2 The Scientific Method Has several stages: Observation of a puzzling phenomenonMaking a guess as to the explanationDevising a way to test whether or not the explanation is accuratePerforming the test(s) and using the results to determine whether the explanation is accurate or not
3 The Dog That Understands French Mr Smith has taught his dog Rover to understand French. Mr Smith noticed that every evening, after dinner, when he went to the door with his coat on and said "Walk", Rover immediately understood and came running. Mr Smith was going to France for the summer, and, as an experiment in international understanding, decided to teach Rover French. He started to say "Allons" instead of "Walk". To his delight, Rover very quickly understood and came running.
4 Analysis What is the observation? The dog apparently responds to the call of ‘allons’What is Mr Smith’s hypothesis?The dog understands the word as meaning ‘walk’Is this the only explanation?No. The dog may respond to a total situation (after dinner, going to the door, coat on, call) of which what is actually called is only a small part. A change in the call may not matter much to the dog.Can we devise a test to discriminate between possible explanations?
5 Possible Tests1) Call "Allons" to the dog in a different situation: for example, in the morning when he does not usually go for a walk. 2) Go to the door, in the normal way (coat on, after dinner) without calling anything. 3) Do likewise and call something silly like "Rhubarb".
6 ConclusionsNotice that these tests do not tell us anything of a dog's ability to learn French words. They are only concerned with the specific case of responding to one French word. We will see later that extrapolating from the specific to the general is very important in scientific methodology.
7 Experimental DesignExperiments should discriminate between different hypothesesUsually experiments need to be repeated several times for the results to be analyzed statisticallyScientists must be careful in generalizing results to others or a populationExperiments must also be well controlledScientists must take into account the accuracy and precision of their measurement instruments
8 Let’s Practice Experiment: Do plants give off water vapour? Forty bean plants, growing in pots, were covered one afternoon by individual glass containers and left in the laboratory overnight. Next morning, the inside of the lid of each container was found to be covered in droplets of a fluid that proved to be water.Conclusion: Plants generally give off water vapour.
9 Critique Lack of Controls The water could have come from the plants, the soil, the pots, or the air in the jar. Control experiments should have been set up to test for these possibilities.2. The conclusion contains some points that are not valid(a) The experiment was done overnight and so can tell us nothing about the behaviour of the plants at other times of day; the word 'generally' is not justified.(b) It was carried out with an adequate number of bean plants but can tell us nothing about other kinds of plants; the word 'plants' should be qualified.(c) There is no evidence in the experiment that water is given off as a vapour.
10 Designing Experiments to Use Statistics Good experimental design is the key to good science.In many cases, good experimental design involves having a clear idea about how we will analyze the results when we get them. That's why statisticians often tell us to think about the statistical tests we will use before we start an experiment.
11 Three important steps in Experimental Design Define the objectives. Record (i.e. write down) precisely what you want to test in an experiment.Devise a strategy. Record precisely how you can achieve the objective. This includes thinking about the size and structure of the experiment - how many treatments? how many replicates? how will the results be analyzed?Set down all the operational details. How will the experiment be performed in practice? In what order will things be done? Should the treatments be randomized or follow a set structure? Can the experiment be done in a day?
12 Common Statistical Terms Suppose that we are measuring the size of cells. The thing that we are measuring or recording (e.g. cell size) is called a variable. Each measurement that we record (e.g. the size of each cell) is a value or an observation. We obtain a number of values (e.g. 100 for cells), and this is our sampleThe sample (e.g. 100 cells) is part of a population. In this case the population (in biological terms) is all the cells in the culture. Theoretically, we could measure every cell to get a precise measure of that population. But often we want to be able to say more than this - something of general significance, based on our sample. For example, that if anyone were to measure the cells of that organism, then they would find a certain average value and a certain range of variation
13 Common Statistical Measures The average, or meanSome measure of the dispersion (range of variation) of data around the sample mean. For this we use the variance and thence the standard deviationHaving obtained those values, we use them to estimate the population mean and the population variance.
14 A SampleIn the following sections we will start from a small sample, describe it in statistical terms, and then use it to derive estimates of a population.
15 Here are some values of a variable: 120, 135, 160, 150. We will assume that they are measurements of the diameter of 4 cells, but they could be the mass of 4 cultures, the lethal dose of a drug in 4 experiments with different batches of experimental animals, the heights of 4 plants, or anything else. Each value is a replicate - a repeat of a measurement of the variable. In statistical terms, these data represent our sample. We want to summarize these data in the most meaningful way. So, we need to state:the meanthe number of measurements (n) that it was based onand a measure of the variability of the data about the mean (which we express as the standard deviation)
16 Why divide by n-1?Dividing by n gives an underestimate of the true underlying population variance. The sample of 4 is small, and hence misleading.In general, this biased value should not be used.We divide by one less than the number of values to make the standard deviation bigger; in doing so, we have taken into account the fact that there could be other values of the population that are not within our sample range, and hence our estimate of the mean is more accurate.n-1 are the degrees of freedom
17 Standard Deviation vs. Standard Error We calculate the sample mean so that we can use it as an estimate of the mean for the whole population.The sample mean will vary from sample to sample; the way this variation occurs is described by the "sampling distribution" of the mean.We can estimate how much sample means will vary from the standard deviation of this sampling distribution, which we call the standard error (SE) of the estimate of the mean. Another way of considering the standard error is as a measure of the precision of the sample mean.
18 Standard ErrorThe standard error (se) balances the dispersion associated with the underlying population and the error associated with the sampling process.We can think of the standard error as measuring how precisely we have estimated the population mean, or another parameter, via the sample mean, or another statistic.As the sample size gets bigger and bigger, the standard error will shrink, reflecting the fact that our estimate for the mean, or another statistic, will become more and more precise.
19 So which do we use?If we want to say how widely scattered some measurements are, we use the standard deviation. If we want to indicate the uncertainty around the estimate of the mean measurement, we quote the standard error of the mean.
20 Confidence IntervalsThe standard error is most useful as a means of calculating a confidence interval. For a large sample, a 95% confidence interval is obtained as the values 1.96xSE either side of the mean.
21 Let’s practice Copy down the following two data sets: b)52, 80, 22, 30, 36Using the graphing calculator, calculate the sample mean and standard deviation for each sample.What do you notice?
22 Another Example Assume that * the first data set ("A") (46,42,44,45,43) represents measurements of five animals that have been given a particular treatment and* the second data set ("B") (52,80,22,30,36) measurements of five other animals given a different treatment.* A third set ("C") of five animals was used as controls; they were given no treatment at all and their measurements were 20,23,24,19,24. The mean of the control group is 22 and the standard error is 2.1.Did treatment A have a significant effect? Did treatment B?
23 Null HypothesisIn principle, a scientist designs an experiment to disprove, or not, that an observed effect is due to chance alone. This is called rejecting the null hypothesis.The value p is the probability that there is no difference between the experimental and the controls; that is, that the null hypothesis is correct. So if the probability that the experimental mean differs from the control mean is greater than 0.05, then the difference is usually not considered significant. If p = <0.05, the difference is considered significant, and the null hypothesis is rejected.