The document discusses hypothesis testing and t-tests, explaining that a hypothesis is a suggested explanation for a phenomenon that can be tested scientifically, and a t-test determines if the means of two groups are statistically different. It provides details on null and alternative hypotheses, how to perform a t-test, and how the t-statistic, degrees of freedom, and p-value are used to evaluate whether to reject the null hypothesis.

1. Hypothesis Testing

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.  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

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. Why do we bother to set up a hypothesis
when we can’t prove it true?

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.  T-test:
Are the two groups statistically
different from each other?
Source: http://www.socialresearchmethods.net/kb/stat_t.php

8.  The "student's" 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

11.  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

12. 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

13. T statistic is negative when the mean of
group 1 is smaller than the mean of group
2
 df is always N – 1