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Statistics

Statistics. Who Spilled Math All Over My Biology?!. Practical Applications. Population studies: Collecting data in the field on a specific population is time consuming and difficult What is the mean length of le Doge tails in Beijing? Much le Doge! Too Many To Measure !

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Statistics

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  1. Statistics Who Spilled Math All Over My Biology?!

  2. Practical Applications • Population studies: • Collecting data in the field on a specific population is time consuming and difficult • What is the mean length of le Doge tails in Beijing? • Much le Doge! Too Many To Measure! • A sample group, rather than the whole population, can be examined and the data applied to the larger population • This is known as a data set • How can we know if the data set really represents the larger population? • Statistical analysis

  3. The Bell Curve • Data sets of significant size should show a normal distribution when plotted out • A Bell Curve • Next, use the data set to calculate: • Standard Deviation • Standard Error • t-Test • These values can allow one le Doge data set to be applied to other le Doge groups

  4. Standard Deviation • Measures how scattered a data set is around its mean • Must use a data set with normal distribution • S= standard deviation • Ʃ= “sum of” • X= value from date set • Ẍ= mean from data set • n= total number of data points • Now we need some le Doge data

  5. Standard Doge-viation • We get the following data set of le Doge tails (cm): • First we find the mean (Ẍ) of the data: • Sum of date points/ # of data points • 10.9 • Second, we apply the equation to all the data points

  6. Standard Doge-viation • Ẍ = 10.9 • Ʃ (x-Ẍ)2 = 49.0 • n= 21 • S = sq root (49.0/(21-1)) = sq root (2.45) • S= 1.57

  7. What Does This All Mean? • Mean le Doge tails (Ẍ = 10.9 cm) • 10.9 cm is the height of our le Doge bell curve • 95% of le Doge tail lengths fall between the upper and lower limit from the mean (10.9 cm) • Lower limit= Ẍ - (2 x S) • Upper limit= Ẍ + (2 x S) • S= 1.57 • 95% of all le Doge tail in the data set are within: 10.9 ± 3.14 cm

  8. Working the Numbers • Now that we mastered the date set of one le Doge group, we can apply our findings to rest of the group • This will save time and energy since we wont need to measure all the le Doge tails of the next group • The data from group 1 can apply to group 2 as long as they are similar in type

  9. Standard Error (SM) • The estimated standard deviation of a whole population based on the mean and standard deviation of one date set • Our data set covered le Doge tails of group A, but we want data on Group B as well • Because these are normally distributed data sets, we can sure that 95% of the means (Ẍ) of other groups will be ± (2xSM) • S= standard deviation • n= number of data points

  10. StanDoge Error (SM) • Standard deviation for le Doge tails in group A; S= 1.57 cm • n= 21 • SM= 1.57/4.58 = 0.34 cm • So we can be 95% certain that the mean le Doge tails in group B is Ẍ (B) = Ẍ (A) ± (2 x SM) • Ẍ (B) = 10.9 ± 0.68 cm • How would using a sample size of 100 in group A effect our prediction for group B? • Decrease SM range; 10.9 ± 0.26 cm • data is more accurate

  11. Comparing Multiple Data Sets • Using standard error saves time, however it only works with populations under the same circumstances • Le Doge groups A and B were le Doges found in Beijing. The data may not apply to le Doges in France. • The more variables that are not accounted for, the less certain the data becomes • Paris le Doge tails study was done: • n= 50 • Ẍ= 9.5 cm • S= 2.03 • Is there a significant difference between these two groups? How can we tell?

  12. t-Tests • Determines the significance in differences between means of multiple data sets • Ẍ1= mean of data set 1 • Ẍ2= mean of data set 2 • S1= standard deviation of set 1 • S2= standard deviation of set 2 • n1= # of data points in set 1 • n2= #of data points in set 2 • t= 3.14 • What does this mean?!

  13. t-Value Table Wow. Such confusion. Time for much practice. • To understand significant difference between data points you need 3 things: 1) t-Test value 2) Degree of freedom from data sets df= (n1-1) + (n2-1) = 69 3) t-Value Table • Use the df to find the t-value under 0.05 • If the t-Test value larger than the t-value on the chart, you “fail to reject” there is a significant difference between the data sets • If is it smaller, the two data sets are not significantly different Many homework. t-test = 3.14; df= 69 T-value= 2.000 3.14 > 2.000 So Pairs le Doge tail lengths and Beijing le Doge tail lengths are significantly different

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