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STATISTICS FOR SCIENCE RESEARCH (The Basics) Why Stats? • Scientists analyze data collected in an experiment to look for patterns or relationships among variables. If we think we see a pattern or a relationship, we must complete one more step before we can be sure of the results. In order to determine that the patterns we observe are real, and not due to chance and our own preconceived notions, we must test the perceived pattern for significance. • Statistical analysis allows scientists to test whether or not patterns are real, and not due to chance or preconceived notions of the observer. We can never be 100% sure, but we can set some level of certainty to our observations. A level of certainty accepted by most scientists is 95%. We will be using tests that allow us to say we are 95% confident in our results Types of Data • Quantitative Data- measurements made using a scale with equal intervals (temp of water in Celsius degrees). Quantitative data consists of numbers representing counts or measurements. • Qualitative Data- data using non-standard scales (descriptions of leaf quality). Qualitative data are placed into categories that may be discrete categories represented by word or number labels. It can also be measurements made with a nonstandard scale with unequal intervals. Quantitative Data Qualitative Data Descriptive Statistics • Descriptive statistics are statistics that describe both the most typical values and the variations that exists within sets of data. • Include the mode, mean, median, range, variance, standard deviation, frequency distribution, and number. Descriptive Stats Mode- value that occurs most often (in a tie, use both) Median- middle value when ranked highest to lowest Mean (x)- mathematical average Range- difference between the smallest and largest average Variance- average squared distance from the mean (how spread out the values in a set of data are). Standard Deviation (SX)- a measure of how closely the individual points of data cluster around the mean. Frequency Distribution - # of cases falling into each category of the variable Number (n)- number of data points Descriptive Stats Inferential Statistics • Inferential statistics are done to determine if the data is statistically significant. They limit the possibility that the data differences occurred by random chance or due to some unknown, uncontrolled variable. If the data is shown to be statistically significant then the data differences can be explained by changes in the independent variable. Inferential Stats Statistical Tests • The t-test (or Analysis of Variance): An analysis of variance is used when you have two or more groups and you want to compare measurements of each group. The t-test analyzes the relationship between two groups. • The Chi-square test: This test is used when you have counts that can be placed into yes or no categories, or other simple categories such as quadrants. • The Pearson R Correlation: The Pearson R Correlation allows you to test how the values of one event or object relates to the values of another event or object Inferential Stats T-test • One-tailed- the probability distribution only involves one end, either the upper or lower end. • Two-tailed- the probability distribution involves both the upper and lower ends. • For most of you, the “two-tailed” test is applicable to your projects. Level of Significance • Level of Significance We will use 0.05 which means that the probability of error in the research is 5/100 (95%). Null Hypothesis • Basically states that there is no difference between the mean of your control group and the mean of your experimental group. Therefore any observed difference between the two sample means occurred by chance and is not significant. • If you can disprove your null hypothesis then there is a significant difference between your control and experimental groups. Helpful Resources • APPENDIX B - Statistics for Science Research: Hints, Tips, Examples (this can be found on my staff webpage, provided much of the info found in this PowerPoint, and contains instructions on how to calculate stats using Excel). • For calculating t-test values, the following website is also useful: http://www.graphpad.com/quickcalcs/ttest1.cfm