Statistics made easy ! ! ! Learn about the t-test, the chi square test, the p value and more
Summary
TLDRThis 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
📊 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.
🔍 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.
📈 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.
Mindmap
Keywords
💡Statistics
💡Sample Data
💡Categorical Variables
💡Numeric Variables
💡Statistical Tests
💡Hypothesis
💡Null Hypothesis
💡P-Value
💡Alpha Value
💡Correlation
💡Correlation Coefficient
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
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next time take care
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