1. Introduction To Biological Research

2. Step-by-step analysis of biological data The statistical analysis of a biological experiment may be broken down into the following steps: The statistical analysis of a biological experiment may be broken down into the following steps: Specify the biological question to be answered. Specify the biological question to be answered. Put the question in the form of a biological null hypothesis and alternate hypothesis Put the question in the form of a biological null hypothesis and alternate hypothesis Put the question in the form of a statistical null hypothesis and alternate hypothesis. Put the question in the form of a statistical null hypothesis and alternate hypothesis.

3. Null vs. Alternative Hypothesis A researcher forms two hypotheses for each experiment: a null hypothesis and an alternative hypothesis. A researcher forms two hypotheses for each experiment: a null hypothesis and an alternative hypothesis. The null hypothesis predicts that the experiment will uphold the status quo or the current theory. The null hypothesis predicts that the experiment will uphold the status quo or the current theory. The alternative hypothesis predicts that the experiment will establish a new theory. The alternative hypothesis generally predicts the results expected by the experimenter. The alternative hypothesis predicts that the experiment will establish a new theory. The alternative hypothesis generally predicts the results expected by the experimenter. How to Figure Alternative Hypothesis | eHow.com http://www.ehow.com/how_8575517_figure-alternative-hypothesis.html#ixzz296YAjZhH How to Figure Alternative Hypothesis | eHow.com http://www.ehow.com/how_8575517_figure-alternative-hypothesis.html#ixzz296YAjZhH How to Figure Alternative Hypothesis | eHow.com http://www.ehow.com/how_8575517_figure-alternative-hypothesis.html#ixzz296YAjZhH How to Figure Alternative Hypothesis | eHow.com http://www.ehow.com/how_8575517_figure-alternative-hypothesis.html#ixzz296YAjZhH

4. The Null Hypothesis The null hypothesis can never be proven. The null hypothesis can never be proven. A set of data can only reject a null hypothesis or fail to reject it. Also Known As: H0, no-difference hypothesis A set of data can only reject a null hypothesis or fail to reject it. Also Known As: H0, no-difference hypothesis For example, if comparison of two groups (e.g.: treatment, no treatment) reveals no statistically significant difference between the two, it does not mean that there is no difference in reality. For example, if comparison of two groups (e.g.: treatment, no treatment) reveals no statistically significant difference between the two, it does not mean that there is no difference in reality. It only means that there is not enough evidence to reject the null hypothesis (in other words, the experiment fails to reject the null hypothesis) It only means that there is not enough evidence to reject the null hypothesis (in other words, the experiment fails to reject the null hypothesis)

5. The Null Hypothesis For example, if you measure the size of the feet of male and female chickens For example, if you measure the size of the feet of male and female chickens The null hypothesis would be that the average foot size in male chickens is the same as the average foot size in female chickens. The null hypothesis would be that the average foot size in male chickens is the same as the average foot size in female chickens. If you count the number of male and female chickens born to 10 hens, the null hypothesis would be that the ratio of males to females is equal to the theoretical expectation of a 1:1 ratio. If you count the number of male and female chickens born to 10 hens, the null hypothesis would be that the ratio of males to females is equal to the theoretical expectation of a 1:1 ratio.

6. Testing the Null Hypothesis Statistics is designed to measure the extent of apparent departure from the null hypothesis Statistics is designed to measure the extent of apparent departure from the null hypothesis The primary goal of a statistical test is to determine whether an observed data set is so different from what you would expect under the null hypothesis that you should reject the null hypothesis. The primary goal of a statistical test is to determine whether an observed data set is so different from what you would expect under the null hypothesis that you should reject the null hypothesis.

7. Testing the Null Hypothesis Increase the Number of Egg Laying Chickens Increase the Number of Egg Laying Chickens Best to have more hens than roosters born Best to have more hens than roosters born Experiment 1: Get a 24:25 ratio of hens to roosters Experiment 1: Get a 24:25 ratio of hens to roosters Accept the null hypothesis Accept the null hypothesis Experiment 2: Get a 45:5 ratio of hens to roosters Experiment 2: Get a 45:5 ratio of hens to roosters Reject the null hypothesis Reject the null hypothesis Experiment 3: Get a 31:17 ratio of hens to roosters Experiment 3: Get a 31:17 ratio of hens to roosters Now what? Now what?

8. Alternative Hypothesis The alternative hypothesis is The alternative hypothesis is Things are different from each other, or different from a theoretical expectation. Things are different from each other, or different from a theoretical expectation. For example, one alternative hypothesis would be that male chickens have a different average foot size than female chickens; another would be that the sex ratio is different from 1:1. For example, one alternative hypothesis would be that male chickens have a different average foot size than female chickens; another would be that the sex ratio is different from 1:1.

9. Step-by-step analysis of biological data Determine which variables are relevant to the question. Determine which variables are relevant to the question. Determine what kind of variable each one is. Determine what kind of variable each one is. Based on the number of variables, the kind of variables, and other information about experiment, choose the best statistical test to use. Based on the number of variables, the kind of variables, and other information about experiment, choose the best statistical test to use. Apply the appropriate statistical test, and interpret the result. Apply the appropriate statistical test, and interpret the result. Communicate your results effectively, usually with a graph or table. Communicate your results effectively, usually with a graph or table.

10. Types of Variables Measurement Variables Measurement Variables Something that can be measured Something that can be measured Attribute Variables Attribute Variables “nominal variable” or “categorical variable” “nominal variable” or “categorical variable” Ranked Variables Ranked Variables “ordinal variable” “ordinal variable”

11. Measurement Variables Can measure something Can measure something t-test t-test ANOVA ANOVA

12. Attribute Variables Typically a name and not a number Typically a name and not a number Male v. Female Male v. Female Found Subject by trailing v. Did not find Subject by trailing Found Subject by trailing v. Did not find Subject by trailing Use G-test of independence Use G-test of independence

13. Ranked Variables Variables that can be put in order from smallest to largest Variables that can be put in order from smallest to largest Non-parametric tests are used Non-parametric tests are used Kruskal-Wallis test Kruskal-Wallis test

14. Ambiguous Variables Two categories Trailed vs. Didn’t Trail Two categories Trailed vs. Didn’t Trail Several measurements under each category Several measurements under each category Consider Dogs trailing as a Attribute Variable Consider Dogs trailing as a Attribute Variable Use a t-test Use a t-test

15. Ambiguous Variables

16. Ratios If both numerator and denominator in a ratio have biological variability it is best to use a statistical test that keeps both numbers separate If both numerator and denominator in a ratio have biological variability it is best to use a statistical test that keeps both numbers separate Analysis of Covariance Analysis of Covariance If you wanted to know whether there was a relationship between obesity and high-density lipoprotein (HDL) levels in blood, you could do Multiple Regression with height and weight as the two X variables and HDL level as the Y variable If you wanted to know whether there was a relationship between obesity and high-density lipoprotein (HDL) levels in blood, you could do Multiple Regression with height and weight as the two X variables and HDL level as the Y variable

17. The Null Hypothesis The null hypothesis is a statement that you want to test. The null hypothesis is a statement that you want to test. In general, the null hypothesis states things are the same as each other, or the same as a theoretical expectation. In general, the null hypothesis states things are the same as each other, or the same as a theoretical expectation.

18. Probability The basic idea of a statistical test is to identify a null hypothesis, collect some data, then estimate the probability of getting the observed data if the null hypothesis were true. The basic idea of a statistical test is to identify a null hypothesis, collect some data, then estimate the probability of getting the observed data if the null hypothesis were true.

19. Probability The likelihood of a particular outcome in an experiment The likelihood of a particular outcome in an experiment The convention in most biological research is to use a significance level of 0.05 The convention in most biological research is to use a significance level of 0.05 For this class, we will always use P<0.05 as our significance level, unless I tell you otherwise. For this class, we will always use P<0.05 as our significance level, unless I tell you otherwise.

20. Probability The probability of sampling a particular kind of individual is equal to the proportion of that kind of individual in the population. For example, in fall 2012 there were 21,121 students at Victor Valley College, and 16,428 of them were over the age of 25. If a single student were sampled at random, the probability that they would be over the age of 25 would be 16,428 / 21,121, or 0.778. In other words, 77.8% of students are over 25, so if I pick one student at random, the probability that they are over 25 is 77.8%. The probability of sampling a particular kind of individual is equal to the proportion of that kind of individual in the population. For example, in fall 2012 there were 21,121 students at Victor Valley College, and 16,428 of them were over the age of 25. If a single student were sampled at random, the probability that they would be over the age of 25 would be 16,428 / 21,121, or 0.778. In other words, 77.8% of students are over 25, so if I pick one student at random, the probability that they are over 25 is 77.8%.

21. Type I verses Type II Error The significance level you use depends on the costs of different kinds of errors. The significance level you use depends on the costs of different kinds of errors. With a significance level of 0.05, you have a 5 percent chance of rejecting the null hypothesis, even if it is true. With a significance level of 0.05, you have a 5 percent chance of rejecting the null hypothesis, even if it is true. If you try 100 treatments on your chickens, and none of them really work, 5 percent of your experiments will give you data that are significantly different from a 1:1 sex ratio, just by chance. If you try 100 treatments on your chickens, and none of them really work, 5 percent of your experiments will give you data that are significantly different from a 1:1 sex ratio, just by chance. This is called a "Type I error," or "false positive." This is called a "Type I error," or "false positive." If there really is a deviation from the null hypothesis, and you fail to reject it, that is called a "Type II error," or "false negative.” If there really is a deviation from the null hypothesis, and you fail to reject it, that is called a "Type II error," or "false negative.”

22. Two Tailed Test For example, we may wish to compare the mean of a sample to a given value x using a t-test. For example, we may wish to compare the mean of a sample to a given value x using a t-test. Our null hypothesis is that the mean is equal to x. Our null hypothesis is that the mean is equal to x. A two-tailed test will test both if the mean is significantly greater than x and if the mean significantly less than x. A two-tailed test will test both if the mean is significantly greater than x and if the mean significantly less than x. The mean is considered significantly different from x if the test statistic is in the top 2.5% or bottom 2.5% of its probability distribution, resulting in a p-value less than 0.05. The mean is considered significantly different from x if the test statistic is in the top 2.5% or bottom 2.5% of its probability distribution, resulting in a p-value less than 0.05.

23. One Tailed Test Our null hypothesis is that the mean is equal to x. Our null hypothesis is that the mean is equal to x. A one-tailed test will test either if the mean is significantly greater than x or if the mean is significantly less than x, but not both A one-tailed test will test either if the mean is significantly greater than x or if the mean is significantly less than x, but not both

24. One Tailed Imagine you have developed a new drug that you believe is an improvement over an existing drug. You wish to maximize your ability to detect the improvement, so you opt for a one-tailed test. In doing so, you fail to test for the possibility that the new drug is less effective than the existing drug. Imagine you have developed a new drug that you believe is an improvement over an existing drug. You wish to maximize your ability to detect the improvement, so you opt for a one-tailed test. In doing so, you fail to test for the possibility that the new drug is less effective than the existing drug. For example, imagine again that you have developed a new drug. It is cheaper than the existing drug and, you believe, no less effective. In testing this drug, you are only interested in testing if it less effective than the existing drug. You do not care if it is significantly more effective. You only wish to show that it is not less effective. For example, imagine again that you have developed a new drug. It is cheaper than the existing drug and, you believe, no less effective. In testing this drug, you are only interested in testing if it less effective than the existing drug. You do not care if it is significantly more effective. You only wish to show that it is not less effective.

25. Two Tailed For this class, we will always use two-tailed probabilities, unless I make it very clear that only one direction of deviation from the null hypothesis would be interesting. For this class, we will always use two-tailed probabilities, unless I make it very clear that only one direction of deviation from the null hypothesis would be interesting.

26. Reporting In the olden days, when people looked up P-values in printed tables, they would report the results of a statistical test as "P 0.10", etc. In the olden days, when people looked up P-values in printed tables, they would report the results of a statistical test as "P 0.10", etc. Nowadays, almost all computer statistics programs give the exact P value resulting from a statistical test, such as P=0.0297 Nowadays, almost all computer statistics programs give the exact P value resulting from a statistical test, such as P=0.0297 That's what you should report in your publications. That's what you should report in your publications.

27. Chi Square Test of Independence The chi-square test may be used both as a test of goodness-of-fit (comparing frequencies of one attribute variable to the theoretical expectations) and as a test of independence (comparing frequencies of one attribute variable for different values of a second attribute variable). The chi-square test may be used both as a test of goodness-of-fit (comparing frequencies of one attribute variable to the theoretical expectations) and as a test of independence (comparing frequencies of one attribute variable for different values of a second attribute variable).

28. Chi Square Test of Independence The chi-squared test of independence is used when you have two attribute variables, each with two or more possible values. The chi-squared test of independence is used when you have two attribute variables, each with two or more possible values. X 2 X 2