Torturing numbers - Descriptive Statistics for Growers (2013)
- 1. Torturing Numbers Dr. Jason S.T. Deveau Application Technology Specialist OMAFRA, Simcoe Station A Grower’s Guide to Descriptive Statistics
- 2. "If you torture the data long enough, it will confess" – Ronald Harry Coase, Economist
- 3. why do we need statistics? • Descriptive statistics are math tools we use to: Describe data Find trends in data against variation Determine if a sample represents a population Draw conclusions about data
- 4. describing data • In 1950, 25 university graduates were asked what they earned in their first year of work $45,000 $15,000 $10,000 $5,700 $5,000 $3,700 $3,000 $2,000 $2,000 $2,000 $10,000 $5,000 $2,000 $2,000 $5,000 $2,000 $3,700 $3,700 $3,700 $2,000 $2,000 $2,000 $2,000 $2,000 $2,000 • What do these data tell you?
- 5. describing data • Here is the same data ordered from greatest to least and weighted to show how many times each value occurs in the data set • Now what do the data tell you? • What is the average income? $45,000 $15,000 $10,000 $5,700 $5,000 $3,700 $3,000 $2,000
- 6. $45,000 $15,000 $10,000 $5,700 $5,000 $3,700 $3,000 $2,000 describing data • BEWARE! The reported ‘average’ might depend on what you are meant to see. Which would you use on your taxes? MEAN (arithmetic average) MEDIAN (midpoint in range) MODE (most frequent) • So, to really understand the data set you need more than just the ‘average’
- 7. spread and variability • You need to know the spread of the data • This histogram shows the ages of smart people that attend spray demos • Is it typical for 90 year olds to attend spray demos?
- 8. spread and variability • When the mean and median are the same, you have a special situation called a ‘normal’ curve • On this symmetrical curve, the variability can be described using standard deviations (SD)
- 9. spread and variability • SD is a way to determine how far a data point is from the mean • You can now say that 90 year olds fall more than 2 SD from the mean, or that they make up less than 2.5% of the data set
- 10. spread and variability • If we collapse the whole data set to one bar, we can show the mean with some measure of variability (std dev, std error, etc.) • Without some indication of variability, you cannot effectively compare two data sets
- 11. spread and variability • Often, data sets are skewed. Here is the effect of a new herbicide on quackgrass. • Means and standard deviations don’t help here…
- 12. spread and variability Min Q1 Median Q3 Max • Perhaps the best way to describe any data set is with five numbers: Minimum, Q1, Median, Q3, Maximum. This helps when comparing data sets, and when there are oddities called outliers 25% 25% 25% 25% * Outlier
- 14. a sample study • Researchers want to know which of three fertilizers produce the highest wheat yield in kg/plot
- 15. a sample study • They design a study with three treatments and five replications for each treatment 3 Treatments (Fertilizers 1, 2 and 3) 5Replicates
- 16. a sample study • Could a nearby forest or river be a confounding variable? • Variables like soil type and other local influences may have unexpected impacts…
- 17. a sample study • This is why a good study is randomized, to defeat potentially confounding variables
- 18. • Does the sample plot in our study represent all the wheat in all the world? POPULATION SAMPLE
- 19. uncertainty • With all the unknown variables, there will always be a degree of uncertainty that our sample represents the population • That’s why the more samples we have, the more confident we are that our study represents the population
- 20. confidence •Any confidence interval could be used, but 95% is often chosen •This means that 95% of the time, you expect your data represents reality •BEWARE reports with no confidence interval
- 21. two ways to present data Fertilizer 1 Fertilizer 2 Fertilizer 3 64.8 56.5 65.8 60.5 53.8 73.2 63.4 59.4 59.5 48.2 61.1 66.3 55.5 58.8 70.2 • Tables are the preferred way to show data, but graphs paint a quick, easy and seductive picture
- 22. drawing conclusions • A presenter may want you to see a relationship between two variables • Fertilizer 3 appears to increase the average yield of wheat – but what kind of average is this? How big was the sample? Where is the indication of variability? Where is the confidence interval?
- 23. drawing conclusions • A presenter may want you to see a relationship between two variables • Fertilizer 3 appears to increase the average yield of wheat – but what kind of average is this? How big was the sample? Where is the indication of variability? Where is the confidence interval? • Bad stats and bad experimental design may lead to bad conclusions 2 SD
- 24. drawing conclusions • Correlation does not imply causation The more firemen fighting a fire, the bigger the fire is observed to be. Therefore more firemen cause an increase in the size of a fire.
- 25. • Often, a presenter wants to lead you to a conclusion. Newspapers, TV and online articles should be scrutinized! • BEWARE: • “This is not a scientific poll…” • “These results may not be representative of the population” • “…based on a list of those that responded” • “Data showed a trend but was not statistically significant” (I’ve used this one!!!) it’s all in how you show it
- 26. it’s all in how you show it • Pies are for eating, and possibly throwing… • It’s very hard to see differences • BEWARE CHARTJUNK!
- 27. it’s all in how you show it • Amusing graphics are nothing but distractions • Again, it’s very hard to see differences • BEWARE CHARTJUNK!
- 28. it’s all in how you show it • Here is the same population growth data shown on two scales. Which would you use to demonstrate rapid growth? • BEWARE tricky scales!
- 29. it’s all in how you show it • BEWARE statements with no context. Here’s a made-up example, but it’s no worse than other ‘factoids’ I’ve encountered Did you know that even speaking to someone that once sprayed pesticides DOUBLES your chance of getting cancer?! • Your odds go from 0.000000001:1 to 0.000000002:1
- 30. conclusion • We started by stating that descriptive statistics are tools • Like any tool, stats can be misused (intentionally or unintentionally) • Maintain a healthy scepticism and question charts, tables and conclusions where insufficient information is provided
- 31. Three statisticians were hunting when they came across a big buck. The first statistician fired, but missed by a meter to the left. The second statistician fired, but missed by a meter to the right. The third statistician threw down his rifle and cheered “We got it!" …one last joke
- 32. - The Cartoon Guide to Statistics (1993) - Larry Gonick and Woolcott Smith references - How to Lie with Statistics (1954) - Darrel Huff
- 33. Tom Wolf @nozzle_guy Jason Deveau @spray_guy Learn moreabout spraying www.sprayers101.com