10: Sample size and statistical inference

Question 1

What is important when sampling?

Answer 1

Have to accept to deal with uncertainity. This can be quantified and controlled. The key to this is standard error. Sampling error tells you about certainity - how much certainty you want. If you decide on certainty - impacts the sample size you choose.

Question 2

If the sample size is large, what would be different?

Answer 2

If the sample size is large relative to the population - need to add a correction to this, by calculating the optimal sample size.

Question 3

What needs to be considered when determining the sample size?

Answer 3

Size of the sampling error, non response error (uninterviewable, not found, not at home, refusals), sample size appropriate for statistical method, sample size appropriate for all variables.

Question 4

What is a significance test?

Answer 4

Uses data to summarise the evidence about hypothesis. It compares point estimates of parameters to the values predicted by the hypothesis.

Question 5

What are the 5 steps of a significance test?

Answer 5

1. Assumptions, 2. Hypothesis, 3. Test Statistic, 4. P-value, 5. Conclusion

Question 6

What is part of the assumption step? (Significance test)

Answer 6

Randomisation, population distribution (here - normal), type of data, sample size.

Question 7

What is part of the hypothesis step? (Significance test)

Answer 7

Empirical social science - whether the data agrees with certain predictions. These predictions result from theories we want to test. Must be falsifiable

Question 8

What is a hypthesis?

Answer 8

In stats - hypothesis is a statement about a population. A prediction that parameter describing some characteristic of a variable takes a numerical value of falls in a certain range of values.

Question 9

What are the two hyptheses?

Answer 9

Null hypothesis and alternative hypothesis.

Question 10

What is a null hypothesis?

Answer 10

A statement that the paramter takes a particular value, that indicates no effect.

Question 11

What is a alternative hypothesis?

Answer 11

States that the paramter falls into some alternative range of values, representing an effect of some type.

Question 12

What is a test statisitc?

Answer 12

The parameter to which the hypotheses reder has a point estimate. It summarises how far the estimate falls from the parameter value in the null hypothesis. Expressed by the no. of standard errors between the estimate and null hypothesis value.

Question 13

What shows evidence of the null hypothesis?

Answer 13

The evidence about the null hypothesis is summarised by the no. of standard errors that the sample mean falls from the null hypothesis value population mean.

Question 14

What is the t-test statistic?

Answer 14

The resulting test-statistic is the t-score. In principle, this is the same as the z-value. But the standard deviation is used to estimate the population standard deviation = introduces additional error. This test uses the t-distribution.

Question 15

What is the p-value?

Answer 15

The probability that the test statistic equals the obsereved value or a valye more ectreme in the direction predicted by the alternative hypothesis.

Question 16

What does a smaller p-value mean?

Answer 16

The stronger the evidence against the null hypothesis. So we reject it and accept the alternative hypothesis.

Question 17

What is the purpose of the p-value?

Answer 17

We need to create a probability statement of the evidence against the null hypothesis. Need to use the test statistic, assuming the null hypothesis is true. Need to fund out how unusual the observed test statistic value is compared to what the null hypothesis predicts.

Question 18

How do you determine the p-value?

Answer 18

Calculate the test statistic, know how far the observed value of the standard error lies from the null hypothesis. Use this value to determine what % under the distribution is covered by this distance. Area beyond the the t-value is the p-value.