Biostatistics
Binomial: https://stattrek.com/online-calculator/binomial.aspx
χ2 : http://courses.atlas.illinois.edu/spring2016/STAT/STAT200/pchisq.html
Normal: https://homepage.divms.uiowa.edu/~mbognar/applets/normal.html
t-distribution: https://homepage.divms.uiowa.edu/~mbognar/applets/t.html
F-distribution: https://homepage.divms.uiowa.edu/~mbognar/applets/f.html
Allerlei: https://www.socscistatistics.com/tests/
Sum of squares: https://calculator-online.net/sum-of-squares-calculator/
Standard error: https://ncalculators.com/statistics/standard-error-calculator.htm
Lecture 1
Stati sti cs and samples, displaying data & describing data
Statistics: the art of collecting, analyzing, interpreting and
presenting data
Why? -> to provide answers when there is uncertainty
Bias: systematic error
Random sampling: ensures unbiased estimates
1. Every unit in the population must have an equal
probability of being included in the sample
2. The selection of units must be independent
Independence: the selection of a unit has no effect
on the probability of any of the other
units of being selected
Describing data: measures of central tendency
- Mode: most frequent value
- Median: the ‘halfway’ value
- Mean: x̄
Measures of variation: the range between the smallest and largest value
, - Interquartile range: range between Q1 & Q3
- Variance
- Standard deviation
- Coefficient of variation
Lecture 2
Esti mati ng with uncertainty & probability
μ = population mean
x̄ = sample mean
the sample mean is an estimate with uncertainty of the population mean, they are therefore
not the same thing.
Sample distribution: used to measure the uncertainty of an estimate, also known as the
standard error ->
Confidence intervals: a range of umbers that is likely to contain the unknown value of the
target parameter
- The 95% confidence of the mean = we are 95% confident that this range contains μ
The 2SE rule-of-thumb:
, The probability of an event: the proportion of times this event would occur is we repeat the
trial over and over again under the same conditions
- Probability of event A happening = Pr(A)
Venn diagram: tool to think about probabilities with an area to represent all possible
outcomes, and the probability of an outcome equal to the proportion of the area occupied.
Mutually exclusive events
- Two events are mutually exclusive if they cannot occur at the same time
- The probabilities can be added
-
Discrete probability distribution describes the probabilities of all mutually exclusive
outcomes
Continuous probability distribution describes the probability of any range of values for the
variable
- Density: height of the curve in the normal distribution
General addition principle:
(In)dependence of events
- Two events are independent if the occurrence of one gives no information about
whether the second will occur
Binomial: https://stattrek.com/online-calculator/binomial.aspx
χ2 : http://courses.atlas.illinois.edu/spring2016/STAT/STAT200/pchisq.html
Normal: https://homepage.divms.uiowa.edu/~mbognar/applets/normal.html
t-distribution: https://homepage.divms.uiowa.edu/~mbognar/applets/t.html
F-distribution: https://homepage.divms.uiowa.edu/~mbognar/applets/f.html
Allerlei: https://www.socscistatistics.com/tests/
Sum of squares: https://calculator-online.net/sum-of-squares-calculator/
Standard error: https://ncalculators.com/statistics/standard-error-calculator.htm
Lecture 1
Stati sti cs and samples, displaying data & describing data
Statistics: the art of collecting, analyzing, interpreting and
presenting data
Why? -> to provide answers when there is uncertainty
Bias: systematic error
Random sampling: ensures unbiased estimates
1. Every unit in the population must have an equal
probability of being included in the sample
2. The selection of units must be independent
Independence: the selection of a unit has no effect
on the probability of any of the other
units of being selected
Describing data: measures of central tendency
- Mode: most frequent value
- Median: the ‘halfway’ value
- Mean: x̄
Measures of variation: the range between the smallest and largest value
, - Interquartile range: range between Q1 & Q3
- Variance
- Standard deviation
- Coefficient of variation
Lecture 2
Esti mati ng with uncertainty & probability
μ = population mean
x̄ = sample mean
the sample mean is an estimate with uncertainty of the population mean, they are therefore
not the same thing.
Sample distribution: used to measure the uncertainty of an estimate, also known as the
standard error ->
Confidence intervals: a range of umbers that is likely to contain the unknown value of the
target parameter
- The 95% confidence of the mean = we are 95% confident that this range contains μ
The 2SE rule-of-thumb:
, The probability of an event: the proportion of times this event would occur is we repeat the
trial over and over again under the same conditions
- Probability of event A happening = Pr(A)
Venn diagram: tool to think about probabilities with an area to represent all possible
outcomes, and the probability of an outcome equal to the proportion of the area occupied.
Mutually exclusive events
- Two events are mutually exclusive if they cannot occur at the same time
- The probabilities can be added
-
Discrete probability distribution describes the probabilities of all mutually exclusive
outcomes
Continuous probability distribution describes the probability of any range of values for the
variable
- Density: height of the curve in the normal distribution
General addition principle:
(In)dependence of events
- Two events are independent if the occurrence of one gives no information about
whether the second will occur
