Statistics in 10 minutes. Hypothesis testing, the p value, t-test, chi squared, ANOVA and more
Summary
TLDRThis script is an educational guide on hypothesis testing in statistics. It explains the concept of a null hypothesis and how statistical tests like the Z-test, T-test, ANOVA, and Chi-Square test work to determine if observed differences in a sample are statistically significant or due to chance. The speaker, Greg Martin, uses the example of a population of purple and yellow people to illustrate the process of testing hypotheses and interpreting P-values. He emphasizes the importance of understanding when to use each test and provides a cheat sheet for further reference.
Takeaways
- đ Understand the concept of sampling: When a full population is too large to measure, a sample is taken to infer about the whole population.
- đš Recognize the colors of the population: The example uses purple and yellow to represent different groups within the population.
- đ Learn about the null hypothesis: It is assumed that there is no difference in the population, which is what statistical tests try to disprove.
- â Grasp the significance of the Z-test: It calculates the probability of observing a sample result if the null hypothesis is true.
- đ Understand P-values: They represent the likelihood of observing the sample results if the null hypothesis is true.
- đ« Rejection of the null hypothesis: If the P-value is smaller than the predetermined alpha level, the null hypothesis is rejected, indicating a statistically significant result.
- đ Learn about different statistical tests: The script discusses T-Test, ANOVA, Chi-Square, and Correlation tests, each suited for different types of data and research questions.
- đ Greg Martin's educational resource: The speaker provides a cheat sheet and encourages learning more about statistics from his website.
- đ Accessing resources: Instructions are given on how to download a statistics cheat sheet from the website for further study.
- đ Apply statistical tests to real scenarios: Examples are given for each test to illustrate how they can be used to analyze data and draw conclusions.
Q & A
What is the purpose of taking a sample from a population in research?
-The purpose of taking a sample from a population is to estimate the characteristics of the entire population when it is impractical to measure every single individual.
What is the null hypothesis in the context of the purple and yellow people example?
-The null hypothesis in the example is that there is no difference in the population, meaning there are equal numbers of purple and yellow people.
How does the Z-test help in determining the likelihood of observing a sample with 90% purple people if the null hypothesis is true?
-The Z-test calculates the probability (P-value) of obtaining a result as extreme or more extreme than what was observed, assuming the null hypothesis is true. A small P-value indicates that it is unlikely to have observed such a sample by chance if the null hypothesis were true.
What is the significance of the P-value in statistical testing?
-The P-value indicates the probability of obtaining a result at least as extreme as the one observed, assuming the null hypothesis is true. A small P-value suggests that the observed difference is statistically significant and not likely due to chance.
What is the Alpha value in hypothesis testing, and how is it used?
-The Alpha value is a predetermined threshold used to determine the significance of the results. If the P-value is smaller than the Alpha value, the null hypothesis is rejected, indicating the results are statistically significant.
Can you explain the concept of hypothesis testing using the T-Test example provided in the script?
-In the T-Test example, the null hypothesis assumes no difference in the average weight between men and women in the population. The T-Test calculates the probability of observing the sample difference if this null hypothesis were true. A small P-value would lead to the rejection of the null hypothesis, suggesting a real difference exists.
What is the main difference between the T-Test and ANOVA?
-The main difference is that the T-Test compares the means of two groups, while ANOVA compares the means of three or more groups to determine if there are any statistically significant differences among them.
How does the Chi-Square test differ from the T-Test and ANOVA?
-The Chi-Square test is used with categorical variables, examining the relationship between two categorical variables to determine if there is a significant association between them, unlike the T-Test and ANOVA, which are used with numeric variables.
What is the purpose of the correlation test mentioned in the script?
-The correlation test is used to determine if there is a statistically significant relationship between two numeric variables, such as a correlation between age and weight.
How can one obtain the statistics cheat sheet mentioned by Greg Martin in the script?
-The statistics cheat sheet can be obtained by visiting Greg Martin's website, learnmore365.com, signing up for a free account, navigating to the free resources section, finding the statistics cheat sheet, and downloading it.
What is the advice Greg Martin gives at the end of the script regarding learning statistics?
-Greg Martin advises to get the basics right, understand the question being asked, and know how to use a particular test to answer that question, which will make understanding more complicated statistics easier.
Outlines
đ Understanding Hypothesis Testing
This paragraph introduces the concept of hypothesis testing in research, specifically focusing on determining the proportion of a certain characteristic within a population. The scenario involves a population of purple and yellow people, and the goal is to estimate the proportion of purple individuals without measuring every single person. A sample is taken, and it's observed that 90% are purple. The paragraph discusses the possibility of this result being due to chance and introduces the null hypothesis, which assumes no difference in the population (50-50 split). It explains the role of the P-value in a Z-test, which measures the probability of obtaining a result as extreme as the sample if the null hypothesis were true. A small P-value suggests that the observed difference is statistically significant, indicating it's unlikely to be due to chance alone. The concept of the Alpha value, which serves as a threshold to determine the significance of the P-value, is also introduced.
đ Exploring Different Statistical Tests
The second paragraph delves into various statistical tests, emphasizing the importance of understanding when to use each test. The speaker, Greg Martin, provides an overview of hypothesis testing and P-value interpretation without focusing on formulas. He introduces a cheat sheet available on his website, learnmore365.com, which can be accessed for free. The paragraph then discusses the application of the T-Test, which is used to determine if a difference observed in a sample, such as the average weight of men and women, is statistically significant or merely a chance occurrence. The paragraph also touches on ANOVA, which extends the T-Test concept to more than two categories, and the Chi-Square test, which is used for analyzing the relationship between two categorical variables. The correlation test, which examines the relationship between two numeric variables, is also mentioned. The speaker concludes by encouraging viewers to understand the basics of these tests to better grasp more complex statistical concepts.
Mindmap
Keywords
đĄPopulation
đĄSample
đĄProportion
đĄNull Hypothesis
đĄStatistical Test
đĄP-Value
đĄAlpha Value
đĄT-Test
đĄANOVA
đĄChi-Square Test
đĄCorrelation Test
Highlights
Exploring the proportion of purple people in a population without measuring every individual.
Using a sample to represent a larger population and the concept of representative sampling.
Observing 90% purple people in a sample and questioning if this could be due to chance.
Introducing the null hypothesis of equal numbers of purple and yellow people.
Performing a z-test to determine the probability of observing the sample results under the null hypothesis.
Defining the P-value as the probability of obtaining a result as extreme or more extreme than observed, assuming the null hypothesis is true.
The significance of a small P-value in rejecting the null hypothesis and concluding statistical significance.
Setting an Alpha value as the cutoff point to determine if the P-value is small enough to reject the null hypothesis.
Applying the principles of hypothesis testing and interpreting the P-value for various statistical tests.
Greg Martin's introduction and the availability of longer videos on statistics.
Accessing the statistics cheat sheet from Greg Martin's website, learn more 365.com.
Applying the T Test to determine if the observed difference in average weight between men and women is statistically significant.
Using the Anova test to analyze variances with more than two categories, such as the weight of people in different countries.
The difference between the T Test and Anova in terms of variable types and the questions they aim to answer.
Introducing the Chi-Square test for analyzing the relationship between two categorical variables, such as sex and height category.
The process of conducting a Chi-Square test and interpreting its P-value to determine the existence of a relationship.
Applying the correlation test to two numeric variables, like weight and age, to determine if there's a statistically significant correlation.
The final message encouraging viewers to always do their best and the promise of future content.
Transcripts
imagine that you have a research
question about a certain population this
is your population now the people in
your population are either purple or
yellow and you want to know what
proportion of the people are purple but
you don't have the time to measure the
color of every single person in the
population so instead you take a sample
of the population and determine the
color of those people hoping that what
you observe will be representative of
what's happening in The Wider population
and You observe that 90% of the people
in your sample are purple and 10% are
yellow but could this be just due to
chance might it be the case that there
are equal number of purple and yellow
people in your population and that you
just happened to by chance select a
sample with this extreme proportion of
purple people while of course this is
possible your intuition is that it's
unlikely or shall we say
improbable let's imagine that there is
in fact no difference that there are
equal numbers of purple and yellow
people and we're going to call this our
null hypothesis now you can perform a
statistical test and in this case it's a
z test and that's going to give you a P
value now the P value is the probability
of obtaining a result as extreme or more
extreme than what you've observed this
assumes the null hypothesis is true in
other words in this example if in the
population 50% of the people were in
fact purple what are the chances that
would get a random sample in which by
chance we found that 90% of the people
were purple it would be very unlikely
the probability would be low in other
words the P value would be very small so
if the P value is small then you can
reject the null hypothesis and conclude
that the difference observed in your
sample is statistically
significant but what do we mean by small
how small is small enough to reject the
null hypothesis before we do our
statistical test we decide on a cut off
and we call that our Alpha value so the
alpha value is the cutof point that you
compare your P value to to determine
whether the P value is small enough to
conclude that your results are un likely
to have occurred by chance now let's
take a look at how to apply the
principles of hypothesis testing and
interpreting the P value for the T Test
the kai Square test an NOA and the
correlation test we're going to take a
quick look at some of the more commonly
used statistical tests if you can
understand which tests to use when with
respect to these tests you'll find the
more complicated statistics much easier
to understand so get the basics right
you'll notice I'm not going to talk
about any formulas here I'm going to
talk about understanding the question
question that you're asking and how to
use a particular test to get an answer
to that question okay so let's Dive
Right In my name is Greg Martin I've got
longer videos on stats that you can
watch this is going to be a real quick
one but just so that you know what
you're seeing on the screen at the
moment is a cheat sheet that I've
created and we're going to talk through
the various bits and pieces there within
but you can get this PDF it's very easy
to get I'll just quickly show you how in
one second my website is learn more
365.com uh I'm signed in signing in is
for free of course you can create an
account for free click on free resources
that'll take you to the free resource
Library you could scroll down you can
filter the resources using these little
categories on the side so I'm going to
click on research and stats here has the
statistics cheat sheet click on download
and boom shakalaka there you go so let's
look at how we can apply the T Test in
this example right we've measured the
average weight of men and the average
weight of women in the sample that we've
got and we've seen that there's a
difference now that difference could be
real or it could just be by chance it
might just be a a fluke we may have
taken a sample that happens to have a
difference that's not really
representative of the wider population
so how do we decide the extent to which
we can have confidence in this sample
that we've got well we make an
assumption let's assume that there's no
difference in the real population right
that we can't really see we're not going
to measure everybody let's assume that
it's the case that in actual fact
there's no difference in the weight of
men and women in the population if that
were true How likely would it be that we
would have gotten a sample that shows
the difference that we've observed and
that is exactly what the T test will
tell you it'll tell you the probability
of by chance getting a sample that shows
this difference if it were the case that
in actual fact in reality there was in
fact no difference so if the P value is
very small we can say it's very unlikely
right because there's a small
probability that the null hypothesis is
true that there is no difference in the
weight of men and women so we can reject
it we can say we don't believe it we
don't have confidence in that idea and
if we can reject the null hypothesis we
then can accept that in actual fact in
the population from where the sample
came there is a difference in the weight
of men and women and that's how the tea
test Works easy peasy lemon squeezy
let's keep going boom shakalaka now
let's talk about the Anova kind of in
its simplest form this is the analysis
of varans essentially it's asking the
same kind of question as the T Test but
in this case you've got a categorical
variable with more than two categories
well you could do it for for two but for
two or more categories so let's say uh
We've looked at the weight of people in
three countries like America Britain and
Russia and in our sample population
we've observed that there is a
difference we conduct an anova test we
get a P value that tells us that if it
were the case that in actual fact the
weight of people in all three countries
was exactly the same it would be very
unlikely the P value
very unlikely that we would have seen
the difference that we did in our sample
so we can reject the null hypothesis and
we can accept the fact that there is a
difference does that make sense now the
Ki Square test is a little different and
the difference is because in the Ki
Square test you've got a different
combination of variable types right
you've got two categorical variables in
other words two variables in which the
data can be put into buckets in both
cases right for the T Test you had one
categorical variable in this case sex
male or female and the other variable
was numeric right so you had this
distribution which had a mean and
average for the Ki Square test you don't
have a numeric variable but you've got a
second categorical variable right so you
could still have sex male or female but
you could also have a second categorical
variable as in small uh medium height
and Tall right short short medium and
Tall so three categories once again and
as you can imagine for these categories
you can think of proportions right so
for short people there'll be a a certain
proportion of them will be men and a
certain proportion will be will be wom
male and female and for medium height
people a certain proportion will be men
and a certain proportion will be women
right so you've got these proportions
that you get from these categorical
variables and now once you understand
that these are the two variables we've
got after that everything about what
we're going to do in terms of
inferential statistics is exactly the
same as the T Test in Anova right we're
going to say we've taken a sample and
we've seen a difference we've seen that
there's some sort of association between
sex and and height category and we're
asking the question is that Association
real is it statistically significant or
is it the case that we happened to by
chance take a sample that represented
that sort of difference but in actual
fact in the population that difference
doesn't really exist so we make the
Assumption we have a null hypothesis we
let's make the assumption that in actual
fact in The Wider population from where
the sample came there's no relationship
between sex and height category that
that the proportions all exactly equal
we do the Ki Square test and it gives us
the P value if the P value is very very
small it means that we cannot have
confidence it's very unlikely that that
null hypothesis is true it's unlikely
that if it were the case that there's no
association between sex and height
category it's unlikely that we would
have gotten the sample that we did with
the differences that we saw so we can
reject that we reject the null
hypothesis and we accept the fact that
in actual fact there is some sort of an
association between six and height
category got it easy peasy lemon squeezy
let's keep going boom shakalaka and for
the correlation test the exact same
principles apply in this case again
we've got a difference in the type of
variable that we've got we've got two
numeric variables right so let's imagine
we've got weight and age both of them
are numeric variables no categorical
variables and if you got two numeric
variables you can imagine that there
could be an observed association between
the two as age goes up weight goes up
right you can imagine that there's a
correlation so we take a sample of data
in our observation we see a correlation
and we ask the question is that real is
it statistically significant or might it
be the case that there's no correlation
and that by chance we happen to get a
sample in which erroneously this
correlation seem to exist so we do a
correlation test once again we get a P
value the P value tells us that uh if
the P value is very small we cannot
accept the assumption that there's no
correlation and we must accept the fact
that there is in fact some sort of
correlation between the two numeric
variables right so uh there'll be a link
on the screen that you can click on so
that you can get uh this cheat sheet and
have a look at it in your own time
thanks for watching don't ever change
don't do drugs always do your best boom
shakalaka speak to you soon take care
bye
Voir Plus de Vidéos Connexes
Uji Hipotesis part 2 (Prosedur Pengujian Hipotesis, Statistik Uji, Wilayah Tolak/ Kritis)
Hypothesis Testing In Statistics | Hypothesis Testing Explained With Example | Simplilearn
Hypothesis Testing - One Sample Proportion
How to Perform and Interpret Independent Sample T-Test in SPSS
How To Know Which Statistical Test To Use For Hypothesis Testing
Statistical Significance versus Practical Significance
5.0 / 5 (0 votes)