statistics
Key statistics and their purposes
• Chi squared test: determines if a data set is
random or accounted for by an unwanted
variable
• Standard deviation: indicates how much variation
there is from the average, or expected data value
– Represented by sigma (σ)
• Standard error: shows quality of data, or
precision
– Indicated on a histogram (bar graph) by error bars
Don’t forget
• Hardy-Weinberg: to look at allele frequencies
in a gene pool and individual frequencies in
population, assuming the population is in
equilibrium
Chi Squared test
• Null hypothesis: there is no significant
difference between observed and expected
– Purpose of chi squared test is to accept/reject null
hypothesis
• Degrees of freedom: number of outcomes-1
• Critical value: number in a table which, if
exceeded, the data is considered unreliable
Chi squared test:
Critical value table
(we accept a 95% certainty)
Chi squared test
• Mission: Are dice rigged to favor a particular
number? Do we have grounds to reject the
null hypothesis that it is random?
• Practice problems
• Two practice problems
Standard deviation:
of normal distribution: shows how much
dispersion from the average there is
• In statistics, the 68–95–99.7 rule — or threesigma rule, or empirical rule — states that for
a normal distribution, nearly all values lie
within 3 standard deviations of the mean.
Standard deviation
• Try an analysis: Here are the scores on a
recent test, what is the deviation?
– 80, 74, 62, 91, 45, 88, 90
Standard error: Expresses the quality
of data
• SEx̄ = Standard Error of Mean
s = Standard Deviation of Mean
n = Number of Observations of Sample
Standard error
data set 1
data set 2
11
10
9
10.1
9.7
10.2
9.5
10.4
10.1
11.1
8.9
mean
st dev
st error