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S5 w1 hypothesis testing & t test


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S5 w1 hypothesis testing & t test

  1. 1. Hypothesis Testing
  2. 2.  Understand what are scientific hypotheses Understand fundamental principles of hypothesis testing Understand what is a t test Understand how to perform a t test
  3. 3.  A hypothesis consists either of a suggested explanation for a phenomenon (an event that is observable) or of a reasoned proposal suggesting a possible correlation between multiple phenomena. The scientific method requires that one can test a scientific hypothesis. Scientists generally base such hypotheses on previous observations or on extensions of scientific theories. Even though the words "hypothesis" and "theory" are often used synonymously in common and informal usage, a scientific hypothesis is not the same as a scientific theory. A Hypothesis is never to be stated as a question. Always as a statement with an explanation following it. It is not to be a question because it states what he/she thinks or believes will answer the problem the best Source:
  4. 4.  The null hypothesis (H0) is a hypothesis (scenario) set up to be nullified, refuted, or rejected (disproved statistically) in order to support an alternative hypothesis. The alternative hypothesis (H1) is the possibility that an observed effect is genuine and the null hypothesis is the rival possibility that it has resulted from chance. A falsifiable theory allows both null & alternative hypotheses.
  5. 5. Why do we bother to set up a hypothesiswhen we can’t prove it true?
  6. 6.  When used, the null hypothesis is presumed true until statistical evidence, in the form of a hypothesis test, indicates otherwise — that is, when the researcher has a certain degree of confidence, usually 95% to 99%, that the data does not support the null hypothesis.
  7. 7.  T-test: Are the two groups statistically different from each other? Source:
  8. 8.  The "students" distribution was actually published in 1908 by W. S. Gosset. Gosset was employed at a brewery that forbade the publication of research by its staff members Gosset devised the t-test as a way to cheaply monitor the quality of beer. To circumvent this restriction, Gosset used the name "Student", and consequently the distribution was named "Student t-distribution" Source: wikipedia
  9. 9.  Critical T values: 1-tailed: 1.65 2-tailed: 1.96 Reject the null hypothesis when the t value is greater than the cut-off critical value Because the signal-to-noise ratio is sufficiently high Source:
  10. 10. T statistic • The ratio of group mean difference relative to the sum of deviations Degrees of Freedom (df) • the number of values in the final calculation of a statistic that are free to varyP value (probability) • the probability that H0 is true, given the statistic (e.g., T, ANOVA F, etc) and the degrees of freedom
  11. 11. T statistic is negative when the mean of group 1 is smaller than the mean of group 2 df is always N – 1