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Terms in this set (53)
null hypothesis
H0
- there is no relationship between the proposed cause and effect
- true until proven otherwise
ex. jury trial- defendant is innocent
Fisher
alternative hypothesis
H1 or Ha
- Hypothesis that contradicts the null hypothesis
-Neyman and Pearson
Type 1 error
False positive
Null hypothesis is falsely rejected
- set at .05 so there is a 5% chance that it is a false positive
Type 2 error
False negative
Null hypothesis fails to be rejected (with no real association)
Standard deviation
the extent that an observation in a sample is different from from a central value (like the sample or the population mean)
Standard error
estimate of the difference btw the sample mean and the population mean
Statistical error
the amount an observation is different from its expected value
If the data does not contradict the null hypothesis, what conclusion can be made?
A weak conclusion that there is no evidence against the null hypothesis
* Null hypothesis can only be disproved
Does the H0 assume a relationship btw variables in the sample population?
No
Test statistic
A measure of an attribute of a sample (in hypothesis testing)
- measures extent of departure from a test statistic
How if the procedure of hypothesis testing?
- does the difference away from the H0 > then the value of the probability of occurence of a more extreme value is small under the null hypothesis?
What conclusions can be drawn if the data does not contradict H0?
- not enough data to make a conclusion
- no evidence to change anything
Other types of H0?
- variability of data is the same
ex. male vs female- null hypothesis is that the mean scores are the same
OR
the samples are from the same population so they could never have a difference
Simple v composite hypothesis
simple- specifies the pop distribution completely
composite- does not specify the population distribution completely (usually H1 is this)
Exact hypothesis v inexact hypothesis
exact- has an exact parameter value
inexact- has a range or interval
One-tailed hypothesis
- inexact hypothesis (range or interval) that is above/below or equal to a certain value
- has directionality
Statistical significance test tests what?
a hypothesis
Why is it not valid to test hypothesis suggested by the data?
Circular reasoning-> there is a limitation on the choice of the null hypothesis
So do not summarize data in your hypothesis
In a complex case ex. drug company trying new drug v old drug, what kind of null hypothesis is better? Why?
Difference is a better than statistical significance bc of ethical reasons
- like for example new v old instead of placebo v new
1. Ex H0- a coin is not biased towards heads.
or
2. Ex H0- this coin is fair
1. v small chance--> data refute the null hypothesis
2. looking for to many heads or tails---> contradict the null hypothesis--> not statistically sig
Ex. H0 is a pop mean (10) for a new tx is improved over an old one (>10).
If the results are -200, then the new tx is better than the existing one
SO what do you look for with H0 studies?
So must indicate if the test was 2 sided (if one sided, should have the direction being tested).
Fisher tea testing--> H0 was no ability (one tailed bc >0 ability)
it was directional
When is it two tailed H0?
3 + groups
Ex of a 1 tailed H0?
Fisher lady tea and chi squared tests
Greatest problem to 1-tailed?
- subjective bc you can change it from your H0
ex. the coin test
positive of 1 sided?
- less likely to ignore real effect (less false negatives)
- so use this by default
- better for tx bc can say "one has a benficial effect" v 2 tailed "one has an effect",
BUT even better to add numerical to a 2 sided which eliminates bias
When do you use a 2 tailed H0?
When you do not have a direction in mind
three outcome test
two tests- once in each direction
statistical significance
the low probability that an observed effect happened by chance
what helps ppl to decided if null hypothesis is rejected?
statistical significance
what is the general p-value (or alpha)?
0.05
*if lower, then it is significant
how do you change the study if you dont get <0.05?
inc sample size
is a one or two tailed test more powerful considering statistical significance p value?
one tailed test- bc the <0.05 has to be on one side vs a two-tailed test where it can be on either side
what is stat significance measured in for particle physics and manufacturing?
sigma
What is effect size and why should it be included with stat significance?
effect size is giving a value to the strength of the effect (estimate of parameters) --> more substantive
what is the critical region of a hypothesis test?
the set of all outcomes which cause the null hypothesis to be rejected
stat hypothesis testing aka?
confirmatory data analysis
Testing process
1. research
2. state H0 (accepted or stays undecided) and Ha
3. consider statistical assumptions in doing the test (imp! invalid assumptions-> invalid test)
4. choose relevant test
5. choose distribution of the test statistic (ex. well known result or normal distribution)
6. select alpha (p-value) of 5 or 1%
7. decided distribution of test statistic for H0 being rejected in the critical region (alpha)
8. compute observations (t obs)
9. reject H0 for Ha (t obs in critical region <0.05) or fail to reject it.
*not good for reporting results
Alternative testing process
1. compute from observations t obs
2. calculate p value
3. reject H0 for Ha if pvalue is less than 0.05
*calculates probability
Biggest problem of hypothesis testing?
Ppl tend to think only a stat sig supports theory
theory appraisal
Clever hans effect
A horse appeared to be able to do arithmatic
Hawthorne effect
industrial workers were better in better light (actually better bxc they were being watched)
Always look at sample size!!!!
...
Bag of beans from a different or the same population size.
what is the one tailed test and what is the two tailed test?
one tailed- there are more white beans in this bag, so from a dif bag
two tailed- a mixed bag with a handful that has too many OR too few white beans (both sides, more math)
Clairvoyance test:
H0- p=1/4 (guessing prob)
H1- p>1/4 (clairvoyant)
if c = 25, then is there a small or large chance of a type 1 error?
false positive would be v low (if they get them all right, then they would)
then they calculate 5% and 1% p value, then they choose the smallest to minimize a tpye 2 error
Statistical test
A procedure whose inputs are samples and whose result is a hypothesis.
Region of acceptance
The set of values of the test statistic for which we fail to reject the null hypothesis.
Critical region
The set of values of the test statistic for which the null hypothesis is rejected.
Critical value
the threshold value of the region of acceptance and rejection fr the test statistic
Power of a test (1 − β)
The test's probability of correctly rejecting the null hypothesis.
-The complement of the false negative rate, β.
- SENSITIVITY
Size / Significance level of a test (α)
the test's probability of incorrectly rejecting the null hypothesis.
- FALSE POSITIVE RATE--> SPECIFICITY
p-value
The probability, assuming the null hypothesis is true, of observing a result at least as extreme as the test statistic.
Conservative test
A test is conservative if, when constructed for a given nominal significance level, the true probability of incorrectly rejecting the null hypothesis is never greater than the nominal level.
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