Chapter 2

Question 1

If we have sample data from just 1 sample, which 3 approaches can be used to obtain the sampling distribution?

Answer 1

1. bootstrapping
2. exact approaches
3. theoretical approximations

Question 2

Bootstrap sample

Answer 2

A random sample drawn from the initial sample. This is done through sampling with replacement

Question 3

How big should a bootstrap sample be?

Answer 3

Equal to the initial sample

Question 4

In bootstrapping, what happens when we have an unrepresentative initial sample?

Answer 4

Results will be skewed if the proportion in the initial sample is very different from the proportion in the population

Question 5

Apart from the proportion in the initial sample, what else affects the accuracy of the sampling distribution?

Answer 5

The size of the initial sample. Bigger samples will yield better results, but will still not be perfectly accurate.

Note: The population should be much larger than the sample size!

Question 6

What is the main limitation of bootstrapping?

Answer 6

We are never sure if our initial sample reflects the population well

Question 7

What is the main advantage of bootstrapping?

Answer 7

Every sample statistic can be bootstrapped

E.g. the median weight of candies

Question 8

When do we use bootstrapping?

Answer 8

• When the assumptions for theoretical approximation are not met
• When we have a continuous variable
• When SPSS does not have a test for the sample statistic we want to examine
• When we know nothing about the population proportion

Question 9

When do we use exact approaches?

Answer 9

When we (think we) know the proportion of the variable in the population.

Question 10

What are limitations of exact approaches?

Answer 10

• Only works for discrete or categorical variables

- Needs a lot of computing power

Question 11

What do we actually do in an exact approach?

Answer 11

We use this approach to calculate the probabilities for all possible outcomes

Question 12

Describe the binomial distribution

Answer 12

It is a frequency distribution of the possible number of successes (vs. failures) for N repeated trials in which there is the same probability of success. There are always 2 possible outcomes

E.g. number of heads in 3x coin toss. Either heads or tails.

Question 13

What would we use an exact binomial test for?

Answer 13

Questions involving population proportions

E.g. “Is 50% of candies in the population sticky?”

Question 14

What would we use an exact cross tabs test for?

Answer 14

To examine the association between 2 categorical variables

Question 15

What would we use an exact chi-squared test for?

Answer 15

To test whether 1 categorical variable follows an hypothesized population mean

Question 16

What do we mean by a theoretical approximation?

Answer 16

We then use a known mathematical function to approximate the sampling distribution

T-distribution / normal distribution

Question 17

Why would we use theoretical approximations?

Answer 17

• Quick computations
• They offer plausible arguments about chance and probabilities (e.g. we would expect a sampling distribution to be symmetrical, so using a normal distribution is then logical)

Question 18

When can we use a theoretical approximation?

Answer 18

sample size * population prop. = ≥ 5

We need a large sample size, and a population proportion of 0.5 is ideal

Question 19

Why do we pay attention to the tail ends of the probability distribution?

Answer 19

These are used for significance tests

Question 20

Repeated measures

Answer 20

Comparing one set of measurements with a second set of measurement from the SAME sample