Statistics 3

Question 0

Normal distributions X and Y:

P(X > Y) ?

Answer 0

Z = (X - Y)/(sqrt[σ^2Χ + σ^2Υ])

φ(Ζ) is your answer

Question 1

Degrees of Freedom (calculating expected values from table)

Answer 1

Normally:

v = (number of cells after combining)
- (number of constraints)

Number of constraints is usually 1, but every time a statistic is calculated from a sample, one degree of freedom is used up. If the estimate of a parameter is CALCULATED then it IS a restriction. If a parameter is GUESSED by using an estimate that seems sensible from observations then it IS NOT a restriction. - e.g having to calculate p from a sample to test a binomial distribution (n,p) is a restriction - merely guessing a value for p is not a restriction.

For a contingency table:

v = (rows -1)*(columns-1)

Question 2

What the hell is a contingency table?

Answer 2

It’s got 2 “criteria” - one across the columns and one in the rows

e.g. The school a pupil attends (rows)
The grades the pupils get (columns)

Question 3

Define population

Answer 3

Whole set of items that are of interest

Question 4

What is a census

Answer 4

A census observes or measures every member of a population

Question 5

What is a sample?

Answer 5

A sample is a selection of observations taken from a sub-set of the population which is used to find out information about the population as a whole. This is known as a SAMPLE SURVEY.

Question 6

What is a key about a random sample?

Answer 6

In a random sample, every possible sample of size n has an equal chance of being selected.

Question 7

What is a Sampling Frame?

Answer 7

A sampling frame is a list identifying every single sampling unit that could be included in the sample.

Question 8

Random number sampling?

Answer 8

In random number sampling, each element is given a number to identify it and the numbers of the required elements are selected by using ransom number tables or other random number generators.

Question 9

Systematic Sampling?

Answer 9

In systematic sampling the required elements are chosen at regular intervals from an ordered list.

Question 10

Stratified Sampling?

Answer 10

In Stratified Sampling the population is divided into mutually exclusive strata and a simple random sample is taken from each. The proportion of units sampled in each strata is the same as the proportion of that strata in the total population.

Question 11

Quota Sampling?

Answer 11

In quota sampling the population is divided into groups in terms of gender, social class etc. The number of people in each group is set to try and reflect the group’s proportion in the whole population. But it is the interviewer who selects the actual sampling units.

Question 12

Advantages/Disadvantages of random sampling

Answer 12

RANDOM NUMBER SAMPLING:

ADVANTAGES:
•Numbers are truly random and free from bias
•Each number has a known equal chance of selection
•It is easy to use
•Standard formulae can be used to analyse the results
•Each person or unit is included only once

DISADVANTAGES:
•It is not suitable where the population size is large

In LOTTERY SAMPLING the same is true, ADVANTAGES include that tickets are drawn at random; it’s an easy process to use; each ticket has a known chance of selection. DISADVANTAGES include: not suitable where population size is large; a sampling frame is needed.

SIMPLE RANDOM SAMPLING (in general):

ADVANTAGES (provided population is small):
•It is cheap to do
•It is easy to do
•Standard formulae can be used to analyse results
•Each person/unit is only included once

DISADVANTAGES:
•It is not suitable where the population size is large
•A sampling frame is required.

Question 13

Advantages/Disadvantages of Systematic Sampling

Answer 13

ADVANTAGES:
•It is simple to use
•It is suitable for large samples

DISADVANTAGES:
•It is only random if the ordered list is truly random
•It can introduce bias.

Question 14

Advantages/Disadvantages of stratified sampling

Answer 14

ADVANTAGES:
•It can give more accurate estimates than simple random sampling where there are clear strata present
•It reflects the population structure

DISADVANTAGES:
•Within the strata, the problems are the same as for any simple random sample
•If the strata is not clearly defined they may overlap

Question 15

Advantages/Disadvantages of quota sampling

Answer 15

ADVANTAGES:
•Enables fieldwork to be done quickly because a representative sample can be achieved with a small sample size
•Costs are kept to a minimum
•Administering the test is easy

DISADVANTAGES:
•It is not possible to estimate the sampling errors as it is not a random process
•The interviewer has to choose the respondents and may not be able to judge characteristics easily
•Non-responses are not recorded
•It can introduce interviewer bias in who is included.

Question 16

Advantages/Disadvantages of using Primary Data

Answer 16

ADVANTAGES:
•Collection method is known
•Accuracy is known
•Exact data needed are collected

DISADVANTAGES:
•It is costly in time and effort as you must collect the data

Question 17

Advantages/Disadvantages of using Secondary Data

Answer 17

ADVANTAGES:
•They are cheap to obtain - government publications, for example, are relatively cheap
•A large quantity of data is available, for example, on the internet

DISADVANTAGES:
•Bias is not always recognised
•It can be in a form that is difficult to deal with (might need to be processed to be useful, for example).

Question 18

When is stratified sampling used?

Answer 18

• sample is large

* population divides naturally into mutually exclusive groups

Question 19

Why use quota sampling?

Answer 19

Can be done quickly, cheaply and the test is easily administered. You can achieve a representative sample with a small sample size.

Question 20

When is systematic sampling used?

Answer 20

When the population is too large for simple random number sampling.

Question 21

What is a SAMPLING FRAME?

Answer 21

A sampling frame is a list identifying every single sampling unit that could be included in the sample.

Question 22

What’s the difference between random number sampling and lottery or ticket sampling?

Answer 22

RANDOM NUMBER SAMPLING - assign each element of sampling frame a number, use random number generator to generate ‘n’ random numbers in the range of numbers that your population covers, where n is the sample size you want. Sample the population members that correspond to the generated numbers in the correct range.

LOTTERY SAMPLING - identify each element of a population, by name or number for example, and put this on a ticket. Tickets should all be same size and shape, put them all into a container and draw one at a time without replacement. Elements of the population corresponding to chosen tickets are selected.