Review of Statistics

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Review of Statistics
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• ??????????????(????)
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• ?????? ??????
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• ?????? ?????

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?? Vs. ??
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????(?)-????

• ????? and Stem-and-Leaf Diagram
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• ??? (Histogram)
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• Box Plot
• ????? (Time Sequence Plots)
• ?????/??

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????(?)-???

• ???? - ???(m ), ???(Me), ??(Mo)
• ????? - ???, ???
• ????? - ??(R), ???(s 2), ???(s ), ????(CV)
• ????? - ??(Skewness), ??(Kurtosis)
• ????
• ???? gt 68.3, 95.4, 99.7
• ?? gt ???????(Chebyshevs Inequality)

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???????

• ?P(A?B) P(A) P(B), ???A?B??
• P(A?B) P(A) P(B) - P(A ? B)
• ????
• ????
• (Bayesian)

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??????????

• ?????(m ) ???????? E(X)
• ?????(s 2) ???????? V(X)

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????(Normal)

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• E(X) m, V(X) s 2
• P(m-sltXltms) 0.683
• P(m-2sltXltm2s) 0.954
• P(m-3sltXltm3s) 0.997
• ???
• ?????

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Standardization
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Central Limit Theorem
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Criteria for Point Estimator

• Unbiased
• Minimum Variance
• Absolute Efficiency
• Relative Efficiency

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????(Hypothesis Testing)

• A person is innocent until proven guilty beyond
  a reasonable doubt. ??????????????, ????????.
• ????
• H0 m 50 cm/s
• H1 m ? 50 cm/s
• Null Hypothesis (H0) Vs. Alternative Hypothesis
  (H1)
• One-sided and two-sided Hypotheses
• A statistical hypothesis is a statement about the
  parameters of one or more populations.

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Errors in Hypothesis Testing
??????? Type I Error(a) Reject H0 while H0
is true. Type II Error(b) Fail to reject H0
while H0 is false.
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Hypothesis Testing on m - Variance Known
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Construction of the C.I.

• From Central Limit Theory,

Use standardization and the properties of Z,
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Summary Table of Influence Procedures for a
Single Sample (I)
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Summary Table of Influence Procedures for a
Single Sample (II)
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Goodness-of-Fit Test (II)

• If the population follows the hypothesized
  distribution, X02 has approximately a chi-square
  distribution with k-p-1 d.f., where p represents
  the number of parameters of the hypothesized
  distribution estimated by sample statistics.
• That is,
• Reject the hypothesis if

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Contingency Table Test- The Problem Formulation
(I)

• There are two classifications, one has r levels
  and the other has c levels. (3 pension plans and
  2 type of workers)
• Want to know whether two methods of
  classification are statistically independent.
  (whether the preference of pension plans is
  independent of job classification)
• The table

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Contingency Table Test- The Problem Formulation
(II)

• Let pij be the probability that a random selected
  element falls in the ijth cell, given that the
  two classifications are independent. Then pij
  uivj, where the estimator for ui and vj are
• Therefore, the expected frequency of each cell is
• Then, for large n, the statistic
• has an approximate chi-square distribution with
  (r-1)(c-1) d.f.