33

The CLT states that the sampling distribution of the mean approaches a normal distribution if the sample size, N, is sufficiently large, typically N ≥ 30.

Question 34

What does the CLT imply about the mean and standard deviation of the sampling distribution of the mean?

Answer 34

The CLT states that the mean of the sampling distribution of the mean will be equivalent to the population mean and the standard deviation of the sampling distribution of the mean (the standard error) will be equivalent to σx / √N, or sigma X (standard deviation of the sample) / sqrt(sample size).

Question 35

How does the standard error indicate the distance between the sample means and the population mean?

Answer 35

The standard error represents the average distance between the sample means and the population mean. A smaller standard error means that the sample means are closer to the population mean.

Question 36

How does the Central Limit Theorem relate to the p-value?

Answer 36

The CLT states that the sampling distribution will be normally shaped. This allows us to determine what proportion of sample means would fall within certain ranges when H0 is true and thereby calculate the p-value.

Question 37

How is the p-value determined in relation to the standard normal distribution?

Answer 37

The p-value corresponds to the area under the curve of the standard normal distribution, indicating the probability of obtaining a result as extreme or more extreme than the observed statistic, given that the null hypothesis is true.

Question 38

Why are standard normal distribution tables used in hypothesis testing?

Answer 38

Standard normal distribution tables provide the proportions of the distribution that fall within different distances from the mean, which can be used to find the exact p-value.

Question 39

What is an alpha level?

Answer 39

The alpha level, denoted by α, is the cutoff value used to determine whether the p-value is small enough to reject the null hypothesis.

Question 40

What happens if the p-value is higher than the alpha?

Answer 40

If the p-value is higher than the alpha, we fail to reject the null hypothesis.

Question 41

What happens if the p-value is lower than the alpha?

Answer 41

If the p-value is lower than the alpha, we reject the null hypothesis.

Question 42

What is a typical alpha level in social sciences?

Answer 42

In social sciences, a typical alpha level is .05.

Question 43

What does it mean when a result is statistically significant?

Answer 43

A result is statistically significant when the p-value is less than the alpha level, indicating that the observed result is unlikely to be due to chance.

Question 44

What is a Type I error?

Answer 44

A Type I error occurs when a true null hypothesis is rejected. It is also known as a false positive.

Question 45

What is a Type II error?

Answer 45

A Type II error occurs when a false null hypothesis is retained. It is also known as a false negative.

Question 46

How can a researcher control the Type I error rate?

Answer 46

A researcher can control the Type I error rate by setting a specific alpha level: one that is not too high that it rejects an insufficiently low p-value.

Question 47

How does changing the alpha level affect Type I and Type II errors?

Answer 47

Lowering the alpha level decreases the likelihood of Type I errors (false positives) but increases the likelihood of Type II errors (false negatives).

Question 48

How can a researcher control the Type II error rate?

Answer 48

A researcher can control the Type II error rate by increasing the effect size or the sample size.

Question 49

What does increasing the effect size mean in the context of Type II error rate?

Answer 49

Increasing the effect size means designing the study to maximize the difference between the conditions being compared.

Question 50

How does increasing the sample size affect the Type II error rate?

Answer 50

Increasing the sample size reduces the errors due to sampling variation, thereby decreasing the Type II error rate.

Question 51

What is the purpose of the frequency distribution of sample means?

Answer 51

The frequency distribution of sample means helps us visualize how often particular sample means occur, which can give us a sense of the likely p-values.

Question 52

Why is the standard error important in understanding the sampling distribution?

Answer 52

The standard error tells us how close to or how far we would expect the various sample means to be from the population mean.

Question 53

What factors affect the standard error?

Answer 53

The standard error is affected by population variability and sample size. The smaller the population variability or the larger the sample size, the smaller the standard error.

Question 54

Can sampling distributions of different statistics have different shapes?

Answer 54

Yes. For example, the F statistic relies on the F distribution, a positively skewed distribution.

Question 55

What is the significance in null hypothesis significance testing?

Answer 55

Significance refers to whether the observed results are unlikely to be due to chance based on the p-value being smaller than the alpha level.

Question 56

What does it mean when we retain the null hypothesis?

Answer 56

If we retain the null hypothesis, it means that the result is not statistically significant, i.e., the observed results could have happened by chance.

Question 57

Why might social scientists set the alpha level to values other than .05?

Answer 57

Social scientists might choose a different alpha level depending on their comfort level about making Type I and Type II errors.

Question 58

What happens when the null hypothesis is true but we reject it?

Answer 58

It means we’ve committed a Type I error or false positive.

Question 59

What happens when the null hypothesis is false but we fail to reject it?

Answer 59

It means we’ve committed a Type II error or false negative.