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Chapter 4

BIOL 180 Chapter 4: Reading 4-1

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BIOL 180
H E R R O N, J O N

BIOL 180 - Reading 4-1: Bioskill 3: Standard Error Bars: Standard error for a the mean is a quantity that indicates the uncertainty in a calculated mean (I-Beams on graphs) Quantifies how confident you are that the mean you’ve calculated is the mean you’d observe if you did the experiment under the same conditions an extremely large number of times Measure of precision Sometimes, error bars represent confidence interval of the mean mean Confidence interval gives an estimated ranged of values that is like to include the population parameter being studied, such as the survival rate of animals after exposure to a pathogen Calculated from a given set of sample data A confidence level of 95 percent means that 95 percent of the confidence intervals would include the population parameter Related to standard deviation, which doesn’t change as a sample size increases Standard error of the mean (SEM) depends on both standard deviation (SD) and sample size Calculated by device standard deviation by square of the sample size SEM decreases as the sample size increases, because the extend of chance variation is reduced To come to an objective (instead of subjective) conclusion about what data may show, you must use a statistical test to determine whether the data in two different trials is significant If he difference is found to be statistically significant, then it is not likely to have occurred by chance - it’s likely to be attributable to an actual facto Using Statistical Tests: Three common statistical tests are: Chi-square test T-test Analysis of variance Chi-square tests: Used to compare observed data with data you would expect to obtain according to a specific hypothesis For example, if according to Mendel’s law you expected equal number of male and female offspring from a cross but you observed 9 males and 23 males, you might want to know whether the difference between the observed and expected number was due to chance or to other factors Chi-square test always tests the null hypothesis, which states that there is no significant difference between the observed and expected results. T-tests: Used to determine if there is a significant difference between the mean values of two groups Can help support hypothesis or null hypothesis Analysis of variance (ANOVA): Compares the means of two or more sets of data by calculating how widely individual values in each data set vary If they vary greatly from the mean, the variance is large, and vice-versa When applied to only two data sets, ANOVA will give the same results as a t-test ANOVA is a powerful statistical test because it allows you to test for each factor while controlling for others and to detect whether one variable affects another As an example, if you were comparing the activity of a particular enzyme in mainland and island tortoises, you might want to determine whether sex affects enzyme activity, so you could also separate the data sets by sex Regression and correlation analyses: Are done when a researcher wants to know whether there is a relationship or correlation between to variables If positive, there is a positive slope, if negative, there is a negative slope For example, when patients are given increasing amounts of a drug, does their blood pressure increase or decrease proportionally? Correlation is a way to express the relationship between two variables, whereas linear regression is about the best fit line in a graph Interpreting P Values and Statistical Significance: There is a three-step process to determine if difference are significant: 1. Specify the null hypothesis: 1. Reactant concentration has no effect on reaction rate 2. Calculate a test statistic 1. Compares the actual differences in reaction rates at the three reactant concentrations to to the difference predicted by the null hypothesis. The null hypothesis predicts that there should be no difference 3. Determine the probability of getting by chance a test statistic at least as large as the one calculated. This probability, called the P value, comes from a reference distribution - a mathematical function that specifies the probability of getting various values of the test statistic if the null hypothesis is correct. The P value is the estimated probability of rejecting the null hypothesis when the hypothesis is correct. 1. A P value of 0.01 means that there is a 1 percent chance that the null hypothesis has been reject when it is actually correct. On percent is considered a very small chance of making such an error, thus, very small P values indicate that researchers have high confidence in the significance of differences in their data Most researchers consider a difference among treatment groups to be statistically significant if there is less a 5 percent probability of observing by chance, or P < 0.05 When presenting P values in the scientific literature, researchers often use an asterisk ratio system as we’ll as quoting P values Examples: Statistical P Value
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