1. Sampling  When we want to study populations.  We don’t need to count the whole population.  We take a sample that will REPRESENT the whole population.

2. How do we know when our sample is representative?  We can use a RUNNING MEAN.  Work out the mean of your data as you collect it.  When the mean doesn’t change then your sample is representative.

3. Sampling works best when…  You take lots of samples  When the samples are RANDOM  When the sample sizes are large  Samples are unbiased

4. Reliable data…  Has been repeated many times  We can then see any anomalies  We can see any variation in our results

5. Accurate data…  When the method has been followed very closely  No errors in the process  All results should be similar (close to the mean)

6. Precise data  Has been carried out using equipment that has good precision i.e. many decimal places or measured to the smallest increment possible.

7. How to take random samples. LEARN THIS!  Dividing the area into a grid (e.g. place a grid underneath a Petri dish)  Coordinates are chosen at random by using a random number generator e.g. using a calculator or random number (such as a phone book!)to select co-ordinates  Sample this area using the relevant method.

8. Methods of sampling  For immobile organisms - QUADRATS Look at % cover Density of species Frequency of species.

9. Types of Quadrat Frame Quadrat Point Quadrat These allow RAPID collection of data We do not need to define individual plants when collecting data about % cover

10. Sampling mobile species  Mark – release – recapture.  To estimate a population size use this equation… Total of 1 st capture x Total of 2 nd Capture Total of 1 st capture x Total of 2 nd Capture Total Marked in 2 nd Capture Total Marked in 2 nd Capture

11. How to catch mobile organisms…  Use a beating tray!  Trapping

12. Take care with marking the organisms!  Always “Mark” the organisms in an area that is not visible. This will reduce the chance of attracting predators

13. Things to consider…  Always allow your 1 st capture to re-integrate into the environment before you carry out your 2 nd capture. This will give representative data.  This process does not consider migration  This process does not consider breeding seasons.

14. To look at the distribution of species in a habitat  We can use a TRANSECT

15. Transects…  Allow us to take a line through an area  This can give us a guide to follow when looking systematically at the distribution of organisms.  Particularly good for looking at zones like sea shores.

16. What do you do with your data? Test a Null Hypothesis Your Null Hypothesis will be that the Independent Variable will have NO EFFECT on the Dependent Variable We use statistical analysis to prove or disprove the Null Hypothesis.

17. Which statistical tests do we carry out?  Standard deviation – Year 12 work  Standard error and 95% confidence limits  Chi Square  Spearman Rank

18. Standard Error and 95% Confidence Limits  S.E. gives us the parameters that the total population can fall into, no matter what sample you take, 95% of the time.  Standard error gives us our 95% confidence limits.  This means that our results happen due to chance less than 5% of the time.

19. How to work out the standard error.  S.E. = Standard deviation n n

20. We plot standard error as bars on a graph. Sample 1Sample 2 X X Draw your axis Plot your means Plot TWO standard errors either side and draw a line. Confidence limits

21. What do these bars tell us? X X Look to see whether the bars overlap. These do not overlap so we can say that the 2 sets of data are significantly different at the 95% confidence limits This means that we can REJECT the Null Hypothesis

22. X X These 2 sets of data do overlap so we say that they are not significantly different at the 95% confidence limits This means that we can ACCEPT the Null Hypothesis

23. Crabs  Crabs were found on 2 different beaches; one sandy and one rocky.  On the sandy beach the crabs were - 5, 7, 8, 8, 7, 10, 14, 3, 6, 7, 11, 20, 21, 3, 17 cm  On the rocky beach the crabs were - 10, 12, 15, 18, 19, 22, 14, 23, 23, 29, 11, 12, 22, 18, 17 cm  What is your Null Hypothesis?  We can use standard error to test the Null Hypothesis.

24. Chi-Square  2 Chi-square (  2) is used to decide if differences between sets of data are significant.  It compares your Observed data with the Expected data and tells you the probability (P) of your Observed results being due to chance.

25. Null Hypothesis  Before we start an investigation we write a null hypothesis.  This tells us that we think there will NOT be any relationship in our results.  We accept or reject this hypothesis at the end of the analysis.

26. How to do Chi-square…

27. Look at this example  Suppose you flip a coin 100 times. You know that if the coin is fair or unbiased that there should be 50% of heads and tails.  How do you know though that the coin really is fair and not biased in some way?  We’re going to test this. What is your null hypothesis?

28. My results… Work out the Chi Square! OutcomeObserved Number, O Expected Number, E (O-E)² E Heads60 Tails40 Total100

30. Try this one… ObservedExpected red34 pink84 white42 Total 160 160 160 Work out Chi-Square! 40 80 40

31. Method… Actual numbers Expected numbers (O-E) 2 (O-E) 2 /E red flowers 34 40 360.9 pink flowers 8480 160.2 white flowers 4240 40.1 Total160 1.2

32. What does this all mean?  The Chi-Square value will help us to find the probability of our results being due to chance, or whether something is significantly influencing them.

33.  In Biology we say that if results occur due to chance more than 5% of the time then we cannot say that they are significant.  Our Chi-Square value can help us find out what % of our results are due to chance.  We have to use a probability table to find this out…

34. Before we look at the probablility table…  The number of variables you have, minus 1 = N-1 gives you your DEGREES OF FREEDOM (dF)

35.  Follow the numbers across until you find the one that is closest to, but not higher than, your Chi-Square result.  Read up  Look at the probability.  If it is 0.05 (5%) or less then it means that 5% (or less) of your results are due to chance – these would be significant results.  You would reject the Null hypothesis

36. Our CRITICAL VALUES

37. 1- I have 4 dF and a Chi-Square value of 16.45. What is my conclusion? 2- I have 3 dF and a Chi-Square value of 4.25. What is my conclusion? 3- I have 5 dF and a Chi-Square value of 3.27. What is my conclusion? 4- I have 6 dF and a Chi-Square value of 13.98. What is my conclusion?

38. Spearman Rank… r s  This statistical test tells us whether there is a significant association between two sets of data.  E.g you could carry out Spearman Rank to prove a significant association between temperature and Enzyme Activity.  You MUST have at least 7 measurements

39. Is there a significant association between wing length in seeds and the distance they fall from the parent tree? Seed NumberLength of wing/mmDistance from tree/ m 13421 22819 34017 43315 54230 63522 72317 82720 9 15

40. First, rank each column from lowest to highest Seed Number Length of wing/mm Distance from tree/ m Rank 1 – wing length Rank 2 – Distance from tree 1342167 2281945 3401783.5 4331551.5 5423099 6352278 7231723.5 8272036 9 1511.5 Notice that for 2 results that are the same we rank them between two levels e.g. 1.5 and 1.5 instead of 1 and 2.

41. Next, find the difference between the ranks. Seed Number Length of wing/mm Distance from tree/ m Rank 1 – wing length Rank 2 – Distance from tree Difference between ranks D 13421671 22819451 3401783.54.5 4331551.53.5 54230990 63522781 7231723.51.5 82720363 9 1511.50.5

42. Next, Square the difference Seed Number Length of wing /mm Distance from tree/ m Rank 1 – wing length Rank 2 – Distance from tree Difference between ranks D Difference Squared D 2 134216711 228194511 3401783.54.520.25 4331551.53.512.25 542309900 635227811 7231723.51.52.25 827203639 9 1511.50.50.25

43. How to work it out… r s = 1- 6 x ΣD 2 r s = 1- 6 x ΣD 2 n 3 -n n = the number of pairs of items in the sample. D 2 = the difference between ranks squared

44. So in our example… 1 – 6 x 47 729-9 Difference Squared D 2 1 1 20.25 12.25 0 1 2.25 9 0.25 1 – 282 720 = 0.61 So, what do we do with the 0.61? r s = 1- 6 x ΣD 2 r s = 1- 6 x ΣD 2 n 3 -n

45. Use the Critical Value Table Number of pairs of measurements Critical Value 51.00 60.89 70.79 80.74 90.68 100.65 120.59 140.54 160.51 180.48 If your Spearman Rank Value is less than the Critical Value then you ACCEPT the Null Hypothesis If your Spearman Rank Value is more than the Critical Value then you REJECT the Null Hypothesis