SDA: Significance testing

Question 1

Null hypothesis H0

Answer 1

No difference between groups under study

Question 2

Research hypothesis H1

Answer 2

There is a difference between groups under study

Question 3

What are the two types of research hypotheses?

Answer 3

Two-tailed

One-tailed

Question 4

Two-tailed research hypothesis

Answer 4

Stating there will be a difference but nothing else

e.g. there will be a difference in average levels of disposable income between two areas

Question 5

One-tailed research hypothesis

Answer 5

Gives an indication of the direction of difference

e.g. People living in Hackney will have less disposable income than people living in Westminster

Question 6

Why do we use hypotheses?

Answer 6

Assess whether the sample and calculated statistics are reasonable: not due to chance and generalisable to the population
Make inferences about a population using data for a sample

Question 7

What is the most common significance level used?

Answer 7

95% i.e. happy to be wrong 5/100 times

May need to use the 99% significance level at times

Question 8

Type 1 error in statistical testing

Answer 8

When H0 is found to be true, but the decision is made to reject H0 - this is a false positive

Question 9

Type 2 error in statistical testing

Answer 9

When H0 is found to be false, but the decision is made to accept H0 - this is a false negative

Question 10

What things should be remembered about sampling?

Answer 10

Larger the sample the more likely the chances of finding a statistically significant result

Always a possibility of chance findings as using sampled data: By using a more demanding significance level, we limit the chances of Type 1 errors. BUT this leads to a trade off - decreasing the chance of a Type 1 error, increases the chance of Type 2 errors, therefore should limit the number of comparisons and statistical calculations made

Question 11

What are the two distinct types of statistical tests?

Answer 11

Parametric

Non-paramertic

Question 12

Non-parametric tests should be used with what type of data?

Answer 12

Nominal
Weak ordinal
Strong ordinal

Question 13

Parametric tests should be used with what type of data?

Answer 13

Interval/Ratio

Question 14

What test is used when analysing NOMINAL data?

Answer 14

Chi-squared one sample test (This increases to a two-sampled and k-sampled when number of samples increases)

Question 15

What test is used with WEAK ORDINAL (and nominal) data?

Answer 15

Kolomogrov-Smirnov one-sample/two-sample test

Question 16

What test is used with ORDINAL data?

Answer 16

Mann-Whitney U test (when 2 samples)

Kruskal-Wallis test (more than 2 samples)

Question 17

What test is used with one and two-samples of INTERVAL/RATIO data?

Answer 17

One sample T-test/Two sample T-test

Question 18

What test is used when there are more than two samples of INTERVAL/RATIO data?

Answer 18

Snecedor F ratio test

Question 19

What assumptions must be followed with parametric tests?

Answer 19

1) Observations must be drawn from a pop. with a normal distribution
2) Observations must be independent i.e. randomly sampled
3) The pop. must have the same amount of variability

Question 20

Key points to remember about Parametric and Non-parametric tests:

Answer 20

Parametric:
demanding assumptions
interval/ratio data

Non-parametric:
less demanding/no assumptions
any data especially nominal/ordinal
fall-back situation if parametic assumptions cannot be met

Question 21

What is the general process for significance testing?

Answer 21

1. State H0
2. Specify the desired significance level (usually 95%)
3. Perform calculations to generate the test statistic
4. Compare the test statistic with the critical value in the sampling distribution
5. Accept or reject H0 - if the test statistic exceeds the critical value at the chosen significance level, then H0 is rejected