Skills for Biosciences
Statistics I
All measurements are subject to variability
- Instrumentation (calibration, consistency)
- Experimenter (errors in reporting)
Biological variations
- Physiological differences
- Genetic, environmental differences between subjects
Main sources of error in a biological experiment
- Measurement error
- Random (chance) differences between subjects
- Random changes between repeated measurements on the same subject
- Systematic difference between subjects
- Systematic differences over time
Statistics is about two things:
- Description (Descriptive Statistics)
o Summarising a large amount of information in simple form
- Inference (Inferential Statistics
o Reducing uncertainty
o Explaining exactly what a collection of data does and does not show
o Planning future experiments
How to summarise experimental data
- Descriptive Statistics
o Mean
o Variance
o Standard deviation
o Standard error
Mean: sum total of all values/number of observations
- Most commonly used average usually the most accurate and easiest to work with
- Sometimes called arithmetic mean
- Thought of as the most
‘common’ value or
observation
, Spread of data: variance and standard deviation
Deviation: difference between each value and the average
Variance (s2): average of square of the deviations
Standard deviation (SD):
- Square root of the variance
- ‘typical deviation’
Statistical concepts
Population: is the set of all the subjects that we require about in a given experiment
- Often too large to study directly
- E.g. all individuals between 18-24 years
Sample: is a subset or a sub-collection of the population
We cannot study all members of a population so we take a sample to study
Sampling
Can’t measure the whole population so we measure a few (sample) and generalize the population
values
Essential that we select samples at random
Avoid bias in selecting sample, sample should be representative of population
How to summarise experimental data graphically?
Graphical methods
- Graphical method of displaying data in a useful way
o Bar charts, dot plots etc
- Frequency histogram is most common way of displaying and summarising data
- Useful when we have a medium-large sample sizes
What is a histogram?
- A chart that shows the distribution of data
Statistics I
All measurements are subject to variability
- Instrumentation (calibration, consistency)
- Experimenter (errors in reporting)
Biological variations
- Physiological differences
- Genetic, environmental differences between subjects
Main sources of error in a biological experiment
- Measurement error
- Random (chance) differences between subjects
- Random changes between repeated measurements on the same subject
- Systematic difference between subjects
- Systematic differences over time
Statistics is about two things:
- Description (Descriptive Statistics)
o Summarising a large amount of information in simple form
- Inference (Inferential Statistics
o Reducing uncertainty
o Explaining exactly what a collection of data does and does not show
o Planning future experiments
How to summarise experimental data
- Descriptive Statistics
o Mean
o Variance
o Standard deviation
o Standard error
Mean: sum total of all values/number of observations
- Most commonly used average usually the most accurate and easiest to work with
- Sometimes called arithmetic mean
- Thought of as the most
‘common’ value or
observation
, Spread of data: variance and standard deviation
Deviation: difference between each value and the average
Variance (s2): average of square of the deviations
Standard deviation (SD):
- Square root of the variance
- ‘typical deviation’
Statistical concepts
Population: is the set of all the subjects that we require about in a given experiment
- Often too large to study directly
- E.g. all individuals between 18-24 years
Sample: is a subset or a sub-collection of the population
We cannot study all members of a population so we take a sample to study
Sampling
Can’t measure the whole population so we measure a few (sample) and generalize the population
values
Essential that we select samples at random
Avoid bias in selecting sample, sample should be representative of population
How to summarise experimental data graphically?
Graphical methods
- Graphical method of displaying data in a useful way
o Bar charts, dot plots etc
- Frequency histogram is most common way of displaying and summarising data
- Useful when we have a medium-large sample sizes
What is a histogram?
- A chart that shows the distribution of data
