Stats: Hypothesis Testing (P-value Method)
Summary
TLDRThis video script introduces the P Value method of hypothesis testing, contrasting it with the traditional method. It explains the fundamental concepts of hypothesis testing, including the null and alternative hypotheses, and the significance level (Alpha). The script clarifies that regardless of the method, a test statistic is calculated. The P Value method stands out by not using critical values, instead comparing the calculated P Value directly to Alpha to decide whether to reject the null hypothesis. The video uses a practical example of push pins to illustrate left, right, and two-tail tests, emphasizing that a low P Value (less than Alpha) leads to the rejection of the null hypothesis, while a high P Value (greater than Alpha) results in failing to reject it.
Takeaways
- 🔍 Hypothesis testing involves comparing two types of hypotheses: the null hypothesis (H₀) and the alternative hypothesis (H₁).
- 📉 The null hypothesis always includes an equal sign, suggesting no difference or a specific value.
- 📈 The alternative hypothesis uses a different symbol, such as 'less than', 'greater than', or 'not equal to', indicating a deviation from the null hypothesis.
- 🎯 The level of significance, denoted by Alpha (α), is a predetermined threshold used to determine the outcome of the hypothesis test.
- 📊 Hypothesis tests can be categorized into left-tail, right-tail, or two-tail tests based on the alternative hypothesis.
- 📚 The choice of test (left, right, or two-tail) depends on the wording of the claim or research question.
- 📉 The traditional method of hypothesis testing uses critical values to make a decision, whereas the P-value method does not.
- 📈 The P-value method involves calculating a test statistic and comparing the resulting P-value to the level of significance (α).
- 📝 A test statistic is calculated using specific formulas depending on the type of data and hypothesis test being conducted.
- 🔑 If the P-value is less than α, the null hypothesis is rejected, indicating support for the alternative hypothesis.
- 🔒 If the P-value is greater than α, the null hypothesis is not rejected, which means there is insufficient evidence to support the alternative hypothesis.
Q & A
What are the two types of hypotheses in hypothesis testing?
-The two types of hypotheses in hypothesis testing are the null hypothesis (often denoted as H₀ or Hₙ) and the alternative hypothesis (often denoted as H₁ or Hₐ).
What does the null hypothesis typically represent in hypothesis testing?
-The null hypothesis typically represents a statement of no effect or no difference, often using an equal sign (e.g., μ = 100), which is assumed to be true unless the evidence strongly suggests otherwise.
How is the alternative hypothesis represented in hypothesis testing?
-The alternative hypothesis is represented using a symbol that is not an equal sign, such as less than (<), greater than (>), or not equal to (≠), indicating a deviation from the null hypothesis.
What is the significance level, or Alpha, in hypothesis testing?
-The significance level, or Alpha, is the probability of rejecting the null hypothesis when it is actually true. Common values for Alpha are 0.01, 0.05, and 0.10.
What are the different types of tail tests in hypothesis testing?
-The different types of tail tests are left-tail, right-tail, and two-tail tests, which depend on the directionality of the alternative hypothesis (less than, greater than, or not equal to, respectively).
What is the purpose of a test statistic in hypothesis testing?
-A test statistic is a numerical value calculated from the sample data, which is used to determine the likelihood of obtaining the observed sample results under the null hypothesis.
How does the P-value method differ from the traditional method in hypothesis testing?
-The P-value method does not use critical values like the traditional method. Instead, it compares the P-value, which is the probability of observing the test statistic or more extreme results, to the significance level (Alpha) to decide whether to reject the null hypothesis.
What is the P-value and how is it used in hypothesis testing?
-The P-value is the probability of obtaining results at least as extreme as the observed results, assuming the null hypothesis is true. It is used to compare with the significance level (Alpha); if the P-value is less than Alpha, the null hypothesis is rejected.
What does it mean to reject the null hypothesis in hypothesis testing?
-Rejecting the null hypothesis means that there is enough evidence to suggest that the alternative hypothesis is true, indicating a significant effect or difference from what was assumed in the null hypothesis.
What does it mean to fail to reject the null hypothesis in hypothesis testing?
-Failing to reject the null hypothesis means that there is not enough evidence to support the alternative hypothesis, and thus the null hypothesis remains the best explanation for the observed data.
How can the concept of a 'push pin' package be used to illustrate a hypothesis test?
-The 'push pin' package example illustrates a situation where the null hypothesis might be that there are 100 push pins in the package. If one suspects there are fewer (a left-tail test) or more (a right-tail test), or simply not 100 (a two-tail test), the hypothesis test would be conducted to determine if there is enough evidence to reject the null hypothesis.
Outlines
🔍 Introduction to Hypothesis Testing with P-Value Method
The video script introduces the concept of hypothesis testing, focusing on the P-Value method as opposed to the traditional method. It explains the fundamental aspects of hypothesis testing, emphasizing the two types of hypotheses: the null hypothesis (H₀), which is always stated with an equal sign, and the alternative hypothesis (H₁ or Hₐ), which uses a symbol other than an equal sign to represent different scenarios. The script also introduces the concept of the level of significance, denoted by Alpha (α), which is a critical threshold in hypothesis testing. It further explains the types of alternative hypotheses related to the direction of the test: less than for a left-tail test, greater than for a right-tail test, and not equal to for a two-tail test. The importance of understanding these concepts is highlighted through a practical example involving a package of push pins, where the number of pins is compared to the expected 100, illustrating how the choice of hypothesis affects the type of test conducted.
📊 Understanding the P-Value Method in Hypothesis Testing
This paragraph delves deeper into the P-Value method of hypothesis testing, contrasting it with the traditional method that uses critical values. The P-Value method disregards critical values and instead focuses on calculating the test statistic from given formulas, which could relate to proportions, means, or other statistical measures. The test statistic is then used to find the P-Value, which represents the area in the tail of the distribution corresponding to the test statistic. The script provides an example of a right-tail test with a test statistic of 2.61 and a P-Value of 0.0045. It explains the decision-making process in hypothesis testing: if the P-Value is lower than the predetermined level of significance (Alpha), the null hypothesis is rejected, supporting the claim of the alternative hypothesis. Conversely, if the P-Value is higher than Alpha, the null hypothesis is not rejected, indicating insufficient evidence to support the alternative claim. The script concludes by reiterating the importance of the P-Value in hypothesis testing and the implications of its comparison with Alpha for accepting or rejecting the null hypothesis.
Mindmap
Keywords
💡Hypothesis Testing
💡Null Hypothesis (H0)
💡Alternative Hypothesis (H1 or Ha)
💡P-value
💡Level of Significance (Alpha)
💡Test Statistic
💡Critical Value
💡One-Tailed Test
💡Two-Tailed Test
💡Rejection Region
💡Type I and Type II Errors
Highlights
Introduction to the P Value method for hypothesis testing, an alternative to the traditional method.
Explanation of the two types of hypotheses: null hypothesis (H0) and alternative hypothesis (H1 or Ha).
The null hypothesis always uses an equal sign, while the alternative hypothesis uses a different symbol.
Introduction of Alpha, the level of significance in hypothesis testing.
Three popular levels of significance: 0.01, 0.05, and 1%.
Different types of alternative hypotheses: less than, greater than, or not equal to.
Tail tests: left tail, right tail, and two-tail tests based on the alternative hypothesis.
Practical example using a package of push pins to illustrate left and right tail tests.
The importance of the wording of the alternative hypothesis in determining the type of test.
Comparison between the traditional method and the P Value method for hypothesis testing.
The P Value method does not use critical values, unlike the traditional method.
Process of finding the test statistic for both traditional and P Value methods.
Explanation of how to calculate and interpret the P Value in hypothesis testing.
The P Value is the area under the curve that is more extreme than the test statistic.
Comparing the P Value to the level of significance (Alpha) to make a decision.
If the P Value is lower than Alpha, the null hypothesis is rejected.
If the P Value is higher than Alpha, the null hypothesis is not rejected (fail to reject).
The implications of rejecting or failing to reject the null hypothesis in terms of supporting the alternative hypothesis.
Clarification of the terminology used in hypothesis testing: reject, fail to reject, and support the claim.
Transcripts
all right in this video I want to show
you the basics of hypothesis testing for
the non-traditional method or the P
Value method to be more specific all
right the P Value method I have shown in
a separate video um the basics of
hypothesis testing using the traditional
method so there are two different kinds
um actually probably more than two but
I'm only showing you two in my videos so
real quickly here the basics of
hypothesis testing no matter what method
you're using traditional or P value is
that there there are going to be two
types of hypotheses right there's the
null hypothesis and there's the
alternative
hypothesis let's see almost every book
I've used uses H subz or H KN as the
null hypothesis and no matter what uh
parameter you're talking about whether
it's a PO uh whether it's a proportion
or a mean or a standard deviation the
null hypoth hthis always uses an equal
sign right it always has an equal sign
in it the alternative hypothesis maybe
your book uses H sub one or H sub a
whatever the case may be always use as a
symbol that is not an equal sign right
so in this case it's a less than symbol
or a greater than symbol or a not equal
to symbol but no matter what type of
hypothesis testing it is you will always
be given some level of significance here
okay so whether it's 01 or 05 or P
something like that now that level of
significance is called Alpha right it's
called Alpha which is the Greek uh
lowercase letter A here that's the first
letter of the Greek alphabet so so and
we're not restricted to 015 or 10% or
something like that it could be any
other type of level of significance but
these are the three more popular
ones okay the other thing I want to tell
you about and keep your eye on these
three alternative hypotheses here right
so less than greater than or not equal
to is depending on what kind of a test
we're talking about you might have a
left tail test a right tail test or a
two-tail test and that all depends on
the alternative hypothesis all right so
I'm using H sub one as my alternative
hypothesis notation here but if the
alternative hypothesis is less than we
have a left tail test if it's greater
than we have a right tail test or if
it's not equal to we have a two-tail
test we have two tail test so that is
also important and significant here and
what do I mean by that I didn't show
this in my previous video but for
example here let's say I've got let's
see I got a little package here of push
pins can you guys see that I think you
can see that in the video here now all
right and it says that there should be
100 push pins in here now if I think I
got jipped right and they're probably
I'm thinking they're putting less than
100 push pins in there then less than
would be a left tail test all right or
maybe I'm thinking there being generous
as I buy these push pins and they're
actually putting more than 100 in well
more than would be a right tail test
greater than okay where if I State the
claim right all of these are claims here
if I State the claim as um I don't think
they're putting 100 in there right
notice I'm not specifying when I say I
don't think they're putting 100 in there
I believe there aren't 100 in there I'm
not specifying whether it's less than
100 or greater than 100 so in that case
it would be a two-tail test so depending
on the wording that you see um it could
be one of those types of alternative
hypotheses or claims okay so what I
showed again in a previous video you
could look it up is the traditional
method and what I'm going to show you in
this video is the P Value method right
but notice I wrote on this little piece
of paper here that both methods doesn't
matter which method you're using both
method methods require you to find a
test statistic so both meth methods use
a test statistic whether your test
statistic is is uh is with proportions
that would be P hat minus p over the
square < TK of uh Little P * Q Over N or
maybe you're you're dealing with with uh
sample means and population means and so
your test statistic would be with this
formula here so you probably are
familiar with those formulas okay but
regardless of the method both of them
use test statistics okay so what the P
value does
separately from the traditional method
is this all right the traditional method
uses something called critical
values right I'll just put this on here
real quick the traditional method so
traditional method uses something called
critical values well guess what and I'm
going to cross that out the P Value
method does not use that at all all
right P Value method says look I don't
really care about the critical value
whatsoever so that's kind of a nice
little thing here so let's say that for
example we were dealing with a right
tail test right so I'll draw a little
right tail here right so let's say for
example we were dealing with the right
tail test that's our um H sub one is a
greater than then what the P value says
is this all right what the P value says
is this what we're going to do is we're
going to find using uh the formulas that
I just showed you a second ago we're
going to
find put here find we're going to find
our test
statistic all right we're going to find
our test statistic using that formula
you just saw in the previous page and
then we're going to put that in I'm
going to write this as uh how about TS
all right test for statistic we're going
to we're going to put that in here and
let's this is a right tail
test um let's say our test statistic
here I don't know I'm just kind of
making something up but let's say our
right our test statistic came out to be
something like uh how about
-
2.61 for example all right sorry
positive this is on the right hand side
so let's say our test statistic came out
to
2.61 okay so for example here 2.61 now
do you see that um this area the area
sitting over here to the far right of
this is
0.0045 okay you can look that up this
area is
0.0045 right it's
0045 and you can look that up on a table
if you want to or you can use um Excel
to figure that that area out but here's
here's the here's the deal that area is
what's called our P value all right so
this area is the P value now all right
so the area sitting over here to the
right in this case of a test statistic
is our P value okay so that area in this
case
0045 is our P value that we are going
going to compare right we're going to
compare the P
value to our Alpha to our level of
significance and that's how P value uh
method or the testing works so in our
case I have a P value
0.0045 and let's say that we had an
alpha let's say that we were looking for
a level of significance of
0.001 for example I don't know we'll
pick on 0.01 all right so our Alpha our
P value is sitting right here our Alpha
is sitting right here of
0.01 and as you compare these two do you
notice that this one here our P value is
less than
01 all right and there's a phrase that
goes along with this if the P value is
low right low lower than my Alpha my
level of significance then the null must
go so we're going to take the null
hypothesis and we're going to reject it
right we're going to reject it what if
though let's just say for instance what
if our P value was greater than our
Alpha right I know this is not the case
in this particular case but let's say we
had a P value of
0.0
28 n or something like that all right
and in this particular case look our
Alpha I mean our P value rather would be
bigger than our Alpha of 0.01 so if this
is the case if your if your P value is
high right is larger than your Alpha
then the null must fly so we're going to
keep all right the null
hypothesis so hypothesis testing is all
about the null we either reject it or we
in my case I put keep here but
technically ter the term is we fail to
reject okay so this is a reject here if
the uh P value is low and if the P value
is high then the null must fly what
we're really doing is we are really
failing to reject that's what's going on
here when I say the words keep okay
we're failing to reject so if the null
is if the P value is low the null must
go if the P value is high the null flies
and what that really means is if we
reject the null hypothesis what we're in
essence saying is we
support the claim of the alternative
hypothesis all right if we keep the null
hypothesis what we're in essence saying
is this may be true therefore we don't
have enough evidence to support our
claim right so the wording of this is
pretty tricky you've got to get your
mind around that as well but this is how
P value testing works
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