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In: Statistics and Probability

What does statistical significance mean? How do you know if something is statistically significant? What is...

What does statistical significance mean? How do you know if something is statistically significant? What is the difference between statistical significance and practical significance?

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Expert Solution

H0: Also known as the null hypothesis, it is a statement of "no effect"
or "no difference" used in tests of significance. The test of
significance is used to obtain substantial evidence against H0.
? Ha
: Also known as the alternative hypothesis, is what we hope to be
correct in rejection of the null hypothesis.
? P-Value: A P-value is essentially the probability that the test statistic
you compute would acquire a value as extreme or more than what you
actually observe. This is after making the assumption that H0 is true.
A common rule is the smaller the P-value, the stronger the evidence is
against H0.
? What does the P-value have to do with significance level?
We can compare the P-value calculated with a fixed value. This fixed
value is called the significance level.
? Significance Level: Is denoted by the Greek letter alpha (?). If the P-
value we calculate is as small or smaller than ?, we say the data is
statistically significant at level ?

What does “statistically significant” mean?
? When we use the term "significant", we are not automatically
implying that the data is "important". It is simply a term that is used to
assess whether the evidence against the null hypothesis has reached
the standard set by ? only.
? For example, significance level at 0.05 is often expressed by the
statement: "The results were significant at (P< 0.05)", where P stands
for the P-value.
? The P-value is helpful in providing basic information rather than a
statement of significance, because we can then assess significance at
any level we choose.

Statistical versus Practical Significance
What is STATISTICAL SIGNIFICANCE?
? Statistical significance refers to the unlikelihood that mean differences
observed in the sample have occurred due to sampling error. Given a
large enough sample, despite seemingly insignificant population
differences, one might still find statistical significance.
What is PRACTICAL SIGNIFICANCE?
? Practical significance looks at whether the difference is large enough
to be of value in a practical sense.


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