Hypothesis Tests – Difference of Two Means
AtMyPace: Statistics
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Módulo A
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False
What is Inference.
Q: Hypothesis testing is based on the idea that we can draw
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conclusions about a sample from the information we get from
the population.
A: In hypothesis testing, and in all inference, we use the information
gained from a sample to make inferences about the population.
Conclusion.
Q: Say we get a p-value of 0.25. We conclude that we have
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X
evidence that the null hypothesis is not true.
A: The p-value must be low – usually lower than 0.05 before we will
reject the null hypothesis.
Tails.
Q: If we don’t know which way we think the effect will be use
a two-tailed test, involving an inequality
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A: Conversely if we have a directional hypothesis, saying greater or
less or more or improve…, then we would use a one tailed test.
Reject, Accept?
Q: If the p-value is less than the previously determined
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significance level we reject the null hypothesis.
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A: A low p-value indicates that is extremely unlikely to get this value
if the null hypothesis is true. Thus we reject the null hypothesis.
p-Value
Q: The p-value is the probability that the null hypothesis is
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wrong
A: Though this is almost correct in essence, it is not correct. The
null hypothesis is either true or not, and we don’t know either way.
There is no probability attached to that. The p-value is the
probability of getting a summary value from sample as extreme as
the one obtained, or worse, if the null hypothesis is true.
Significance level
Q: The most usual value for a significance level is 0.05.
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A: 0.05 allows a 5% chance of a Type 1 error – rejecting the null
hypothesis when we shouldn’t, and thus saying is an effect when
really there isn’t. It is the most usual significance level used in
statistical analysis.
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X
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Process Order.
Q: You should take the sample and calculate the p-value before
you decide on the level of significance at which to reject the
null hypothesis.
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A: In order to reduce personal bias by choosing a significance level
to suit, you should choose the significance level before sampling and
analysis. That being said, with the use of p-value, the level of
rejection is less arbitrary than it used to be.
Hypothesis Generation.
Q: The following is a valid alternative hypothesis: “the mean
weight of corn chips in all the packets is 50g or less”.
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A: * An alternative hypothesis must refer to the population (all the
packets) – OK
* An alternative hypothesis should not generally represent the status
quo (there are not enough chips) - OK.
* and it should NOT include an equality (is 50g). – Not OK.
This is not a valid alternative hypothesis, as it has an equality
statement in it.
Hypothesis Generation.
Q: The following is a valid null hypothesis: “the mean weight
of corn chips in all the packets is 50g or more”.
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X
A: Yes. A null hypothesis must refer to the population (all packets),
it should generally represent the status quo (there are enough
chips), and it should include an equality (is 50g). This is a valid
statement of a null hypothesis.
Basic Ideas.
Q: Inferential statistics operates on the premise that we cannot
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prove something to be true.
A: Yes. We cannot prove something to be true. However we can set
up an opposing hypothesis and disprove that..
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Módulo B
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False
What is Inference?
Q: In hypothesis testing we take a sample and use it to draw
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conclusions abut the population
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A: Yes. In hypothesis testing, and in all inference, we use the
information gained from a sample to make inference about the
population.
Basic Ideas.
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Q: Inferential statistics operates on the premise that we can
prove something to be false.
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A: Proving something to be false is easier than proving something
to be true. Thus we set up an opposing hypothesis and test to see if
we can prove it to be false.
Conclusion.
Q: Say we get a p-value of 0.00025. We would conclude that
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we have evidence that the null hypothesis is not true
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A: Yes. This p-value is very low – it would be almost impossible to
get this result or worse if the null hypothesis were true. Thus we
conclude that it isn’t !.
Tails.
Q: If the alternative hypothesis has words like improve, better,
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more, worse or less in it, then we are looking at a one-tailed
test.
A: Yes. The words improve, better, more, worse, etc, imply a
directional hypothesis, or one-tailed test. The words change and
different imply an exploratory or tw0-tailed test.
Reject, Accept?
Q: if the p-value is less than the previously determined significance
level we reject the alternative hypothesis.
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X
A: A low p-value indicates that is extremely unlikely to get this
value if the null hypothesis is true. Thus we reject the null
hypothesis. We never reject the alternative hypothesis.
p-Value.
Q: The p-value is the probability that the alternative hypothesis is
correct
A: No. This is not correct because we do not talk about the
probability that either hypothesis is correct, only of getting such a
result were the null hypothesis true. The p-value is the probability of
getting a summary value from the sample as extreme as the one
obtained, or worse, if the null hypothesis is true.
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X
Significance Level.
Q: The most usual value for a significance level is 0.5.
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A: No. 0.5 allows a 50% chance of a Type 1 error – rejecting the
null hypothesis when we shouldn’t, and thus saying there is an effect
when really there isn’t. We would be very unlikely to allow a 50%
chance for error..
Process Order.
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Q: You should decide on the level of significance at which to
reject the null hypothesis before you take the sample and
calculate the p-value.
X
A: Yes. In order to reduce personal bias by choosing a significance
level to suit, you should choose the significance level before
sampling and analysis. That being said, with the use of p-value, the
level of rejection is less arbitrary than it used to be.
Explainable Variation.
Q: Many types of statistical analysis attempts to find out how
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much variation is attributable to known aspects. We call this
explainable variation?
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A: Yes. For example, we may wish to see how different training
methods compare, so we measure the outcomes and see how much of
the variation in results can be said be due to the training method.
Hypothesis Generation.
Q: The following is a valid alternative hypothesis: “the mean
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weight of corn chips in all the packets is less than 50g”.
X
A: Yes. * An alternative hypothesis must refer to the population (all
the packets) – OK
* An alternative hypothesis should not generally represent the
status quo (there are not enough chips) – OK
* and it should NOT include an equality (is 50g) – OK.
This is a valid alternative hypothesis
Hypothesis Generation.
Q: The following is a valid null hypothesis: “the mean weight
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of corn chips in all the packets is more than 50g”.
A: No. * A null hypothesis must refer to the population (all the
packets) – Not OK
* A null hypothesis should generally represent the status quo (there
are enough chips) – OK
* and it should include an equality (is 50g) – Not OK.
For two reasons, this is not a valid statement of a null hypothesis.
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