Section 3 (Pg 25 - end of section 1)

Question 1

Name the 3 types of distribution?

Answer 1

Normal
Binomial
Poisson

Question 2

When is normal distribution used?

Answer 2

For continuous variables

Question 3

When is binomial distribution used?

Answer 3

For binary data

Question 4

When is poisson distribution used?

Answer 4

For events occurring at random intervals of time or space and rare events such as drug side effects

Question 5

What is another name for normal distribution?

Answer 5

Gaussian distribution

Question 6

Give the 6 characteristics of normal distribution?

Answer 6

Bell-shaped
Single central peak
Symmetrical
Equal mean, median and mode
Continous
Takes values between - infinity and + infinity

Question 7

What 2 descriptive statistics are used to describe the normal distribution?

Answer 7

Mean

Variance

Question 8

How would you write that X is a normally distributed variable with mean mu and standard deviation sigma?

Answer 8

X~N(μ, σ^2)

Question 9

What is the mean and standard deviation of the standard normal distribution?

Answer 9

Mean = 0

Standard deviation = 1

Question 10

How to standardise a normally distributed variable?

Answer 10

Subtract the mean and divide by the standard deviation

Question 11

What is the standard normal variable referred to as?

Answer 11

z

Question 12

What does the total area under the normal distribution density function curve equal?

Answer 12

1

Question 13

If an observation selected at random from the population lies outside of the 95% range, what does this suggest about the population mean?

Answer 13

Casts doubt on the fact that the population mean is mu

Question 14

Why standardise a normal distribution?

Answer 14

To calculate probabilities for normal (probability tables on exist for the standard normal)

Question 15

What is the z-score?

Answer 15

The standardised normal distribution

Question 16

What probability is associated with the mean?

Answer 16

0.5 (there is a 50% chance you will get a score that is less than the mean)

Question 17

In the standard normal distribution, approximately what % of values lie within 1 standard deviation of the mean?

Answer 17

68%

Question 18

In the standard normal distribution, approximately what % of values lie within 2 standard deviation of the mean?

Answer 18

95%

Question 19

In the standard normal distribution, approximately what % of values lie within 3 standard deviation of the mean?

Answer 19

99.9%

Question 20

Do standardised normal distribution tables give the probability that z is less than or more than the specified value?

Answer 20

Less than

Question 21

How can we assess normality of distribution of a variable? (3)

Answer 21

Informal review of the properties of the normal distribution
Inspection of a normal plot
Formally through a statistical test e.g. Shapiro-Wilk

Question 22

What is a normal plot?

Answer 22

A diagram constructed to show the extent of the departure of a data distribution from the normal

Question 23

What shape is the cumulative frequency distribution of a normally distributed variable?

Answer 23

s-shaped

Question 24

What does any departures form the straight line in normal plot suggest?

Answer 24

Deviation from normality

Question 25

For shapiro-wilk, what does a result less than 0.05 indicate?

Answer 25

The distribution is significantly different to the normal

Question 26

For shairo-Wilk, what does the closer the P-value is to 1 indicate?

Answer 26

The closer it is to being normally distributed

Question 27

Give the 5 possible ways to transform data to be normally distributed?

Answer 27

``` Logarithmic transformation Square root transformation Reciprocal transformation Cube transformation Logit transformation ```

Question 28

What type of transformation is used for data that is fairly skewed or groups of data in which the variances are proportional to the mean?

Answer 28

Logarithmic transformation

Question 29

What type of transformation is used for data that is slightly skewed or counts?

Answer 29

Square root transformation

Question 30

What type of transformation is used for data that is highly skewed?

Answer 30

Reciprocal transformation

Question 31

What type of transformation is used for data that relates to volume?

Answer 31

Cube transformation

Question 32

What type of transformation is used for proportions?

Answer 32

Logit transformation

Question 33

What is the logit transformation equation?

Answer 33

logit (p) = ln (p/ 1-p)

Question 34

What would be the most likely transformation appropriate for the number of units of alcohol consumed per week?

Answer 34

Square root

Question 35

What would be the most likely transformation appropriate for the proportion of women in favour of breast screening?

Answer 35

Logit transformation

Question 36

What would be the most likely transformation appropriate for the stimulated saliva flow (cc per minture)?

Answer 36

Cube root transformation

Question 37

If 2 normally distributed variables are added or subtracted, what does the variance of the outcome equal?

Answer 37

The sums of the variances

Question 38

If 2 normally distributed variables are added, what does the mean of the sum equal?

Answer 38

The sum of the means

Question 39

If 2 normally distributed variables are subtracted, what does the mean of the differences equal?

Answer 39

The difference of the means

Question 40

What is a prospective study?

Answer 40

A study that watches for outcomes during the study

Question 41

How to calculate the expected number of events for binomial data if you know n and p?

Answer 41

n X p

Question 42

How to calculate variance of the expected number of events for binary data?

Answer 42

n X p X (1-p)

Question 43

How to calculate the probability that there will be x events for binary data?

Answer 43

P (x) = n!/ x! (n-x)! X p^x (1-p) ^n-x

Question 44

What is factorial of 0?

Answer 44

1

Question 45

Does the binomial distribution get closer or further from normality as the size of the group increases?

Answer 45

Closer

Question 46

When can the binomial distribution with parameters n and p be approximated as normal?

Answer 46

When both: np >5 n(1-p) >5

Question 47

How can the binomial distribution with parameters n and p be approximated as normal?

Answer 47

N(np, square root (np(1-p))

Question 48

For poisson data, what symbol is used for the average number of occurences in a fixed interval?

Answer 48

Llamda

Question 49

For poisson data, what is the equation for the probability of r events?

Answer 49

e^-llambda X llamda^r / r(r-1)(r-2)... 1

Question 50

What is e?

Answer 50

The exponential constant

Question 51

What are the mean and standard deviation of the poisson distribution?

Answer 51

llamda

Question 52

What happens for poisson distribution as llamda increase?

Answer 52

The poisson distribution approaches normality