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Test of significance
A statistical test used to help answer the question of whether an observed difference is real or just due to chance error.
Nully Hypothesis
This is the hypothesis used in creating the box model for a test of significance. This hypothesis about the box (population parameter) corresponds with the idea that any observed difference between the sample outcome and the expected value is due to chance.
Alternative Hypothesis
This hypothesis regarding the box (population parameter) corresponds with the idea that any observed difference between the sample outcome and expected value is real.
Test Statistic
A computed value that measures the size of the difference between the observed data and the expected value from the null hypothesis. (Two example from this chapter are the ‘z-statistic’ and ‘t-statistic’.)
P-value
The term used to refer to the observed significance level.
Z-tests
Hypothesis tests (tests of significance) for large samples that use a z-statistic.
Observed Significance
The chance of getting a test statistic as extreme or more extreme than the observed one, if the null hypothesis is true.
Statistical Significance
The observed difference is too large to be due to chance.
Highly Significant
The P-value is smaller than 1%
test of significance
a statistical test used to help answer the question of whether an observed difference is real or just due to chance error
null hypothesis
this is the hypothesis used in creating the box model for a test of significance. this hypothesis about the box (population parameter) corresponds with the idea that any observed difference between the sample outcome and the expected value is due to chance.
alternative hypothesis
this hypothesis regarding the box (population parameter) corresponds with the idea that any observed difference between the sample outcome and expected value is real.
test statistic
a computed value that measures the size of the difference between the observed data and the expected value from the null hypothesis. (two example from this chapter are the ‘z-statistic’ and ‘t-statistic’.)
p-value
the term used to refer to the observed significance level.
z-tests
hypothesis tests (tests of significance) for large samples that use a z-statistic.
observed significance level
the chance of getting a test statistic as extreme or more extreme than the observed one, if the null hypothesis is true.
statistical significance
the observed difference is too large to be due to chance.
highly significant
the P-value is smaller than 1%
the bias equals 0
the null hypothesis
the bias is different from 0
the alternative hypothesis
degrees of freedom
number of measurements -1
SD+
larger estimate for the SD
true
with regard to sample size: t-Tests are appropriate for SMALL samples, while z-Tests are appropriate for LARGE samples; when using a t-Test, the SD+ is appropriate; as the number of degrees of freedom gets LARGER, a ‘t-curve’ (actually called a ‘Student’s-curve’) looks more like a normal curve.
how does Student’s t-curve differ from the normal curve?
the t-curve is shorter in the middle and more spread out.
true
if the amount of data is small, and the histogram for the contents of the error box is unknown but probably not too different from the normal curve, you can use Student’s curve.
two sample z-tests
name of tests based on the z-statistic computed using the formula at the bottom of page 504.
in the face of these apparent mistakes (the draws are made without replacement, but the SEs are computed as if drawing with replacement; the two averages are dependent, but the SEs are combined as if the averages were independent.) why is it that two-sample z-Tests remain valid?
because the two mistakes offset each other 