Environmental science

 Need a clear paper including this requirement

You will need entries for:

  • Descriptive statistics: Mean, Median, Mode, Standard deviation, variance, range (100 pts)
  • z test (100)
  • T-Tests (multiple types) (100)
    • Dependent
    • Independent
  • ANOVA (One and Two)
  • Correlation
  • Regression
  • Notes on creating graphs
  • Discussion of errors and probability distributions.
  • Suggestion: a glossary for all the terms. (Bonus 100)

Outline for each entry:

  1. The written description of the test.
  2. Why you would use this test.
  3. Formula
    1. with clear variable definitions
    2. can reference formulas
  4. Clear handwritten example calculations
  5. Code for R with an example
    1. Can come from homework or a project.
  6. Explain what the results mean. (accept or reject the hypothesis. p-value meaning, etc)
  • · Chi-Square Test (ꭓ2)

    · Definition – a test to determine the various deviations expected by chance, if the hypothesis is true.

    · Say you have a known distribution that you sample from. You expect to get the same distribution within your sample. This test determines the deviation from the known distribution in your sample. Genetics is a common field this is used in. There is a known probability for genotypes within a population. Chi-square can be used to determine if your sample deviates from this known genotypes distribution.

    ·

    · Where O = the observed frequency

    · E = expected frequency

    · You have plants with red, yellow, and orange petals with the following genotypes and probabilities:

    · RR = Red – 25%

    · Rr = Orange – 50%

    · rr = Yellow – 25%

    · In a population of 320 you expect an observation of

    · RR = 80

    · Rr = 160

    · rr = 80

    · IF there is incomplete dominance.

    · You grow these plants in your garden, this is what you see:

    · RR = 65

    · Rr = 189

    · rr = 66

    · Calculate

    Observed

    Expected

    (O-E)2

    (O-E)2/E

    Red

    65

    80

    225

    2.81

    Orange

    189

    160

    841

    5.25

    Yellow

    66

    80

    196

    2.45

    10.51

    · ꭓ2 = 10.51

    · Using the Critical Values of Chi Square distribution. A df of 2, p would be between 0.01 or 0.005.

    · My null hypothesis is that the Observed and Expected outcomes would be equal if there is incomplete dominance.

    · If my null hypothesis is true, deviations this large should only be expected 0.5-1% of the time.

    · In this case, the hypothesis will be rejected because this is too unlikely that you would get these results with incomplete dominance.

    · R code and example

    · chisq.test(x, p = rep(1/length(x), length(x))

    · x = data set

    · p = probabilities for each data point in the data set

    > genetest <- c(65, 189, 66)
    > chisq.test(genetest, p = c(1/4, 1/2, 1/4))
    Chi-squared test for given probabilities

    data: genetest

    X-squared = 10.519, df = 2, p-value = 0.005199

    · Conclusion is that the probability is so small of this happening, the expected outcome is not correct. You reject the null hypothesis.

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