S5 w1 hypothesis testing & t testPresentation Transcript
Understand what are scientific hypotheses Understand fundamental principles of hypothesis testing Understand what is a t test Understand how to perform a t test
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: http://en.wikipedia.org/wiki/Hypothesis
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.
Why do we bother to set up a hypothesiswhen we can’t prove it true?
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.
T-test: Are the two groups statistically different from each other? Source: http://www.socialresearchmethods.net/kb/stat_t.php
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
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: http://janda.org/c10/Lectures/topic07/L19-Ttestresearch.htm
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 varyP value (probability) • the probability that H0 is true, given the statistic (e.g., T, ANOVA F, etc) and the degrees of freedom
T statistic is negative when the mean of group 1 is smaller than the mean of group 2 df is always N – 1