Confirmatory statistics and regression analysis

Question 1

What is the difference between a one and two tailed test?

Answer 1

One tailed - directionality is specified

Two tailed - direction of difference not specified.

Question 2

What is a type one error?

Answer 2

Rejecting H0 when in fact it is true.

Question 3

What is a type two error?

Answer 3

Failing to reject H0 when it is false

Question 4

What is a parameter?

Answer 4

A representative value for the total population, true but unknown.

Question 5

What are the five determinants when choosing an appropriate statistical test?

Answer 5

Number of samples, nature of data, type of data, power and assumptions.

Question 6

For the KS D statistic, what do both a larger N and more specific H1 result in?

Answer 6

A smaller D

Question 7

What question does a chi squared test answer?

Answer 7

Whether the observed differences between two populations are genuine (or the result of sampling error and chance fluctuations)

Question 8

What measurement scales are parametric procedures used on? what is the exception to this?

Answer 8

High measurement scales - interval/ratio

Exception = randomisation test (Interval/ratio but non-parametric)

Question 9

Why are parametric tests more powerful?

Answer 9

There is less chance of getting a type 2 error, and fewer observations are required than non-parametric equivalent.

Question 10

Non parametric tests are based on ranks of observed data, whereas parametric tests are not. What extra step(s) have to be taken therefore?

Answer 10

Parametric tests are two stage tests

• Estimating the parameters of the population (Mean, standard deviation)
• Derive test statistic for the parameters

Question 11

N, μ, σ^2 and σ are parameters. What do they represent and what are their sample equivalents?

Answer 11

N = number. Sample equivalent = n
μ = mean. Sample equivalent x^‾
σ^2 = Varience. Sample equivalent = S^2
σ = Standard deviation. Sample equivalent = S

Question 12

Sample statistic =

Answer 12

Population parameter + Sampling error

Question 13

What is accuracy?

Answer 13

How far the mean of the samples is from the true mean - the degree of bias.

Question 14

What is precision?

Answer 14

The degree of spread around the estimate (measured by standard error)

Question 15

The sample mean is unbiased in repeated samples. Therefore what is the mean of the sample mean (X double-bar) equal to?

Answer 15

μ

Question 16

As n increases, what happens to distribution of values?

Answer 16

Becomes more normal

Question 17

What is the standard error?

Answer 17

The standard deviation of the sampling distribution.

Question 18

SE=σ / √n However when calculating this with sample data, two complications arise and the formula must be corrected. What are these and what is it corrected to?

Answer 18

S is not an unbiased estimate of σ and small samples underestimate true population standard deviation. Therefore the formula is corrected to SE= s√(n/(n-1)).

Question 19

The bias correction for sample size of 2 is to multiply SD by 1.4. What are the bias corrections for n=10 and n=100.

Answer 19

n=10 - 1.05

n=100 - 1.005