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STATISTICAL ANALYSIS Frequency Distribution # Indivi duals Median Mean MedianMean Median Figure 2.Frequency distributions of three different samples. ABC negativenormalpositive

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Descriptive Statistics: used to describe, simplify, and summarize a collection of data in a clear understandable way. Ex. Mean, standard deviation, frequency Inferential Statistics: allows you to make inferences about a population from a sample. Its used to test the Ho. Ex. t-test, ANOVA, ANCOVA Raw Data: the data you collect directly from the organisms or environment you are studying. Population (N): the total # of individuals in the population of interest. Sample (n): the number of observations or individuals measured

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Mean: _ X = = 1.7 m Median: Middle number in a data set. Order from smallest to largest Range: Difference between the largest and smallest data points in a sample = 2.5 m Fern Height (m) Hand calculations

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Sample Variance _ _ X X-X(X-X) n = 5 _ X = S 2 == Standard Deviation S = = Standard Error

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Confidence Interval 95% confidence interval mean Mean = 1.7 SE = Standard Error df = n-1 df = 5-1 = 4

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df = n-1 _ X - u s n t = Testing Ho using t-test Distribution must be normal Use when n > 30 Ho = 0 Ha > 0 t = / 5 = 0.39 df=5-1=4 Ignore - signs t-Table two tail is more strict one-tailtwo-tail Your t-value is less than t- critical. Fail to reject Ho.

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Comparing two sample means All right. It is time to use Excel! X1X X1X t = _ X 1 - X 2 s s 2 2 n 1 n 2 df = n 1 + n 2 -2 Variances must be equal Ho: X 1 =X 2 Ha: X 1 =X 2

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Using Excel Click Tools, Data Analysis, t-test: Two-sample Assuming Unequal Variances Enter data Data Set 0

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t-critical Value Your Value Reporting results in the literature: Sample X1 and sample X2 are significantly different, t(12) = -4.26, p < 0.05, 2-tail. df Do you accept or reject the Ho? Lets the reader know that you set alpha to The p-value is less than 0.05, therefore the results are significant.

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When you compare more than 2 samples, you need to do an Analysis of Variance (ANOVA). The relationship between an ANOVA and t-test: F=t 2 An ANOVA is the similar to a t-test in the sense that you compare the F value to the critical F value. You also need to look at the p-value. If you set alpha to 0.05 and your p value is less that alpha, you can reject the Ho; if greater than alpha then fail to reject the Ho. ANOVA

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Descriptive Stats

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Correlation & Regression Correlation: describe the strength of association between two variables. The correlation coefficient is designated as r. r can range from -1 to = a strong positive correlation 0 = no correlation -1 = a strong negative correlation r = +1 r = -1 r = 0

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This relationship can be represented by a regression equation. Equation for a straight line: y = bx + a y = DV, b = slope, x = IV, a = intercept Simple Linear Regression: shows relationship between variables.

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