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Statistic (Basic Methods (Experimental Design (Randomization, Blocking,…

- - - - Geometric random variable
        
        Assumption
        
        independent
        
        only one or two outcomes(success/failure)
        
        same probability for each trail
      - Normal & Sampling Distributions
        
        Normal basic properties
        
        3）Standard normal distributionμ=0 σ=1
        
        2）Normal probability plot: scatter plot of (normal score, observed value) pairs.
        
        Law of Sample distribution
        
        Normal Distribution Estimate
        
        Point Estimate
        
        Bias
        
        Unbias
        
        6)Error
        
        1.Standard error: estimate standard deviation
        
        2.Bond error:(reverse z/t for confidence level)(standard error)
      - Linear function y=a+bx
      - Linear combination
      - Binomial
        
        Without Order
        
        With order
        
        Assumption
        
        fixed number
        
        only success or failure
        
        independent
        
        same probability for each trail
    - - ∑p(x)=1 p(x)≥0
      - μx=∑x*p(x)
  - - - Independence Vs dependence
      - Law of Large Numbers
      - Complementary Events
      - General Addition Rule
      - If two events are mutually exclusive, that is, they cannot occur simultaneously.
      - The probability that at least one event will occur is equal to the sum of the respective probabilities of the two events
      - Multiplication Rule
      - Bayes formula
    - - Tree diagram
      - Venn diagram
- - - - Confounding variable
      - Extraneous factor
  - - - Relative Frequency
    - - Sample
      - Population
- - - - Process
- - - - Histograms
    - - Modes
      - Center & Spread
      - Range
      - Standard Deviation
      - Variance
      - Lower & Upper Quartile (IQR)
      - Outlier
      - CLUSTERS AND GAPS
      - Shape
        
        Symmetric
        
        Skewed to the right
        
        Bell-shaped
        
        Skewed to the left
        
        Uniform
- - - - Test statistic
      - Assumptions
        
        The sample sizes are large (n1>=30, n2>=30), or the population distributions are approximately normal (box plot)
        
        1.The two samples are independently selected random samples.
      - Ho: μ1-μ2=hypothesized value
    - - Test statistic
        
        where xd and sd are the sample mean and standard deviation of the differences, df=n-1
      - Assumptions
        
        The samples are paired
        
        The n sample differences can be viewed as a random sample from a population.
        
        The number of sample differences is large (n>=30) or the distribution of differences is approximately normal
      - Ho: μd=hypothesized value
    - - Assumption
        
        Random
        
        Large
        
        Normal
      - Two Sample t: mean x1 - mean x2 +- (t cv)(Math.sqrt(s1^2/n1+s2^2/n2))
      - Paired t: mean xd+-(t cv)*(sd/Math.sqrt(n))
      - (p1-p2)+-(z cv)(Math.sqrt(p1(1-p1)/n1+p2(1-p2)/n2)
  - - - confidence level
      - least sample size
    - - Alternative Hypothesis: Ha: population characteristic >/</≠ hypothesized value
      - Null Hypothesis: Ho: population characteristic = hypothesized value
    - - Test statistic (The reference)
      - P-value
        
        Denotation: the area under the standard normal curve
        
        Population characteristic > hypothesized value: area in upper tail
        
        Population characteristic < hypothesized value: area in lower tail
        
        Population characteristic ≠ hypothesized value: area in both tails (equivalent to confidence interval)
        
        Function: To determine whether Ho should be rejected or not
        
        Meaning: Signifies the inconsistency between the observed value and the hypothesized value
        
        Application: Reject Ho when P-value < α， vice versa
    - - Large sample z test for π
        
        Ho: π = hypothesized value
        
        Test statistic: z = (p-hypothesized value)/√(((hypothesized value)(1-hypothesized value))/n)
        
        Assumptions
        
        The sample size is large. n(hypothesized value)>=10 and n(1-hypothesized value)>=10
        
        If sampling without replacement, the sample size should be no more than 10% of the population size
        
        P is the sample proportion from a random sample
      - The one sample t test for population mean
        
        Ho: μ=hypothesized value
        
        Test statistic:
        
        Assumptions
        
        X and s are the sample mean and sample standard deviation from a random sample
        
        The sample size is large enough n>=30, or the distribution of population is approximately normal. (box plot)
- - - - Test statistics(X^2):
      - Bivariate Data
        
        Tests for Homogenity
        
        Tests for Independence
        
        expected cell count=((row marginal total)(column marginal total))/grandtotal
      - Univariate Data
        
        one-way frequency table
  - - - normal distribution
      - mean value: (True or population regression line)
      - standard deviation:
    - - The distribution of e at any particular x value is normal.
      - e are independent of one another
    - - estimated population variance and standard deviation σ^2 and σ
      - Estimated population regression line: the least-squares line: y=a+bx
        
        properties of sampling distribution of b
        
        estimated standard deviation of b:
        
        normal distributions
      - inference about the slope of the population regression line β
        
        confidence interval for β:
        
        Hypothesis Tests concerning β: Utility tests
        
        Assumptions
        
        Random sample
        
        Linear pattern
        
        The basic assumptions of the simple linear regression model
        
        Model utility test for simple linear regression