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A test method is a method for a test in science or engineering, such as a physical test, chemical test, or statistical test. It is a definitive procedure that produces a test result.[1] In order to ensure accurate and relevant test results, a test method should be "explicit, unambiguous, and experimentally feasible.",[2] as well as effective[3] and reproducible.[4]
A test can be considered an observation or experiment that determines one or more characteristics of a given sample, product, process, or service. The purpose of testing involves a prior determination of expected observation and a comparison of that expectation to what one actually observes.[5] The results of testing can be qualitative (yes/no), quantitative (a measured value), or categorical and can be derived from personal observation or the output of a precision measuring instrument.
Usually the test result is the dependent variable, the measured response based on the particular conditions of the test or the level of the independent variable. Some tests, however, may involve changing the independent variable to determine the level at which a certain response occurs: in this case, the test result is the independent variable.
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Hypothesis testing and p-values | Inferential statistics | Probability and Statistics | Khan Academy
Science, Engineering and Design! Video 2: Engineering Design Process
Simple Machines for Kids: Science and Engineering for Children - FreeSchool
Transcription
A neurologist is testing the
effect of a drug on response
time by injecting 100 rats with
a unit dose of the drug,
subjecting each to neurological
stimulus and
recording its response time.
The neurologist knows that the
mean response time for rats
not injected with the
drug is 1.2 seconds.
The mean of the 100 injected
rats response times is 1.05
seconds with the
sample standard
deviation of 0.5 seconds.
Do you think that the drug has
an affect on response time?
So to do this we're going to
set up two hypotheses.
We're going to say, one, the
first hypothesis is we're
going to call it the null
hypothesis, and that is that
the drug has no effect
on response time.
And your null hypothesis is
always going to be-- you can
view it as a status quo.
You assume that whatever your
researching has no effect.
So drug has no effect.
Or another way to think about
it is that the mean of the
rats taking the drug should be
the mean with the drug-- let
me write it this way-- with the
mean is still going to be
1.2 seconds even
with the drug.
So that's essentially saying it
has no effect, because we
know that if you don't give
the drug the mean response
time is 1.2 seconds.
Now, what you want is an
alternative hypothesis.
The hypothesis is no,
I think the drug
actually does do something.
So the alternative hypothesis,
right over here, that the drug
has an effect.
Or another way to think about
it is that the mean does not
equal 1.2 seconds when
the drug is given.
So how do we think about this?
How do we know whether we should
accept the alternative
hypothesis or whether we should
just default to the
null hypothesis because the
data isn't convincing?
And the way we're going to do it
in this video, and this is
really the way it's done in
pretty much all of science, is
you say OK, let's assume that
the null hypothesis is true.
If the null hypothesis was true,
what is the probability
that we would have gotten these
results with the sample?
And if that probability is
really, really small, then the
null hypothesis probably
isn't true.
We could probably reject the
null hypothesis and we'll say
well, we kind of believe in the
alternative hypothesis.
So let's think about that.
Let's assume that the null
hypothesis is true.
So if we assume the null
hypothesis is true, let's try
to figure out the probability
that we would have actually
gotten this result, that we
would have actually gotten a
sample mean of 1.05 seconds with
a standard deviation of
0.5 seconds.
So I want to see if we assumed
the null hypothesis is true, I
want to figure out the
probability-- and actually
what we're going to do is
not just figure out the
probability of this, the
probability of getting
something like this or even
more extreme than this.
So how likely of an
event is that?
To think about that let's just
think about the sampling
distribution if we assume
the null hypothesis.
So the sampling distribution
is like this.
It'll be a normal
distribution.
We have a good number
of samples, we
have 100 samples here.
So this is the sampling
distribution.
It will have a mean.
Now if we assume the null
hypothesis, that the drug has
no effect, the mean of our
sampling distribution will be
the same thing as the meaning
of the population
distribution, which would
be equal to 1.2 seconds.
Now, what is the standard
deviation of our sampling
distribution?
The standard deviation of our
sampling distribution should
be equal to the standard
deviation of the population
distribution divided by the
square root of our sample
size, so divided by the
square root of 100.
We do not know what the standard
deviation of the
entire population is.
So what we're going to do is
estimate it with our sample
standard deviation.
And it's a reasonable thing to
do, especially because we have
a nice sample size.
The sample size is
greater than 100.
So this is going to be a pretty
good approximator.
This is going to be a pretty
good approximator
for this over here.
So we could say that this is
going to be approximately
equal to our sample standard
deviation divided by the
square root of 100, which is
going to be equal to our
sample standard deviation is
0.5, 0.5 seconds, and we want
to divide that by square
root of 100 is 10.
So 0.5 divided by 10 is 0.05.
So the standard deviation of our
sampling distribution is
going to be-- and we'll put a
little hat over it to show
that we approximated it with--
we approximated the population
standard deviation with the
sample standard deviation.
So it is going to be equal
to 0.5 divided by 10.
So 0.05.
So what is the probability--
so let's think
about it this way.
What is the probability of
getting 1.05 seconds?
Or another way to think about
it is how many standard
deviations away from this mean
is 1.05 seconds, and what is
the probability of getting a
result at least that many
standard deviations away
from the mean.
So let's figure out how many
standard deviations away from
the mean that is.
Now essentially we're just
figuring out a Z-score, a
Z-score for this result
right over there.
So let me pick a nice color--
I haven't used orange yet.
So our Z-score-- you could
even do the Z-statistic.
It's being derived from these
other sample statistics.
So our Z-statistic, how far
are we away from the mean?
Well the mean is 1.2.
And we are at 1.05, so I'll
put that less just so that
it'll be a positive distance.
So that's how far away we are.
And if we wanted it in terms
of standard deviations, we
want to divide it by our best
estimate of the sampling
distribution's standard
deviation, which is this 0.05.
So this is 0.05, and what is
this going to be equal to?
This result right here,
1.05 seconds.
1.2 minus 1.05 is 0.15.
So this is 0.15 in the numerator
divided by 0.05 in
the denominator, and so
this is going to be 3.
So this result right here
is 3 standard deviations
away from the mean.
So let me draw this.
This is the mean.
If I did 1 standard deviation,
2 standard deviations, 3
standard deviations-- that's
in the positive direction.
Actually let me draw
it a little bit
different than that.
This wasn't a nicely drawn
bell curve, but I'll do 1
standard deviation, 2 standard
deviation, and then 3 standard
deviations in the positive
direction.
And then we have 1 standard
deviation, 2 standard
deviations, and 3 standard
deviations in
the negative direction.
So this result right here, 1.05
seconds that we got for
our 100 rat sample is
right over here.
3 standard deviations
below the mean.
Now what is the probability
of getting a result
this extreme by chance?
And when I talk about this
extreme, it could be either a
result less than this or a
result of that extreme in the
positive direction.
More than 3 standard
deviations.
So this is essentially, if we
think about the probability of
getting a result more extreme
than this result right over
here, we're thinking about
this area under the bell
curve, both in the negative
direction or in
the positive direction.
What is the probability
of that?
Well we go from the empirical
rule that 99.7% of the
probability is within 3
standard deviations.
So this thing right here-- you
can look it up on a Z-table as
well, but 3 standard deviation
is a nice clean number that
doesn't hurt to remember.
So we know that this area right
here I'm doing and just
reddish-orange, that area
right over is 99.7%.
So what is left for these two
magenta or pink areas?
Well if these are 99.7% and
both of these combined are
going to be 0.3%.
So both of these combined are
0.3-- I should write it this
way or exactly-- are 0.3%.
0.3%.
Or is we wrote it as a decimal
it would be 0.003 of the total
area under the curve.
So to answer our question, if we
assume that the drug has no
effect, the probability of
getting a sample this extreme
or actually more extreme
than this is only 0.3%
Less than 1 in 300.
So if the null hypothesis was
true, there's only a 1 in 300
chance that we would have
gotten a result
this extreme or more.
So at least from my point of
view this results seems to
favor the alternative
hypothesis.
I'm going to reject the
null hypothesis.
I don't know 100% sure.
But if the null hypothesis was
true there's only 1 in 300
chance of getting this.
So I'm going to go with the
alternative hypothesis.
And just to give you a little
bit of some of the name or the
labels you might see in some
statistics or in some research
papers, this value, the
probability of getting a
result more extreme than this
given the null hypothesis is
called a P-value.
So the P-value here, and that
really just stands for
probability value, the P-value
right over here is 0.003.
So there's a very, very small
probability that we could have
gotten this result if the null
hypothesis was true, so we
will reject it.
And in general, most people
have some type
of a threshold here.
If you have a P-value less than
5%, which means less than
1 in 20 shot, let's say, you
know what, I'm going to reject
the null hypothesis.
There's less than a 1 in 20
chance of getting that result.
Here we got much less
than 1 in 20.
So this is a very strong
indicator that the null
hypothesis is incorrect,
and the drug
definitely has some effect.
In software development, engineering, science, manufacturing, and business, its developers, researchers, manufacturers, and related personnel must understand and agree upon methods of obtaining data and making measurements. It is common for a physical property to be strongly affected by the precise method of testing or measuring that property. As such, fully documenting experiments and measurements while providing needed documentation and descriptions of specifications, contracts, and test methods is vital.[6][2]
Using a standardized test method, perhaps published by a respected standards organization, is a good place to start. Sometimes it is more useful to modify an existing test method or to develop a new one, though such home-grown test methods should be validated[4] and, in certain cases, demonstrate technical equivalency to primary, standardized methods.[6] Again, documentation and full disclosure are necessary.[2]
A well-written test method is important. However, even more important is choosing a method of measuring the correct property or characteristic. Not all tests and measurements are equally useful: usually a test result is used to predict or imply suitability for a certain purpose.[2][3] For example, if a manufactured item has several components, test methods may have several levels of connections:
test results of a raw material should connect with tests of a component made from that material
test results of a component should connect with performance testing of a complete item
results of laboratory performance testing should connect with field performance
These connections or correlations may be based on published literature, engineering studies, or formal programs such as quality function deployment. Validation of the suitability of the test method is often required.[4]
Content
Quality management systems usually require full documentation of the procedures used in a test. The document for a test method might include:[7][8]
descriptive title
scope over which class(es) of items, policies, etc. may be evaluated
date of last effective revision and revision designation
reference to most recent test method validation
person, office, or agency responsible for questions on the test method, updates, and deviations
significance or importance of the test method and its intended use
terminology and definitions to clarify the meanings of the test method
types of apparatus and measuring instrument (sometimes the specific device) required to conduct the test
sampling procedures (how samples are to be obtained and prepared, as well as the sample size)
Test methods are often scrutinized for their validity, applicability, and accuracy. It is very important that the scope of the test method be clearly defined, and any aspect included in the scope is shown to be accurate and repeatable through validation.[4][7][9][10]
Test method validations often encompass the following considerations:[2][4][7][9][10]
accuracy and precision; demonstration of accuracy may require the creation of a reference value if none is yet available
^ abNigh, P.; Gattiker, A. (2000). Test method evaluation experiments and data. Proceedings from the International Test Conference, 2000. 2000. pp. 454–463. doi:10.1109/TEST.2000.894237. ISBN978-0-7803-6546-9.
^ abcdeBridwell, H.; Dhingra, V.; Peckman, D.; et al. (2010). "Perspectives on Method Validation: Importance of Adequate Method Validation". The Quality Assurance Journal. 13 (3–4): 72–77. doi:10.1002/qaj.473.
^"Glossary: S–Z". Understanding Science. University of California Museum of Paleontology. Retrieved 8 February 2018.
^ abOffice of Regulatory Science (12 May 2014). "5.4 Test Methods and Method Validation"(PDF). Laboratory Manual Of Quality Policies For ORA Regulatory Laboratories: Volume 1. U.S. Food and Drug Administration. Retrieved 8 February 2018.