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Test 3 - Coggle Diagram

- - - - Symmetric
      - Unimodal
      - Bell-shaped
    - - A normal curve is completely determined by the mean μ and standard deviation σ: N (μ, σ)
      - N = Normal
      - σ = Standard deviation
      - μ = mean
- - - - "above"
      - "below"
    - - "changed"
      - neutral wording
      - "different than"
  - - - One
        
        Quantitative or Categorical
        
        Quantitative
        
        Mean μ (H0: μ=number --> given)
        
        Categorical
        
        Proportion p (H0: p=# --> given)
      - Two
        
        Quantitative or Categorical
        
        1 Quantitative and 1 categorical
        
        Difference in Means μ1 - μ2 (H0: μ1=μ2 --> always)
        
        2 Categorical
        
        Difference of proportions p1 - p2 (H0: p1=p2 --> always)
        
        2 Quantitative
        
        Correlation ρ (H0: ρ=0 --> always)
    - - Proportion: p = proportion of (whole) that (part)
      - Correlation: ρ = correlation between (variable 1) and (variable 2) for (population)
- - - - P-value of 0.0001 or lower = overwhelming evicence
      - P-value of 0.15 or higher = no evidence
      - P-value of 0.1 or higher = weak evidence
      - P-value between 0.05 and 0.1 = moderate/weak evidence
      - P-value between 0.01 and 0.05 = moderate/strong evidence
      - P-value of 0.01 or higher = very strong evidence
  - - - Reject H0 = convict null-hypothesis (find guilty)
      - Exonerate H0: exonerate null-hypothesis (find not guilty)
    - - Values or α are 0.01, 0.05 or 0.1
      - If α is below given value we have enough evidence to reject the null-hypothesis
      - If α is above given value we would fail to reject the null-hypothesis
      - Difference to informal statistical conclusion is that for informal we describe with wording (strong/moderate/...) and for formal we have a base that is determined beforehand
      - If p-value is less than the significance level α we're given, we say that we have statistically significant evidence
      - If the p-value is greater than α, we say that we do NOT have statistically significant evidence
    - - Reject H0 (small p-value): We have statistically significant evidence that (Ha is true)
      - Fail to reject H0 (large p-value): We do not have statistically significant evidence that (Ha is true)
    - - If we are given a significance level, we follow the formal conclusions model
      - If we are not given a significance level, we follow the informal conclusions model
  - - - Getting p-value
        
        Add both p-values together
        
        Find one side and then double it
      - P-value comes from both tails
- - - - Probability of opposite = 1 - probability of statement
    - - Multiply probabilities to calculate probability of an AND
    - - To get exactly one outcome --> add all possible sequences together
      - To get at least one outcome --> add all possible sequences together
  - - - 5! = 5x4x3x2x1
    - - "n choose k" (n over k)
    - - = n! / k!(n-k)!
- - - - Answers yes/no question
      - Ex.: Compare something to see if something happens/happened
    - - Gives us numeric answers (interval of numbers)
      - Ex.: Estimate the percentage
      - Confidence Intervals
      - Ex.: Estimate the correlation
      - Ex.: Estimate the average difference
    - - No inference
      - Ex.: Find the average number of all students in the room.
      - Ex.: Estimate from a scatterplot the correlation between the percent of residents in each state who drink and the percent of residents who exercise more than 150mins per week
      - Ni inference if data set is equal to population
  - - - 1) Find 95% CI
      - 2) Means that μ1=μ2
      - 3) Is it possible that there is no difference? Yes, if 0 is within the CI
      - 4) If 0 is within the CI ==> Fail to reject H0
    - - If hypothesized value μ0 is not in the 95% CI
        
        Reject at the 0.5 level
      - If hypothesized value μ0 is not in the 99% CI
        
        Reject at the 0.1 level
      - If we reject at a 90% Ci but fail to reject at a 95% CI ==> p-value is between .05 and .10
      - This method is used for yes/no questions with CI