LEC 4 Statistics

Question 1

2 branches of statistics

Answer 1

1. Descriptive statistics
   - describe the attributes of a group or population
2. Inferential statistics
   - draw conclusion from a sample and make inference to the entire population

Question 2

3 types of variables

Answer 2

1. Nominal
   - categories that are not ordered
   - categorical
   eg subject count
2. Ordinal
   - categories that are ordered
   - no fixed interval
   eg scale & cancer stages
3. Continuous
   - with real values that reflect order and relative magnitude
   - fixed interval
   - normal or non-normal distribution
   eg age

Question 3

Describing Nominal data & graphical presentation

Answer 3

n(%)
n = frequency
% = proportion
Graphical presentation
- pie chart
- bar chart (normal, clustered, stacked & segmented)

Question 4

Describing Ordinal data & graphical presentation

eg Likert scale

Answer 4

n(%)
n = frequency
% = proportion
Graphical presentation :
- pie chart
- bar chart (normal, clustered, stacked & segmented)

OR

median (IQR)
Graphical presentation :
- box plot (box-and-whiskers plot)

Question 5

Box plot whiskers

Answer 5

Whiskers (1.5x of IQR)

Mild outlier : 1.5-3x below Q1 or above Q3
Extreme outlier : >3x below Q1 or above Q3

Question 6

Describing Continuous data & graphical presentation

• normal
• non-normal

Answer 6

Graphical presentation :

• histogram
• box plots

Normal distribution - mean +/- SD
Non-Normal distribution - median (IQR)

Question 7

Types of distribution of Continuous data (5)

Answer 7

1. Normal distribution
2. Positively skewed (right)
3. Negatively skewed (left)
4. Bimodal distribution (U shape)
5. Several peaks

Question 8

Measure of central tendency

Answer 8

• mean

- median

Question 9

Measure of variability

Answer 9

• SD

- IQR

Question 10

How to ensure sample will lead to reliable and valid inferences

Answer 10

Random sampling

Question 11

Types of inferential statistics (2)

Answer 11

1. Parameter Estimation

2. Hypothesis Testing

Question 12

Population mean

Answer 12

Mean of all sample means

Question 13

Central Limit Theorem

Answer 13

For sufficiently large sample sizes, the sampling distribution of the mean is approximately normally distributed
even if the underlying distribution of individual observation in the population is not normally distributed

Question 14

Factors affecting the width of CI (3)

Answer 14

1. Confidence level
2. Sample size
3. Standard deviation

Question 15

p-value

Answer 15

• Probability that the observed result or a more extreme result would occur by chance alone, assuming Ho is true
• The smaller the p-value, the stronger the evidence against Ho

Question 16

Type l error

Answer 16

= alpha

• false positive
• reject Ho when Ho is true (no significant difference/no effect)

Question 17

Type ll error

Answer 17

= beta

• false negative
• failure to reject Ho when Ho is not true (there is significant difference/effect)

Question 18

Statistical power

Answer 18

1-beta

Probability of correctly rejecting Ho when Ho is not true (there is significant difference/effect)

Question 19

Why CI is more informative than p-value? (2)

Answer 19

1. Precision of the point estimate
   - width of CI
2. Statistical significance

Question 20

95% CI of difference

Answer 20

• If does not include 0, there is statistical difference
• p<0.05

eg mean diff = 0.45, 95% CI (0.3,0.6)

Question 21

95% CI of ratio

Answer 21

• If does not include 1, there is statistical difference
• p<0.05

eg odds ratio = 2.51, 95% CI (1.04,3.28)

Question 22

Assessing normality of continuous data (3)

& hypothesis

Answer 22

Visual inspect of histogram or box plot

Shapiro-Wilk test (n<50)
Kolmogorov-Smirnov test (n>=50)

Ho = normal distribution
H1 = not normal distribution

Question 23

(( comparing data ))

Test for :

• continuous data (normal)
• 2 groups
• independent

Answer 23

Independent t-test

Question 24

(( comparing data ))

Test for :

• continuous data (normal)
• 2 groups
• paired

Answer 24

Paired samples t-test

Question 25

(( comparing data )) Test for : - continuous data (normal) - >2 groups - independent

Answer 25

One-way ANOVA

Question 26

(( comparing data )) Test for - continuous data (non-normal) or ordinal data - 2 groups - independent

Answer 26

Wilcoxon rank sum test (Mann-Whitney U test)

Question 27

(( comparing data )) Test for : - continuous data (non-normal) or ordinal data - 2 groups - paired

Answer 27

Wilcoxon signed-rank sum test

Question 28

(( comparing data )) Test for : - continuous data (non-normal) or ordinal data - >2 groups - independent

Answer 28

Kruskal-Wallis test

Question 29

(( comparing data )) Test for : - nominal data - 2 groups - independent

Answer 29

Chi-square test or Fisher's exact test

Question 30

(( comparing data )) Test for : - nominal data - 2 groups - paired

Answer 30

McNemar's test

Question 31

(( comparing data )) Test for : - nominal data - >2 groups - independent

Answer 31

Chi-square test or Fisher-Freeman-Halton test

Question 32

Describing Ordinal data | eg Cancer stages

Answer 32

``` n(%) n = frequency % = proportion Graphical presentation : - pie chart - bar chart (normal, clustered, stacked & segmented) ```

Question 33

Ordinal data & graphical presentation | Cancer stages = Likert scale

Answer 33

No. Cancer stages can only be described in - frequency (n) and proportion (%) Likert scale can be described in both - frequency (n) and proportion (%) - median & IQR

Question 34

Skewing of graph

Answer 34

Where the tail is at

Question 35

Determine types of distribution from box plot

Answer 35

- rotate box plot 90 degrees clockwise | - check where is the longer whiskers (right or left)

Question 36

If data given in median (Q1, Q3), how to differentiate between continuous data & ordinal data?

Answer 36

- check the type of data collected eg length of hospital stay vs Likert scale

Question 37

Parameter Estimation

Answer 37

- seeks an approximate calculation of a population parameter eg "by how much __ reduce blood pressure?" (a) Point estimate (b) Interval estimate (confidence interval)

Question 38

Hypothesis Testing

Answer 38

- seeks to validate a supposition based on limited evidence (hypothesis testing) eg "does __ reduce blood pressure?" (a) Null hypothesis (b) Alternate hypothesis

Question 39

SD of the sample means

Answer 39

SD of population divided by square root of sample size

Question 40

SD of sample means vs SD of sample scores

Answer 40

SD of sample means = SEM SD of sample scores = sample SD

Question 41

SEM

Answer 41

Standard Error of the Mean | - quantification of the variability of the sample mean values

Question 42

Point estimate

Answer 42

eg population mean

Question 43

Interval estimate (2)

Answer 43

- provide a range of reasonable values that are intended to contain the point estimate - with a certain degree of confidence (usually 95%) eg confidence interval

Question 44

Confidence level affecting CI

Answer 44

- larger confidence level, wider CI | - smaller confidence level, narrower CI

Question 45

(( correlation )) Test for : - continuous normally distributed data

Answer 45

Pearson Product-Moment Correlation (r)

Question 46

(( correlation )) Test for : - continuous non-normally distributed data - ordinal data

Answer 46

Spearman Rank Correlation (rs)

Question 47

(( regression )) Dependent variable is : - continuous (normally or non-normally distributed)

Answer 47

Linear regression - simple - multiple / multivariable

Question 48

(( regression )) Dependent variable is : - ordinal

Answer 48

Ordinal regression - simple - multiple / multivariable

Question 49

(( regression )) Dependent variable is : - nominal (dichotomous/binary) variable

Answer 49

Logistic regression - simple - multiple / multivariable

Question 50

When comparing data, consider (4)

Answer 50

1. No. of groups 2. Independent or paired/related groups 3. Type of data - nominal - ordinal - continuous (normal or non-normal) 4. Assumptions - esp nominal data (chi square or fisher's exact test)