Section B.2: Hypothesis Testing (1)

Question 1

What is a hypothesis?

Answer 1

A hypothesis is a proposed explanation for a phenomenon, based on existing knowledge or initial observations, that can be proven or disproven.

Question 2

What makes a good hypothesis? (5)

Answer 2

A good hypothesis is testable, specific, falsifiable, relevant, and clear.

Question 3

Null hypothesis

Answer 3

The null hypothesis states that there is no relationship between the variables being tested, denoted by H0.

Question 4

Alternative hypothesis

Answer 4

The alternative hypothesis states that there is a relationship between the variables being tested, it is denoted by H1, and contradicts the H0.

Question 5

Directional hypothesis

Answer 5

A directional hypothesis is a statement that predicts the direction of the relationship between variables being tested, it is known as a one-tailed hypothesis.

eg. positive or negative relationship…

Question 6

What is hypothesis testing?

Answer 6

Hypothesis testing is a statistical method used to test a hypothesis about a population parameter using sample data, it has two categories: Parametric tests, and Nonparametric tests.

Question 7

Steps in hypothesis testing (4)

Answer 7

1. Formulate a null and alternative hypothesis
2. Choose a statistical test based on the type of data, variables, and parameters
3. Collect data and analyse it using the chosen test
4. Determine whether the results support or reject the null hypothesis

Question 8

Type 1 error

Answer 8

Type I error occurs when we reject a true null hypothesis. The probability of a Type I error is denoted by the alpha level or significance level (alpha - a) and is usually set at 0.05, or 0.01.

Question 9

Type 2 error

Answer 9

Type II error occurs when we fail to reject a false null hypothesis. The probability of a Type II error is denoted by Beta and depends on factors such as sample size, effect size, and alpha level.

Question 10

What are parametric tests?

Answer 10

A parametric test is one that assumes the sample data being tested comes follows a particular distribution, with a fixed set of parameters.

Examples: t-test, z-test, ANOVA, regression analysis

Question 11

What key assumptions are made about the data in parametric tests? (3)

Answer 11

Normality: The data follows a normal distribution
Homogeneity of variance: The variance of the data is equal across groups or samples
Independence: The observations are independent from each other

Question 12

What are advantages of parametric tests? (3)

Answer 12

High statistical power: Able to detect small differences between groups

Precise: Provide highly accurate estimates of population parameters

Wide applicability: Can be applied to many study designs

Question 13

What are the disadvantages of parametric tests? (3)

Answer 13

Strict assumptions, sensitivity to outliers, sample size requirements*.

*May require larger sample sizes to produce reliable results

Question 14

What are one sample parametric tests?

Answer 14

One sample parametric tests are used to compare the sample mean to a known population mean.

Examples: One-sample t-test, one-sample z-test, one-sample mean confidence interval

Question 15

What is a one-sample t-test?

Answer 15

A one-sample t-test is a parametric test used to test whether the mean of a sample is equal to a known population mean

Question 16

When should a one-sample z-test be used instead of t-test?

Answer 16

When the population standard deviation is known and the sample size is <30.

Question 17

One-sample mean confidence interval

Answer 17

A one-sample parametric test used to estimate the range of values which the true population mean likely falls

Question 18

What are two sample parametric tests?

Answer 18

Two sample parametric tests are used to compare the means of two independent groups.

Examples: Independent samples t-test, Paired samples t-test, ANOVA

Question 19

What are non-parametric tests?

Answer 19

Non-parametric tests are statistical tests that do not assume a specific distribution for the population.

Question 20

When should a non-parametric test be used? (3)

Answer 20

1. When the median more accurately represents the centre distribution/non-normal distribution
2. Unequal variances
3. Small sample size

Question 21

Advantages of non-parametric tests (3)

Answer 21

1. Robust - They are less sensitive to outliers and non-normality in data
2. Wide applicability - They can be used with many different study designs and data types
3. Ease of interpretation - They often have simple and intuitive interpretation

Question 22

Disadvantages of non-parametric tests (3)

Answer 22

1. Lower statistical power - less sensitive, therefore require higher sample sizes to detect significant differences
2. Limited scope - some tests are limited by type of study design or data types
3. Less precise - they provide less precise estimates of population parameters

Question 23

How do you determine to use parametric or non-parametric tests? (2)

Answer 23

1. If the mean more accurately represents the centre of distribution of the data, and the sample size is large, use a parametric test.
2. If the median more accurately represents the centre of distribution, use a non-parametric test

Question 24

Significance level

Answer 24

The significance level, represented by alpha, is the probability of rejecting a null hypothesis when it is true.
Most commonly it is 0.05, and 0.01.

Example: A significance level of 0.05 means there is a 5% chance of rejecting a null hypothesis that is actually true

Question 25

P-value

Answer 25

The p-value is the probability of the observed outcome occurring, assuming that the null hypothesis (no effect or difference) is true.

p-value > a = Accept H0
p-value < a = Reject H0

Question 26

p-value > a

Answer 26

Accept H0

Question 27

p-value < a

Answer 27

Reject H0

Question 28

Z-value

Answer 28

z-value, also known as z-score, is a measure of how many standard deviations a data point is away from the mean. It is used to compare a sample mean to a population mean.

z-value > critical value @ a = Reject H0
z-value < critical value @ a = Accept H0

Question 29

z-value > critical value

Answer 29

= Reject H0

Question 30

z-value < critical value

Answer 30

= Accept H0

Question 31

A z-value of 1.5 means what?

Answer 31

A z-value of 1.5 means that the observed value for the sample is 1.5 standard deviations away from the mean

Question 32

Confidence interval

Answer 32

A confidence interval is a range of values around a sample estimate that is likely to contain the true population parameter, with a certain degree of confidence. Common intervals are 90%, 95%, and 99%.

Question 33

Degree of Freedom

Answer 33

The degree of freedom (df) is a parameter used in statistical tests that determines the number of independent observations in a sample. It is important for calculating critical values for tests such as t-tests and F-tests. As the df increases, critical value decreases, indicating a greater likelihood of rejecting the null hypothesis.

Question 34

What is the degree of freedom (df parameter) important for?

Answer 34

1. It is important for calculating critical values for t-tests and f-tests
2. It affects the precision of confidence intervals, with a larger df leading to a narrower confidence interval, and more accurate model

Question 35

Types of Distribution

Answer 35

Normal, log, skew, kurtosis

Question 36

Deciding statistical tests: Categorical data (2)

Answer 36

Categorical nominal - Chi-squared
Categorical ordinal - Non-parametric