COMMERCE 2QA3 Study Guide - Final Guide: Standard Deviation, Confidence Interval, Type I And Type Ii Errors
28 Jun 2018
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Hypothesis
The null hypothesis specifies a population model parameter and proposes a value for that parameter. Null
hypothesis for a proportion is written in the form . The alternative hypothesis contains the
values of the parameter considered plausible if the null hypothesis is rejected.
In examples with deviations on either side of the null hypothesis, the alternative hypothesis is a two-sided
alternative. If only focusing on deviations in one direction, the alternative hypothesis is a one-sided alternative.
It is important not to: fudge the null or alternative hypothesis, put the investigated issue into the null hypothesis
(should be in the alternative hypothesis), or have difference values in the null or alternative hypothesis.
P-Values
Probability of seeing the observed data given the null hypothesis.
When p-value is
The data is
Low
Unlikely if null hypothesis is true so reject the null hypothesis
High[er]
Consistent with model from null hypothesis so "fail to reject" the null hypothesis
Not low
Indicates insufficient evidence so "fail to reject"
Alpha Levels and Significance
A rare event can arbitrarily be defined by setting a threshold for the p-value, the alpha level denoted by . If it
falls below that point, we reject the null hypothesis. These results are statistically significant. Select the alpha
level before looking at the data.
If p-value
Then
Reject
Fail to reject
Report the p-value as an indication of the strength of the evidence. Small deviations from the null are
statistically significant in large samples, but not so in smaller samples. Report the magnitude of the difference
between the observed statistic value and null hypothesis value along with the p-value.
Reasoning of Hypothesis Testing
PLAN
Plan by interpreting the business situation in terms of hypothesis.
General Principle
Algorithm
Choose numerical parameter important to business context
We want to know
Decide whether business situation requires investigation into
whether the parameter has increased, decreased, or changed
in either direction
We want to see if
has increased
Formulate hypothesis related to this parameter
Formulate alternative hypothesis; the sign depends on
whether we're investigating an increase or decrease, or a
change in either direction
Plan by interpreting the business situation in terms of significance level .
General Principle
Algorithm
Choose a value of that corresponds to a business context
for life/death business situations needing accuracy
for behavioural situations where parameters are open
to interpretation
Testing Hypothesis about Proportions
October 14, 2017
12:35 PM
Statistics Page 1
Document Summary
The null hypothesis specifies a population model parameter and proposes a value for that parameter. Null hypothesis for a proportion is written in the form . The alternative hypothesis contains the values of the parameter considered plausible if the null hypothesis is rejected. In examples with deviations on either side of the null hypothesis, the alternative hypothesis is a two-sided alternative. If only focusing on deviations in one direction, the alternative hypothesis is a one-sided alternative. It is important not to: fudge the null or alternative hypothesis, put the investigated issue into the null hypothesis (should be in the alternative hypothesis), or have difference values in the null or alternative hypothesis. Probability of seeing the observed data given the null hypothesis. Unlikely if null hypothesis is true so reject the null hypothesis. Consistent with model from null hypothesis so "fail to reject" the null hypothesis. Alpha levels and significance falls below that point, we reject the null hypothesis.
