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BMSc Statistics > Section 3 (Pg 25 - end of section 1) > Flashcards

Section 3 (Pg 25 - end of section 1) Flashcards

1
Q

Name the 3 types of distribution?

A

Normal
Binomial
Poisson

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2
Q

When is normal distribution used?

A

For continuous variables

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3
Q

When is binomial distribution used?

A

For binary data

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4
Q

When is poisson distribution used?

A

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

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5
Q

What is another name for normal distribution?

A

Gaussian distribution

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6
Q

Give the 6 characteristics of normal distribution?

A 
Bell-shaped
Single central peak
Symmetrical
Equal mean, median and mode
Continous
Takes values between - infinity and + infinity
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7
Q

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

A

Mean

Variance

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8
Q

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

A

X~N(μ, σ^2)

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9
Q

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

A

Mean = 0

Standard deviation = 1

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10
Q

How to standardise a normally distributed variable?

A

Subtract the mean and divide by the standard deviation

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11
Q

What is the standard normal variable referred to as?

A

z

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12
Q

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

A

1

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13
Q

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

A

Casts doubt on the fact that the population mean is mu

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14
Q

Why standardise a normal distribution?

A

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

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15
Q

What is the z-score?

A

The standardised normal distribution

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16
Q

What probability is associated with the mean?

A

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

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17
Q

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

A

68%

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18
Q

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

A

95%

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19
Q

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

A

99.9%

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20
Q

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

A

Less than

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21
Q

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

A

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

22
Q

What is a normal plot?

A

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

23
Q

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

A

s-shaped

24
Q

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

A

Deviation from normality

25
Q

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

A

The distribution is significantly different to the normal

26
Q

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

A

The closer it is to being normally distributed

27
Q

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

A 
Logarithmic transformation
Square root transformation
Reciprocal transformation
Cube transformation
Logit transformation
28
Q

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?

A

Logarithmic transformation

29
Q

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

A

Square root transformation

30
Q

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

A

Reciprocal transformation

31
Q

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

A

Cube transformation

32
Q

What type of transformation is used for proportions?

A

Logit transformation

33
Q

What is the logit transformation equation?

A

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

34
Q

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

A

Square root

35
Q

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

A

Logit transformation

36
Q

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

A

Cube root transformation

37
Q

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

A

The sums of the variances

38
Q

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

A

The sum of the means

39
Q

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

A

The difference of the means

40
Q

What is a prospective study?

A

A study that watches for outcomes during the study

41
Q

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

A

n X p

42
Q

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

A

n X p X (1-p)

43
Q

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

A

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

44
Q

What is factorial of 0?

A

1

45
Q

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

A

Closer

46
Q

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

A

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

47
Q

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

A

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

48
Q

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

A

Llamda

49
Q

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

A

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

50
Q

What is e?

A

The exponential constant

51
Q

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

A

llamda

52
Q

What happens for poisson distribution as llamda increase?

A

The poisson distribution approaches normality

BMSc Statistics (9 decks)

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