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Statistical Concepts (continued) Concepts to cover or review today: –Population parameter –Sample statistics –Mean –Standard deviation –Coefficient of variation –Standard error –Confidence interval You should understand these terms by the end of the lecture and be able to conduct estimations.

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Steps in Conducting an Assessment using Inventory and Monitoring 1.Develop Problem Statement—may include goals 2.Develop specific objectives 3.Determine important data to collect 4.Determine how to collect and analyze data 5.Collect data 6.Analyze data 7.Assess data in context of objectives principles of statistics allows us to better plan how to collect the data AND analyze it - they work in tandem

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How do we estimate Mean and Standard Deviation ? Mean:Standard Deviation:

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10 samples (truth)

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100 samples (truth)

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1000 samples (truth)

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1000 samples (truth)

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100 samples (truth)

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1000 samples (truth) 1 sd What is Standard Deviation ?

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(truth) SD = 1.8 SD = 3.6 SD = 7.2 1 sd 1000 samples Population variability and SD

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How good is our estimated mean? How might we determine how good is an estimate ? –Quantify precision and bias How might we quantify precision ? –We can quantify standard error of mean How might we quantify bias ? –Usually requires “truth” to be known

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Estimating standard error Standard DeviationStandard Error

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Distribution of Means n = 100 (truth) Mean

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n = 10 n = 1000 n = 100 Distribution of Means (truth) Mean

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Distribution of Means n = 100 1 se 2 se 2.5 % (truth) Mean

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Distribution of Means n = 100 1 se 2 se 2.5 % (truth) Mean 1 se 2 se 1 se 2 se 1 se 2 se

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Estimating Confidence Intervals Standard Error95 % Confidence Intervals CI 95 = Mean ± 1.96 * SE

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Confidence Intervals Usually set at 95 % What does that mean ? –Intervals constructed this way will contain the true mean (assuming no bias) 95 % of the time Why 95 % ? –Presumes high probability of interval containing true mean Are other ranges of confidence intervals valid or useful ?

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Estimation Problem: Mice weights (g): CI 95 = Mean ± 1.96 * SE Estimate:

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