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 three-sigma 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

• SEx = Standard Error of Mean̄s = Standard Deviation of Meann = Number of Observations of Sample

Standard errordata 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