Hypothesis Testing

Question 1

What is a null hypothesis?

Answer 1

Supported if chance finding

Not statistically significant

H0

Question 2

What is an alternative hypothesis?

Answer 2

Supported when the null hypothesis is rejected

so not a chance finding (real event rep)

Statistically significant

HA

Question 3

What is a false-positive error (type 1 or alpha)

Answer 3

null hypothesis rejected in error

protection against this type of error provided by:
- setting alpha level,
- usually 0.05 (i.e. only 5% risk)

Question 4

Whats a false-negative error?

Answer 4

null hypothesis accepted in error

protection against this type of error provided by:
- beta level is rarely set

Question 5

What is the p-value ?(probability)

Answer 5

Measured probability of finding occurring by chance

If p > alpha level
- the null hypothesis is
supported
- finding not statistically
significant

If p < alpha level
- null hypothesis is rejected
- so, alternative hypothesis
is supported
- finding is statistically
significant

Question 6

How do you check if you data is normally distributed?

Answer 6

Chi-square (x^2) goodness of fit

Question 7

Explain Chi-square (x^2) goodness of fit

Answer 7

Chi-square distribution is positively skewed with values between 0 and ∞.

Chi-square distribution are labelled based on degree of freedom (df ).

Mean and variance of the chi-square distribution are given by
𝜇 = df and 𝜎^2 = 2df.

Question 8

What is the Kolmogorov-smirnov one-sample test?

Answer 8

Is used to test whether a sample comes from a specific distribution.

Determine whether a sample comes from a
population that is normally distributed

Question 9

What is a one tailed test?

Answer 9

One-tailed test - alternative hypothesis states that one group mean is
higher or lower than another

only one tail of normal distribution considered
- e.g. if z = 1.96 then p = 0.025

Question 10

What is a two tailed test?

Answer 10

Two-tailed test - alternative hypothesis states that two group means are
different
- both tails of normal distribution
considered
- e.g. if z = 1.96 then p = 0.05

Question 11

Parametric tests: Difference between pairs of sample means (look at lect 7, slide 10)

Answer 11

Lect 7 slide 10

Question 12

What is the equation for the unpaired T-test?

Answer 12

shows degree of variation between 2 means

Equation for t = C- T / s√ (1/n1 + 1/n2)

Where:
- C* = Mean of control group
- T* = Mean of treated group
- s = Estimate of the standard deviation
based on both

samples
- n1 = Number of observation in group 1
- n2 = Number of observations in group 2

Question 13

How is the T value judged as significantly significant?

Answer 13

Value taken to a statistical table of the T distribution for comparison.

Question 14

t-distribution graph (look at lect 7 slide 12)

Answer 14

F(t) = Frequency of ‘t’ values
DF = Degrees of freedom

Question 15

What is the equation for the paired t-test?

Answer 15

Equation for paired design, t = d*/ (sd/√n)

Where:

d* = mean of the differences between each paired
observation
Sd = standard deviation of the differences between each paired observation

Enter t table with n – 1 degrees of freedom, where n = number of pairs of subjects

Question 16

Give advantages of the paired design

Answer 16

A paired design is often employed to reduce the effect
of subject variability

Pairing subjects will often reduce the standard error

Pairing should only be considered when a logical
method of pairing is present

Question 17

What are the assumption of t-test?

Answer 17

Individual measurements, the treatment
means, or the differences between the means are normally distributed

Question 18

What is data transformation?

Answer 18

sometimes data collected needs to be transformed to make it close to a normal distribution

one method is o convert or transform the original measurements so they are expressed on a new scale which is closer to a normal distribution than the original scale

The usual parametric test can then be carried out on the transformed values

if the data is in the form of percentages the data can be transformed into angular or arcsine scale using :
Angle = sin-1 √(%/100)

transformation for small whole numbers (x) or quantities with
limited scales
- √ x
- √ x + 1 (if many zeroes are present)

transformation for data (x) that lack homogeneity of variance
- Log(x)

Question 19

Name 3 other statistical tests

Answer 19

Mann-Whitney U Test

Wilcoxon Matched-Pairs Signed-Ranks Test

Kruskal-Wallis Test