1. STATISTICS!!!
The science of data

2. What is data?
Information, in the form of facts or figures obtained from experiments or surveys, used as a basis for making calculations or drawing conclusions Encarta dictionary

5. Statistics in Science
Data can be collected about a population (surveys)
Data can be collected about a process (experimentation)

6. 2 types of Data
A. Qualitative
B. Quantitative

7. A. Qualitative Data
Information that relates to characteristics or description (observable qualities)
Information is often grouped by descriptive category

8. Qualitative data are forms of information gathered in a nonnumeric form.
Common examples of such data are:
1.Interview transcript
2. Field notes (notes taken in the field being studied)
3. Video
4. Audio recordings
5. Images
6. Documents (reports, meeting minutes, s)

9. Some types of qualitative data:
Species of plant
Type of insect
Shades of color
Rank of flavor in taste testing
Remember: qualitative data can be “scored” and evaluated numerically

10. Qualitative data, manipulated numerically
Survey results, teens and need for environmental action

11. B. Quantitative data Chemical concentration Temperature Length
Quantitative – measured using a naturally occurring numerical scale
Examples
Chemical concentration
Temperature
Length
Mass…etc.

12. Quantitative
Measurements are often displayed graphically

13. Quantitation = Measurement
In data collection for Biology, data must be measured carefully, using laboratory equipment
(ex. Timers, meter sticks, pH meters,
balances , pipettes, etc)

14. The limits of the equipment used add some uncertainty to the data collected.
All equipment has a certain magnitude of uncertainty. For example, is a ruler that is mass-produced a good measure of 1 cm? 1mm? 0.1mm?
For quantitative testing, you must indicate the level of uncertainty of the tool that you are using for measurement.

15. How to determine uncertainty?
Usually the instrument manufacturer will indicate this – read what is provided by the manufacturer.
Be sure that the number of significant digits in
the data table/graph reflects the precision of the instrument used (for ex. If the manufacturer states that the accuracy of a balance is to 0.1g – and your average mass is 2.06g, be sure to round the average to 2.1g)
Your data must be consistent with your measurement tool regarding significant figures.

16. Finding the limits As a “rule-of-thumb”, if not specified, use
+/- 1/2 of the smallest measurement unit (ex. = metric ruler is lined to 1mm,so the limit of uncertainty of the ruler is +/- 0.5 mm.)
If the room temperature is read as 25 degrees C, with a thermometer that is scored at 1 degree intervals – what is the range of possible temperatures for the room?
(ans.s +/- 0.5 degrees Celsius - if you read 25oC, it may in fact be 24.5 or 25.5 degrees)

17. Looking at Data
How accurate is the data? (How close is the data to the “real” results?) This is also considered as BIAS.
How precise is the data? (All test systems have some uncertainty, due to limits of measurement) Estimation of the limits of the experimental uncertainty is essential.

20. Comparing Averages
Once the 2 averages (means) are calculated for each set of data, the mean values can be plotted together on a graph, to visualize the relationship between the 2.

23. Biological systems are subject to a genetic program and environmental variation.
When we collect a set of data for a given variable it shows variation.
When displaying data in graphical formats we can show the variation by using error bars.

24. Error bars can be used to show either the range of the data or the standard deviation.

25. Drawing error bars
The simplest way to draw an error bar is to use the mean as the central point, and to use the distance of the measurement that is furthest from the average as the endpoints of the error bar. The ends of the error bar are equidistant from the mean at the center.

26. Value farthest from average
Calculated distance
Average value

27. What do error bars suggest?
If the bars do overlap, there is not a significant difference between those values (the numbers in the data).

28. Another way of stating this:
When SE bars do overlap, you can be sure the difference between the two means is not statistically significant .

30. What can you conclude when standard error bars do not overlap?
When standard error (SE) bars do not overlap, you cannot be sure that the difference between two means is statistically significant.
T-test is commonly used to compare these groups.

31. Quick Review – 3 measures of “Central Tendency”
mode: value that appears most frequently
median: When all data are listed from least to greatest, the value at which half of the observations are greater, and half are lesser.
The most commonly used measure of central tendency is the mean, or arithmetic average (sum of data points divided by the number of points)    

32. How can leaf lengths be displayed graphically?

33. Simply measure the lengths of each and plot how many are of each length

34. If smoothed, the histogram data assumes this shape

35. This Shape?
Is a classic bell-shaped curve, AKA Gaussian Distribution Curve, AKA a Normal Distribution curve.
Essentially it means that in all studies with an adequate number of data points (>30) a significant number of results tend to be near the mean. Fewer results are found farther from the mean.

36. Standard Deviation
The standard deviation is a statistic that tells you how tightly all the various examples are clustered around the mean in a set of data

37. Standard deviation
The STANDARD DEVIATION is an indicator of the precision of a set of a given number of measurements
The standard deviation is like an average deviation of measurement values from the mean. In large studies, the standard deviation is used to draw error bars, instead of the maximum deviation.

38. A typical standard distribution curve

39. According to this curve:
One standard deviation away from the mean in either direction on the horizontal axis (the red area on the preceding graph) accounts for somewhere around 68 percent of the data in this group.
Two standard deviations away from the mean (the red and green areas) account for roughly 95 percent of the data.

40. Three Standard Deviations?
Three standard deviations (the red, green and blue areas) account for about 99 percent of the data
-3sd -2sd +/-1sd 2sd +3sd

41. Graphs from: http://www.childrensmercy.org/stats/definitions/stdev.htm
Standard Deviation
SD=1
SD=3
SD=2
Graphs from:

42. How is Standard Deviation calculated?
With this formula!

43. DO I NEED TO KNOW THIS FOR THE TEST?????
AGHHH! MRS. C.-
DO I NEED TO KNOW THIS FOR THE TEST?????

44. Not the formula! This can be calculated on a scientific calculator
OR…. In Microsoft Excel, type the following code into the cell where you want the Standard Deviation result, using the "unbiased," or "n-1" method: =STDEV(A1:A30) (substitute the cell name of the first value in your dataset for A1, and the cell name of the last value for A30.)

45. You DO need to know the concept!
Standard deviation is a statistic that tells how tightly all the various datapoints are clustered around the mean in a set of data.
When the data points are tightly bunched together and the bell-shaped curve is steep, the standard deviation is small.(precise results, smaller sd)
When the data points are spread apart and the bell curve is relatively flat, a large standard deviation value suggests less precise results.