Statistics in 10 minutes. Hypothesis testing, the p value, t-test, chi squared, ANOVA and more

Summary

This 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

• 🔍 Understand the concept of sampling: When a full population is too large to measure, a sample is taken to infer about the whole population.
• 🎨 Recognize the colors of the population: The example uses purple and yellow to represent different groups within the population.
• 📊 Learn about the null hypothesis: It is assumed that there is no difference in the population, which is what statistical tests try to disprove.
• ✅ Grasp the significance of the Z-test: It calculates the probability of observing a sample result if the null hypothesis is true.
• 📉 Understand P-values: They represent the likelihood of observing the sample results if the null hypothesis is true.
• 🚫 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.
• 📈 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.
• 📚 Greg Martin's educational resource: The speaker provides a cheat sheet and encourages learning more about statistics from his website.
• 🔗 Accessing resources: Instructions are given on how to download a statistics cheat sheet from the website for further study.
• 📋 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

00:00

🔍 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.

05:02

📊 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.

Keywords

💡Population

In the context of the video, 'population' refers to the entire group of individuals or items that are the subject of the research. The script discusses a hypothetical scenario where the population consists of people who are either purple or yellow. The concept is crucial as it sets the stage for understanding sampling and statistical inference. The video aims to explain how researchers use samples to make inferences about the larger population.

💡Sample

A 'sample' is a subset of the population selected for the purpose of study. The script mentions taking a sample to determine the color of individuals in the population, as measuring every single person is impractical. The concept of a sample is fundamental to statistical analysis because it allows researchers to make inferences about a larger population based on a smaller, more manageable group.

💡Proportion

The 'proportion' refers to the share or part of a whole, often expressed as a percentage. In the script, the researcher is interested in the proportion of purple people in the population. The video uses the example of observing that 90% of the sample are purple to illustrate how proportions can be used to make inferences about the population.

💡Null Hypothesis

The 'null hypothesis' is a fundamental concept in statistics. It represents the assumption that there is no significant relationship between the variables being studied, or no difference between groups. The script introduces the null hypothesis as the starting point for statistical testing, suggesting that there is no difference in the number of purple and yellow people in the population.

💡Statistical Test

A 'statistical test' is a method used to determine if a result from a sample is statistically significant. The video explains how a Z-test can be used to calculate the probability of obtaining a sample result as extreme as the one observed, assuming the null hypothesis is true. This helps to decide whether the observed differences are likely due to chance or represent a real effect.

💡P-Value

The 'P-value' is the probability of obtaining a result at least as extreme as the one observed, assuming the null hypothesis is true. The script uses the P-value to determine the likelihood of observing a sample with 90% purple people if the null hypothesis (equal numbers of purple and yellow people) were true. A small P-value suggests that the observed difference is statistically significant.

💡Alpha Value

The 'alpha value' is a predetermined threshold used to decide whether the results of a statistical test are significant. If the P-value is lower than the alpha value, the null hypothesis is rejected. The script mentions choosing an alpha value before conducting a statistical test to determine the cut-off point for what is considered statistically significant.

💡T-Test

A 'T-Test' is a type of statistical test that compares the means of two groups to see if there is a significant difference between them. The script uses the T-Test as an example to explain how to determine if the difference in average weight between men and women in a sample is statistically significant or could be due to chance.

💡ANOVA

ANOVA (Analysis of Variance) is a statistical test used to compare the means of three or more groups. The script mentions ANOVA in the context of comparing the average weight of people from three different countries. It helps determine if the observed differences are statistically significant or could be due to chance.

💡Chi-Square Test

The 'Chi-Square Test' is used to determine if there is a significant association between two categorical variables. The script explains how the Chi-Square Test can be used to test for an association between sex and height category, which are both categorical variables. It helps to determine if the observed association in the sample is statistically significant.

💡Correlation Test

A 'Correlation Test' is used to measure the strength and direction of a linear relationship between two numeric variables. The script uses the example of weight and age to illustrate how a correlation test can determine if there is a statistically significant relationship between the two variables in the population.

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