Biostatics summary and step-by-step plan to solve biostatistical problems

Lecture 1
What is the difference between population and sample?
Population
• Parameters: Variables (numbers), which characterize the properties of the population in Greek letters
o μ (mu) = mean of a property of the population;
o σ (sigma) = standard deviation of a property of the population
Sample
• Why is sample important?
o subset of the population used to draw conclusions about the entire population.
• Parameters are called statistics
o Sample: X (mean) and s (standard deviation)
• One sample is a limited number of elements from one population.
Data types
• Categorical data:
o what is categorical data?
 Data which is qualitative (no numbers) by nature
o Kinds
 Nominal (‫ )اسمى‬scale
 classification only , no ranking
o E.g. Blood groups (A, B, AB, O)
 Ordinal (‫ )ترتيبي‬scale
 classification and rank orderapple
• Numerical data:
o What is numerical data?
 (Continuous, quantitative); measurement with numbers
o Kinds
 Interval scale
 measurement with fixed unit; null point is arbitrarily chosen
o E.g. temperature in Celsius or Fahrenheit or Kelvin
 Ratio scale
 fixed unit; fixed null point
o 200 km/h is twice as fast as 100 km/h
 Censored data


Other things
What is the difference between probability distribution and frequency distribution?
• Red line represent the population  no uncertainty here
• Blue bars represent the sample  there is a degree of uncertainty

,Additional information
 The mode is the most frequent value
 The median is the middle value.
 The mean is the sum of all figures divided by the number of figures.



Which-test-for-what-question troubleshoot
1. Read and analyze the question FIRST!
2. See which type of data is given → is it frequency/ scale data?
3. Are the values NORMAL or NON-PARAMETRIC (will be stated if non-parametric) → if not
stated, assume normal (sample size is large enough → CLT)
4. If normal, proceed with t- test → check if data are paired (related) or independent
5. If independent → check if t-test condition is MET → F test needs to be valid then can
proceed

**in case of F test fail, data is considered to be non-parametric**
NB: please always start the question with Null/Alternative Hypothesis (mark will be awarded)

,
,Lecture 2
Tips to approach probability question:
1. Analyze the given variables 🡪 let A be the first event… / B be the second event…
2. Write down the info known in numerical value 🡪 convert from %
3. Understand problem given in probability notation 🡪 conditional probability phrase indication: “of this sample [outcome
A], [probability] has also [outcome B]….
4. Use appropriate equation given
Independent probabilities




Dependent probabilities




Parametric and non-parametric distribution
 What is the difference between parametric and non-parametric distribution?
o Parametric statistical analysis: Assumption (‫ )افتراض‬that observations in a sample originate from
population
o Non-parametric: No assumption about the underlying distribution is necessary

,Probability distribution with discrete (fixed) outcomes
Uniform probability
 equal and unbiased probability for a particular event
Binomial probability
 Categorical data with 2 properties/characteristics A and B; dichotomy
Basic
Parameters
 Proportion 𝝅 (pi): Each object has the probability 𝜋 to have property A and the probability (1 − 𝜋) to have
property B
 Sample size: 𝑛 objects which belong to groups A or B
 The probability to have precisely 𝑥 objects with property A is




Steps to answer the question
1. Based on the question you determine how to solve it?
a. Normally they ask about what the event’s probability in which X is larger smaller than a specific number
i. E.g. what is the probability that pations does not have money to pay there treatment
b. Therefore: you have to calculate the probability one by one
c. Sum the probabilities up
d. 1-the sum of probabilities



Poisson distribution
Random (rare) events occurring incidentally in fixed time or space
Basic
Parameters

 Average number of events per time or space =
 𝑥 events occur per time- or space-unit

,Lecture 3
Steps to approach a typical normal distribution question
1. Analyze the question first → find out what is μ∧σ given in the qn
2. Express the data in the form of X N ( μ , σ 2 )
3. Perform standardization (see formula below)
4. Check Z value in 2a (one-sided) or 2b (two-sided) → based on what is asked
5. Do interpolation (if needed) → give corresponding p value


Normal distribution
Standardization
 Role
( X −μ)
o Z=
σ
 X = given value



If given data set is not normally distributed → possible to approximate to normal distribution
when n (sample size) > 30

,Difference between 2 sample means

,Lecture 4
Confidence interval
Confidence interval




Hypothesis testing

H0 → usually it is a commonly accepted / taken to be true statement in the context of the question


H1 → alternative hypothesis → contentious claim that we want to prove the accuracy




If n increases, Z increases


One-sided or two-sided test? → based on the question context
- Look out for phrases like: (more / less/ greater than… minimum / maximum) → one-sided

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-

**when perform hypothesis testing, answer can be on either p value or CI → either one
is fine unless stated by question to give BOTH values**

1. P value
- P < 𝛼 (tested significance level) → reject H0
- P > 𝛼 (tested significance level) → do NOT reject H0
2. CI
- Tested value is not in the CI range → reject H0
- Tested value within CI range → do NOT reject H0


Step-by-step approach to hypothesis testing question:

, 1. Analyze the question → pick out mean + standard deviation
2. Look out for command word in the question → hint to do one or two-sided test
3. WRITE DOWN THE HYPOTHESIS (H0 / HA) → MARKS WILL BE AWARDED
4. Solve for p value or CI
5. Compare and conclude


Different types of errors




Power of test

Power of decision → 1 - β
- Increase power by increasing n → decrease type II error


One-sided test




Two-sided test