Introduction to quantitative statistics

Question 1

What is a research hypothesis?

Answer 1

Working assumption or prediction about the expected outcome of a study

Question 2

Which statistics inform on the hypothesis testing?

Answer 2

Inferential statistics

• is there enough empirical support?

Question 3

What is the meaning of the null hypothesis (H_0)?

Answer 3

Any differences or relationships between variables are due to random or chance

Question 4

What is the meaning of the experimental (alternative) hypothesis (H_1)?

Answer 4

The independent variable does have an effect on the dependent variable

Question 5

Can we treat the experimental (alternative) hypothesis as true or proven?

Answer 5

No
We can only prove that something is not true.

-> demonstrate that null hypothesis is not true = IV has an effect on DV

Question 6

What is the purpose of descriptive statistics?

Answer 6

Summarise aspects of the results (collected data)

Question 7

What is the purpose of inferential statistics?

Answer 7

• Inform of significant patterns or relationships in the data
• Generalise results from sample to general population

Question 8

When is the null hypothesis (H_0) rejected?

Answer 8

When the observed difference between experimental groups (conditions) is significantly large

Question 9

Which statistical tests explore relationships or differences between two variables?

Answer 9

Bivariate statistical tests

Question 10

Which statistical tests explore relationships or differences between a number of variables?

Answer 10

Multivariate statistical tests

Question 11

What is the purpose of a test statistic?

Answer 11

Summarizes the relationship between variables or groups

Question 12

Which statistical index informs on the correlation between values?

Answer 12

Pearson’s r

Question 13

Which statistical index informs on the statistical significance of a relationship between variables?

Answer 13

p-value

Question 14

What is the meaning of the p-value?

Answer 14

Probability of finding the test statistic if there was no difference between variables or groups
-> How probable is it that a random error alone could produce the changes in the DV?

Unlikely (p < .05): it’s the IV having an effect on the dependent variable

Question 15

How is the probability that the independent variable is having an effect on the dependent variable calculated?

Answer 15

Indirectly calculated by discounting the likelihood of the effect being produced by random error
= p-value

Question 16

What does empirical probability refer to?

Answer 16

Calculation of probability when the outcomes are not equally likely to occur

Question 17

How is empirical probability calculated?

Answer 17

[number of favourable outcomes] / [total number of trials]

Question 18

When does the empirical probability of an event increase?

Answer 18

As the observed sample (number of trials) increases

e. g. 9 successes out of 100 trials
- > increasing the number of trials increase the likelihood of favourable outcomes

Question 19

With a 95% confidence interval, when can the null hypothesis be rejected at the 5% level?

Answer 19

If the null value (0) is not contained in the 95% CI

Question 20

With a 95% confidence interval, when can the null hypothesis be accepted at the 5% level?

Answer 20

If the 95% CI contains the null value (0)

Question 21

What is a ‘Type I error’?

Answer 21

‘false positive’

Falsely rejecting the null hypothesis

Question 22

What is a ‘Type II error’?

Answer 22

‘false negative’

Accepting our null hypothesis in error

Question 23

What is the power of a hypothesis?

Answer 23

The probability of not committing a Type II error

Question 24

Which factors determine the power of a test?

Answer 24

• Sample size
• Effect size
• Variability
• Alpha level (α)
• Type of test

Question 25

What is the meaning of the alpha level (α) of a test?

Answer 25

Likelihood of detecting a difference

• increasing the alpha level increases the risk of Type I error

Question 26

How do you estimate the sample size needed to have a good chance to detect a defined effect size?

Answer 26

Do a power analysis