Statistics made easy ! ! ! Learn about the t-test, the chi square test, the p value and more

Summary

This script offers a simplified approach to learning statistics by focusing on practical thinking rather than complex formulas. It introduces common statistical questions and explains how to analyze sample data to identify differences between groups and relationships between variables. The video covers summarizing and visualizing data, selecting appropriate statistical tests, and interpreting results. It also discusses the importance of defining hypotheses and choosing an alpha value before analyzing data. Examples include t-tests, chi-square tests, and correlation tests, emphasizing the significance of statistical findings in understanding population characteristics.

Takeaways

• 📊 **Understanding Statistics**: The script emphasizes a simplified approach to learning statistics by focusing on thought processes rather than complex formulas and theories.
• 🔍 **Analyzing Sample Data**: It discusses the common tasks in statistics, which include identifying differences between groups and relationships between variables within sample data.
• 🤔 **Questioning Realness**: The script raises the question of whether observed differences and relationships in sample data are 'real' and how to define this term.
• 📈 **Data Variables**: It explains the importance of understanding the two types of variables in datasets: categorical (like gender) and numeric (like height).
• 📋 **Summarizing Data**: The script outlines methods for summarizing data, such as counting observations for categorical data and calculating median, mean, and standard deviation for numeric data.
• 📊 **Visual Representation**: It describes how to visualize data using tables, bar charts, box plots, and histograms to better understand the distribution and central tendencies.
• 🧐 **Combining Variables**: The script explores analyzing combinations of variables to uncover specific differences or relationships, such as comparing average heights between genders.
• 📚 **Statistical Tests**: It introduces the concept of applying statistical tests to determine if sample observations can be generalized to the wider population.
• 🔑 **Hypothesis and Null Hypothesis**: The script stresses the importance of defining a hypothesis and a null hypothesis before analyzing data, along with setting an alpha value to determine statistical significance.
• 📝 **Research Questions**: It provides examples of how to form research questions based on the type of variables involved, such as comparing a single numeric variable to a theoretical value or examining the relationship between two numeric variables.
• 🔗 **Sponsorship Acknowledgement**: The script includes a thank you note to Biomed Central (BMC) for sponsoring the video and briefly discusses the importance of open access journals.

Q & A

What is the main focus of the video script?

The main focus of the video script is to simplify the learning of statistics by introducing a way of thinking that enables addressing common statistical questions when analyzing sample data.

What are the two primary types of variables typically found in data sets?

The two primary types of variables typically found in data sets are categorical variables (like gender) and numeric variables (like height).

How does the script suggest summarizing categorical data?

The script suggests summarizing categorical data by counting the number of observations in each category and representing them in a table and on a bar chart.

What are the key summary measures for numeric data mentioned in the script?

The key summary measures for numeric data mentioned in the script include the range, interquartile range, standard deviation, median, and mean.

What visualization tools are suggested for numeric data?

The script suggests using box plots and histograms as visualization tools for numeric data.

What is the significance of the term 'real' in the context of the script?

In the context of the script, the term 'real' refers to whether the observed differences or relationships in sample data are statistically significant and can be inferred to represent the wider population.

What is the role of statistical tests in analyzing data according to the script?

Statistical tests play a role in determining if the observed differences or relationships in sample data are statistically significant and can be generalized to the wider population.

What is the significance of the alpha value in statistical analysis as discussed in the script?

The alpha value is significant in statistical analysis as it represents the probability threshold below which the null hypothesis is rejected, indicating that the observed difference is statistically significant.

What is the null hypothesis and how is it used in the script?

The null hypothesis is a statistical assumption that there is no effect or difference. In the script, it is used as a baseline to compare against observed data, and if the observed data is unlikely under the null hypothesis, it can be rejected.

How does the script explain the process of analyzing data with one categorical variable?

The script explains that with one categorical variable, such as gender, a one-sample proportion test can be conducted to determine if there is a statistically significant difference in proportions between groups.

What is the purpose of the chi-square test as mentioned in the script?

The purpose of the chi-square test, as mentioned in the script, is to determine if there is a statistically significant association between two categorical variables.

How does the script describe the process of analyzing two numeric variables?

The script describes the process of analyzing two numeric variables by using a correlation test to determine if there is a statistically significant relationship between the variables, as indicated by the correlation coefficient and the p-value.

Outlines

00:00

📊 Introduction to Statistical Thinking

The script begins by simplifying the approach to learning statistics, emphasizing a conceptual understanding over complex formulas. It discusses the examination of sample data to identify differences between groups and relationships between variables. The speaker introduces the concept of determining whether observed differences and relationships are 'real'. A hypothetical scenario involving the height and weight of people in Ireland is used to illustrate the process of analyzing a dataset with variables such as gender and age group. The script explains the importance of summarizing and visualizing data to make it more interpretable, including the use of tables, bar charts, box plots, and histograms. The goal is to transform raw data into meaningful insights.

05:01

🔍 Hypothesis Testing and Statistical Significance

This section delves into the process of hypothesis testing, starting with defining a research question and hypothesis. It underscores the importance of setting a null hypothesis and an alpha value before analyzing data. The speaker uses the example of gender distribution to explain how to apply a one-sample proportion test. The concept of statistical significance is introduced, discussing p-values and the decision to reject or fail to reject the null hypothesis based on the alpha value. The script also covers the chi-square test for comparing categorical variables and the t-test for numeric variables, providing a framework for determining if observed differences are statistically significant.

10:02

📈 Advanced Statistical Analysis Techniques

The final paragraph explores more complex statistical analyses involving multiple variables. It discusses how to analyze a single numeric variable against a theoretical value using a t-test and how to use ANOVA for comparing means across multiple categories. The script then introduces the concept of correlation between two numeric variables, explaining the use of the correlation coefficient to measure the strength and direction of a relationship. The speaker emphasizes the importance of statistical tests in determining if observed correlations are statistically significant. The section concludes with a brief mention of resources for further learning in statistical analysis and programming for statistical purposes.

Keywords

💡Statistics

Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data. In the video, the presenter aims to simplify the learning of statistics by focusing on a way of thinking rather than complicated formulas, which is central to understanding the data presented.

💡Sample Data

Sample data refers to a subset of a larger population that is used to represent the whole for the purpose of research or analysis. The video emphasizes the examination of sample data to observe differences between groups and relationships between variables, which is a common practice in statistical analysis.

💡Categorical Variables

Categorical variables are variables that can take on one of a limited number of possible values, which are usually words or categories. In the script, gender is given as an example of a categorical variable, which is used to group data for analysis.

💡Numeric Variables

Numeric variables are variables that represent quantities or numerical values. Height is used as an example in the video, where numeric variables are analyzed for their distribution, range, and relationships with other variables.

💡Statistical Tests

Statistical tests are methods used to determine if a result from sample data is statistically significant. The video discusses various tests like t-tests and ANOVA, which are used to analyze the sample data and infer about the larger population.

💡Hypothesis

A hypothesis is a proposed explanation for a phenomenon, which can be tested through experimentation or further research. The video script mentions defining a hypothesis before analyzing data, which is a fundamental step in the scientific method.

💡Null Hypothesis

The null hypothesis is a default position that there is no relationship between the variables being studied, used especially in statistics. The video explains that one must consider the null hypothesis and calculate the probability of observing the sample results if it were true.

💡P-Value

The p-value is the probability of obtaining results at least as extreme as the ones observed, assuming that the null hypothesis is true. The video script discusses calculating the p-value to determine the significance of observed differences in the sample data.

💡Alpha Value

The alpha value is the level of statistical significance used to determine whether to reject the null hypothesis. In the video, an alpha value of 0.05 is used as the threshold to decide if the observed difference is statistically significant.

💡Correlation

Correlation measures the extent to which two variables are linearly related. The video discusses the use of a correlation test to determine if there is a relationship between two numeric variables, such as height and weight.

💡Correlation Coefficient

The correlation coefficient is a statistic that measures the strength and direction of a linear relationship between two variables. The video explains that it ranges from -1 to 1, with -1 indicating a perfect negative correlation, 1 a perfect positive correlation, and 0 no correlation.

Highlights

Learning statistics can be simplified by focusing on a way of thinking rather than complex formulas and theories.

Statistical analysis often involves looking at differences between groups and relationships between variables.

The key question in statistics is determining whether observed differences and relationships are real.

A simple dataset can reveal specific differences between groups and relationships between variables.

Statistical tests should be used to interpret results and determine if sample data implies anything about the wider population.

Data sets typically contain categorical and numeric variables, which are summarized and visualized for analysis.

Categorical variables are grouped into categories, while numeric variables are measured on a numerical scale.

Summarizing data involves counting observations for categorical data and describing distribution for numeric data.

Visual representations like bar charts, box plots, and histograms help in understanding data distribution and central tendencies.

Combining variables can reveal interesting insights, such as differences in average height between genders.

Statistical tests are chosen based on the type of variables involved, such as t-tests for numeric variables or chi-square tests for categorical variables.

The process of hypothesis testing involves defining a null hypothesis, selecting an alpha value, and calculating a p-value.

A low p-value (less than the alpha value) indicates that the observed difference is statistically significant.

The correlation coefficient measures the strength and direction of the relationship between two numeric variables.

A correlation coefficient of -1 to 1 indicates the degree of linear relationship, with -1 being perfectly negative and 1 being perfectly positive.

The video is sponsored by Biomed Central, a publisher of open access journals.

The speaker is the editor-in-chief of one of Biomed Central's journals, 'Globalization and Health'.

The speaker emphasizes the importance of defining research questions and hypotheses before analyzing data.

The video provides an overview of the five most important combinations of data types and the corresponding statistical tests.

The speaker offers additional resources for learning more about statistical analysis and programming languages for statistics.

Transcripts

learning statistics does not need to be

difficult

now instead of bombarding you with a

complicated formula and statistical

theory I'm gonna walk you through a way

of thinking and that's gonna enable you

to address the most common statistical

questions when we look at sample data

for the most part we see two things we

see differences between groups so men

are taller than women and we see

relationships between variables like

taller people way more than shorter

people committed and the big question is

are those differences and are those

associations or relationships real and

I'm going to talk you through what it is

that we mean by the term real over the

next few minutes we're going to take a

look at a very simple data set and we're

gonna see how by looking at various

combinations of variables and variable

traps we can identify very specific

differences between groups and very

specific relationships between variables

and I'm gonna walk you through when and

how to use statistical tests and how to

interpret your results now let's imagine

that we have a research question and

it's about the height and the weight of

people living in Ireland of course we

can't measure the height in the weight

of the entire population so instead we

take a random sample of the population

and we measure the weight and the height

of that sample and we clicked some

additional information like gender and

age group from each of the people in our

sample and we arranged these data in a

spreadsheet or data set with the various

attributes in columns and these are

called variables and these variables

will be the object of our inquiry

[Music]

now most data sets that you work with

will contain two types of variables

categorical and numeric variables

categorical variables like gender

content categories as the name suggests

think of them as groups or buckets that

the data can be arranged into in this

case males and females numeric variables

like height on numbers as the name

suggests and can be arranged on a number

line now to better understand our data

and to make sense of it we summarized it

and we visualize it in the case of

categorical data we can count up the

number of observations in any given

category and we can represent them in a

table and on a bar chart and to

summarize numeric data we firstly

interested in the spread

the distribution of the data so we might

describe the range of the data the

interquartile range we could also

include the standard deviation to get a

sense of the middle of the data we use

the median which divides the doctor into

two equal halves and we use the mean

which is the average the mean is

probably the most commonly used summary

value to represent this kind of data we

can visualize that data using a box plot

which is a visual representation of the

range the interquartile range and the

median and of course we can create a

histogram and this gives us the shape of

the data so I hope you can see that this

process of summarizing and visualizing

the data takes it from being just

numbers and words on a spreadsheet and

turns it into something that is

meaningful to us something that we can

get our heads around something that we

can think about now in this very simple

data set we've got two categorical and

two numeric variables and things start

to get interesting when we start looking

at combinations of variables so for

example we can take a look at a

categorical and a numeric variable like

gender and height and so we can group

the data by gender which is the

categorical variable and create a

summary of the numeric variable in this

case height that is separated out into

those two groups and looking at the

summary we can see that in our sample

data men are on average taller than

women what I want you to see here is

that we've looked at a combination of

the categorical and a numeric variable

but as you can imagine there are other

possible combinations of variables that

we could have looked at we could have

looked at height and weight which are

both numeric we could have looked at

gender and age group both categorical

and in each case we might see either

differences between groups or

relationships between variables and in

each of these cases there are specific

statistical tests that we can apply to

see if what we are seeing in the sample

data has implications for what we think

about the wider population can we infer

anything is what we are seeing

statistically significant so let's take

a quick look at the five most important

combinations of data that we have and

we'll look at firstly what might we

observe in our sample data given that

sort of combination of data types and

secondly what statistical test we might

apply to determine whether or not we can

infer anything about the wider

population so we might look at a single

categorical variable like gender and we

could do a one sample proportion taste

for two categorical variables we would

do a chi-square test for a single

numeric

with the t-test if we have a categorical

and a numeric variable we do a t-test or

analysis of variance or ANOVA if there

are more than two categories in a

categorical variable and for two numeric

variables we do a correlation test now

I'm going to come back to each of these

scenarios in each of these tests so

don't panic at this point what I want

you to see is how the data can be

divided up and in just a few minutes

we're going to take each of these

scenarios and work through exactly what

questions you can ask and how it is that

you can apply statistical tests and

importantly how to interpret your

results now before we carry on I just

want to say a big thank you to biomed

central or BMC for sponsoring this video

BMC are a publishing company that

published open access journals and that

means that the full-text of all of the

papers published are available for free

to anyone in the world I'm the

editor-in-chief of one of the journals

that they publish called globalization

and health and genuinely impressed with

them as a company I believe that they

have integrity and I honestly believe

that they are making the world a better

place they have a portfolio of over 300

journals that they publish so check them

out at biomed central com I'll put a

link in the description below

at this point I want to say this it's

not good science to take a data set and

just randomly stab around blindly hoping

to find something that's statistically

significant

before you interrogate the data you

start off by defining your question your

hypothesis you define your null

hypothesis you identify the alpha value

that you're going to use and then you

analyze the data so let's look at what

we can do with just one categorical

variable like gender we might ask the

question is there a difference in the

number of men and women in the

population now we could state that as a

hypothesis which is that there is a

difference between the number of men and

women in the population and we could

check to see whether or not we think

that that is the case and when we look

at our sample data well we do in fact

see that there's a difference in the

proportion of men and women so should we

get excited well no not yet

remember this is just sample data we

could have by chance selected a sample

that just happened to show a difference

so let's consider the possibility that

in actual fact there is no difference in

the number of men and women in the

population and we call that our null

hypothesis and if that were true how

likely would it be what

the chances what is the probability that

we would see the difference that we have

observed or greater difference for that

matter and if we can show that that

probability is low then we can have a

degree of confidence that the null

hypothesis is wrong and we can reject it

but before we calculate this probability

which we're going to call our p-value we

must be clear about how small is small

enough below what value of P would we

reject the null and we must decide on

that cutoff before we calculate the

p-value and we call that cutoff the

alpha value and for the rest of the

examples in this video we're going to

use an alpha value of point zero five or

five percent so we've really got two

scenarios we've got the null hypothesis

which is that there's no difference and

the alternative hypothesis which is that

there is a difference and the next step

is to apply a statistical test and in

this case we're doing one sample

proportion test and we generate a

p-value if the P is less than the alpha

then we can reject the null hypothesis

and state that the difference that we

observe is statistically significant if

we add another categorical variable in

this case age group we may have a

research question like does the

proportion of males and females differ

across these groups so our hypothesis is

that the number of men and women that we

observe is dependent on the age calorie

that we look at in other words the

proportions change or depend on or are

dependent on the age category now we can

collect our sample data we look at it

and we can see that yes in fact the

proportions do change across the age

groups in other words in our sample data

the proportions are dependent on age

category now is that JooJoo chance well

let's test the idea that the proportions

are all the same well that they are

independent of age category that's our

null hypothesis now here we can conduct

a chi-square test and that gives us a

p-value and if the p-value is less than

the Alpha we can reject the null

hypothesis and state that our

observation is statistically significant

if we want to look at just one numeric

variable on its own like height then we

don't have any groups to look for

differences between and we don't have

another numeric variable to look for

some sort of associational relationship

with so what questions can we ask well

we might have some theoretical value

that we want to compare our data to for

example in the case of average height we

might have some historic data we might

wonder if the current population is

significantly different from that

historic daughter so our question might

be is the average height different from

a previously established height let's

imagine that the previously established

height was one point four meters we want

to know if the average height in our

current population is different to that

our hypothesis is that there is a

difference again we collect some sample

data we find that the average height is

indeed different from the historic

height is that statistically significant

well if there were no difference what

would the chances be that we observed

the difference that we do or a greater

difference we conduct a t-test comparing

the averages and if the p-value is less

than the alpha then we can reject the

null hypothesis and state that the

observed difference is statistically

significant now let's consider a

categoric and a numeric variable and

remains the question is there a

difference between the average height of

men and women in this case our

hypothesis is that there is a difference

in our sample we do observe a difference

let's assume that there's no difference

we conduct a t-test which gives us a

p-value if the P is less than the Alpha

will reject the null and we state that

the observation is statistically

significant if we had a categorical

variable with more than two categories

like age group that's got three

categories then instead of doing a

t-test we would do an analysis of

variance or ANOVA now let's look at the

last combination of variable types in

the Stata said two numeric variables

height and weight here we might start

with the question is there a

relationship between height and weight

our hypothesis is that there is a

relationship we collect sample data we

look at it and one lakh we do see some

sort of relationship is drill or let's

assume that it's not it's assumed that

there's no correlation between the two

variables and if it weren't real then

what are the chances that we'd see the

relationship that we do and here we

conduct a

correlation tastes now a correlation

test is going to give us two things

firstly it's going to give you a

correlation coefficient which tells us

something about the nature of the

association between the two variables

and I'm going to talk about that in just

a minute

but of course it also gives us a p-value

and again if the p-value is less than

the Alpha we can reject the null

hypothesis and state that the

correlation that we see is statistically

significant and the correlation that we

see can be represented by a number that

we call the correlation coefficient so

let's talk about that for a second

correlation coefficient is a number

between negative 1 and 1 and it looks at

the relationship between two numeric

variables if as the X variable gets

larger the Y variable gets smaller we

say that they are negatively correlated

if they are perfectly negatively

correlated then the correlation

coefficient will be negative 1 if

there's no relationship between the two

variables then the correlation

coefficient will be 0 and if there's a

perfectly positive correlation as X goes

up Y goes up then the correlation

coefficient will be 1 and of course you

can have any value in between and by the

way it doesn't matter which of your

variables is on the x and the y axis the

correlation coefficient will be the same

of course we've only just been able to

scratch the surface in terms of what

there is to learn about statistical

analysis if you want to learn more then

go to learn more 365.com and I've got

some courses there that you can love if

you'd like to learn about our

programming which is a programming

language that gets used for statistical

analysis and it's free it's very

powerful it's easy to use it's

absolutely fantastic I have a YouTube

channel that focuses specifically on

that so that's our programming 101 I'll

put a link in the description below go

and check it out otherwise please

subscribe to this channel hit the bell

notification if you want notification of

future videos leave your comments below

and share this video with anyone that

you think might find it useful until

next time take care