L6

• A hypothesis is a statement about the way some aspect of nature works, put forward as an initial explanation for a particular observation
• The "Null" hypothesis (Hθ):

  • Statement of no effect
  • What is statistically tested
  • Accept or reject the null hypothesis
• The "alternative hypothesis" (Ha) is a potential alternative explanation of the relationship between the variables of interest
• Scientific hypotheses are testable and falsifiable proposed explanations to account for observed patterns or trends, while statistical hypotheses are statements about whether or not a pattern or trend or difference is present in your data
• In hypothesis testing, P-values from statistical tests are used to determine whether to reject or not, with P<0.05 indicating rejection of the null hypothesis and acceptance of the alternative hypothesis
• Type I error involves rejecting the null hypothesis when it is true, while Type II error involves accepting the null hypothesis when it is false
• Controlling error in hypothesis testing involves understanding that even with large sample sizes, you cannot control both Type I and Type II errors simultaneously
• In a decision matrix, the reality of the situation is compared to the decision made, which can result in correct decisions, Type I errors, or Type II errors
• Hypothesis

  there is no effect of X on Y
• Prediction

  The mean Y of populations that differ in X will not differe
• Statistical Hypothesis

  • statements about whether a pattern or trend difference is present in your data
• P Values : P>0.05

  P>0.05

  • accept null hypothesis
  • not statisitcally different
• P Value: P<0.05


  accepts null hypothesis

  • Statistically different
• Type I Error

  Rejects null Hypothesis when it is TRUE

  • accepts Ha when H0 is true
  • represented by a
• Type II Error

  accepting Null hypothesis when it is false

  • accept H0 when Ha is true
  • represented by β
• Controlling Error

  • you can decrease α and β by increasing sample size
• Controlling Error

  • you can decrease α and β by increasing sample size
  • β depends on sample size and Effect size