Terms Populations versus samples Populations of organisms vary

Terms • Populations versus samples – Populations of organisms vary in characteristics • Weight, growth rate, size – Statistics enable summarization of characteristics • Takes a sample from the population – ****MUST BE RANDOM**** » All individuals have equal chance of being chosen – Larger the better • Enable us to determine whether two populations are statistically different 1

• A parameter is a numeric quantity – usually unknown – describes a certain population characteristic – Ex. Mean and median – Represented by Greek letters • μ • A statistic is a quantity, calculated from a sample of data, used to estimate a parameter – Ex. Mean 2

Mean • Most commonly used parameter to describe the central tendency of a population • Parameter: μ (true mean) • Statistic: 3

Median • • Think middle of the road Another measure of central tendency Middle measurement in ranked listing If there is even number of individuals in the sample, median is mean of the two middle measurements 4

• When it might be better to use the median to describe the central tendency: – OUTLIERS! 11, 12, 13, 14, 15, 14, 16, 18, 13, 110 5

Variability • How data falls around the mean Sample 1 9 22 16 13 11 19 Mean = 15 Sample 2 15 16 17 15 13 14 Mean = 15 6

Histograms are a good way of displaying variability 7

• Range is one measure of data variability – Difference between the largest and the smallest measurement • Ex. Range (9, 22) for Sample 1 • Range gives us a good “eyeball” estimate for variability BUT: – Range almost always underestimates actual population range 8

Sum of Squares • More accurate method of estimating variation from the mean is the standard deviation • Sum of Squares SS = Σ(X – )2 9

Sum of Squares example Sample 1 9 22 16 13 11 19 Mean = 15 SS = Σ(X – )2 (9 -15)2 (22 -15)2 (16 -15)2 (13 -15)2 (11 -15)2 (19 -15)2 122 ***Why is it important that we square the values? 10

• Try it with sample 2 – What is the sum of squares value? 11

SS= 10 12

Variance (s 2) • Value from SS can be used to calculate the sample variance s 2 = SS/DF DF= Degrees of freedom (n-1) n is the number of samples Ex. Sample 1 has n=6, n-1=5 ***DF will be n-1 13

• What is variance for Sample 2? 14

2 s =2 15

Standard Deviation (s) • Report the standard deviation, rather than the sample variance ***Shows us the variability in samples*** s or SD = 2 16

• What is SD or s of sample 2? 17

s= 1. 41 18

Why is this important? • STDEV and relationship with mean – Histogram on board • Sample 2 had s= 1. 41 • Sample 1 had s= 4. 94 – SS=122 – s 2 = 122/5= 24. 4 – Square root of 24. 4= 4. 94 19