Shadowing Practice: What is Statistics? A Beginner's Guide to Statistics (Data Analytics)! - Learn English Speaking with Video

If you want to finally understand statistics, this is the place to be.

After this video, you will know what statistics is, what descriptive statistics is, and what inferential statistics is.

So, let's start with the first question: What is statistics?

Statistics deals with the collection, analysis and presentation of data.

An example: We would like to investigate whether gender has an influence on the preferred newspaper.

Then gender and newspaper are our so -called variables that we want to analyze.

In order to analyze whether gender has an influence on the preferred newspaper, we first need to collect data.

To do this, we create a questionnaire that asks about gender and preferred newspaper.

We will then send out the survey and wait two weeks.

Afterwards, we can display the received answers in a table.

In this table, we have one column for each variable one for gender and one for newspaper.

On the other hand, each row is the response of one surveyed person.

The first respondent is male and stated "New York Post".

The second is female and stated "USA Today" and so on and so forth.

Of course, the data does not have to be from a survey.

The data can also come from an experiment in which you, for example, want to study the effect of two drugs on blood pressure.

Now the first step is done.

We have collected data and we can start analyzing the data.

But what do we actually want to analyze?

We did not survey the entire population, but we took a sample.

Now the big question is: do we just want to describe the sample data

or do we want to make a statement about the whole population?

If our aim is limited to the sample itself, i .e we only want to describe the collected data, We will use descriptive statistics.

Descriptive statistics will provide a detailed summary of the sample.

However, if we want to draw conclusions about the population as a whole, Inferential statistics are used.

This approach allows us to make educated guesses about the population based on the sample data.

Let us take a closer look at both methods, starting with descriptive statistics.

Why is descriptive statistics so important?

Let's say a company wants to know how its employees travel to work.

So, the company creates a survey to answer this question.

Once enough data has been collected, this data can be analyzed using descriptive statistics.

But what is descriptive statistics?

Descriptive statistics aims to describe and summarize a dataset in a meaningful way.

But it is important to note that descriptive statistics only describe the collected data without drawing conclusions about a larger population.

Put simply, just because we know how some people from one company get to work,

we cannot say how all working people of the company get to work.

This is the task of inferential statistics, which we will discuss later.

To describe data descriptively, we now look at the four key components: measures of central tendency,

measures of dispersion, frequency tables and charts.

Let's start with the first one: Measures of Central Tendency.

Measures of Central Tendency are for example the mean, the median and the mode.

Let's first have a look at the mean.

The arithmetic mean is the sum of all observations divided by the number of observations.

An example.

Imagine we have the test scores of 5 students.

To find the mean score, we sum up all the scores and divide by the number of scores.

The mean test score of these 5 students is therefore 86 .6.

What about the median?

When the values in a dataset are arranged in ascending order, the median is the middle value.

If there is an odd number of data points, The median is simply the middle value.

If there is an even number of data points, the median is the average of the two middle values.

It is important to note that the median is resistant to extreme values or outliers.

Let's look at this example: No matter how tall the last person is, The person in the middle remains the person in the middle,

so the median does not change.

But if we look at the mean, it does have an effect on how tall the last person is.

The mean is therefore not robust to outliers.

Let's continue with the mode.

The mode refers to the value or values that appear most frequently in a set of data.

For example, if 14 people travel to work by car, 6 by bike, 5 walk and 5 take public transport,

Then "car" occurs most often and is therefore the mode.

Great, let's continue with the measures of dispersion.

Measures of dispersion describe how spread out the values in a dataset are.

Measures of dispersion are for example the variance and standard deviation, the range and the interquartile range.

Let's start with the standard deviation.

The standard deviation indicates the average distance between each data point and the mean.

But what does that mean?

Each person has some deviation from the mean.

Now we want to know how much the persons deviate from the mean value on average.

In this example, the average deviation from the mean value is 11 .5 cm.

To calculate the standard deviation, we can use this equation: sigma is the standard deviation, n is the number of persons,

xi is the size of each person and x bar is the mean value of all persons.

But attention, there are two slightly different equations for the standard deviation.

The difference is that we have once 1 /n and once 1 / .

To keep it simple, if our survey doesn't cover the whole population, we always use this equation to estimate the standard deviation.

Likewise, if we have conducted a clinical study, then we also use this equation to estimate the standard deviation.

But what is the difference between the standard deviation and the variance?

As we now know, the standard deviation is the quadratic mean of the distance from the mean.

The variance now is the squared standard deviation.

If you want to know more details about the standard deviation and the variance, please watch our video.

Let's move on to range and interquartile range.

It is easy to understand.

The range is simply the difference between the maximum and minimum value.

Interquartile range represents the middle 50 % of the data.

It is the difference between the first quartile, Q1, and the third quartile, Q3.

Therefore, 25 % of the values are smaller than the interquartile range and 25 % of the values are larger.

The interquartile range contains exactly the middle 50 % of the values.

Before we get to the last two points, let's briefly compare measures of central tendency and measures of dispersion.

Let's say we measured the blood pressure of patients.

Measures of central tendency provide a single value that represents the entire dataset,

helping to identify a central value around which data points tend to cluster.

Measures of dispersion, like the standard deviation, the range and the interquartile range, indicate how spread out the data points are,

whether they are closely packed around the center or spread far from it.

In summary, while measures of central tendency provide a central point of the dataset,

Measures of dispersion describe how the data is spread around the center.

Let's move on to tables.

Here we will have a look at the most important ones: frequency tables and contingency tables.

A frequency table displays how often each distinct value appears in a dataset.

Let's have a closer look at the example from the beginning.

A company surveyed its employees to find out how they get to work.

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The options given were car, bicycle, walk and public transport.

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Here are the results from 30 employees: the first answered car, the next walk, and so on and so forth.

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Now we can create a frequency table to summarize this data.

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To do this, we simply enter the four possible options: car,

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bicycle, walk and public transport in the first column and then count how often they occurred.

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From the table, it is evident that the most common mode of transport among the are with 14 employees preferring it.

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The frequency table thus provides a clear and concise summary of the data.

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But what if we have not only one but two categorical variables?

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This is where the contingency table, also called crosstab, comes in.

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Imagine the company doesn't have one factory but two: one in Detroit and one in Cleveland.

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So, we also ask the employees at which location they work.

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If we want to display both variables, we can use a contingency table.

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A contingency table provides a way to analyze and compare the relationship between two categorical variables.

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The rows of a contingency table represent the categories of one variable, while the columns represent the categories of another variable.

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Each cell in the table shows the number of observations that fall into the corresponding category combination.

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For example, the first cell shows that Carr and Detroit were answered six times.

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And what about the charts?

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Let's take a look at the most important ones.

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To do this, let's simply use datadap .net.

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If you like, you can load this sample data set with the link in the video description.

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Or you just copy your own data into this table.

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Here below you can see the variables distance to work, mode of transport and site.

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Datadap gives you a hint about the level of measurement, but you can also change it here.

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Now, if we only click on Mode of Transport, we get a frequency table and we can also display the percentage values.

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If we scroll down, we get a bar chart and a pie chart.

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Here on the left we can adjust further settings.

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For example, we can specify whether we want to display the frequencies or the percentage values,

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or whether the bars should be vertical or horizontal.

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If you also select "Side", we get a cross table here, and a grouped bar chart for the diagrams.

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Here we can specify whether we want the chart to be grouped or stacked.

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If we click on Distance to Work and Mode of Transport,

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we get a bar chart where the height of the bar shows the mean value of the individual groups.

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Here we can also display the dispersion.

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We also get a histogram, a box plot, a violin plot and a rainbow plot.

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If you would like to know more about what a box plot, a violin plot and a rainbow plot are, take a look at my videos.

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Let's continue with inferential statistics.

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At the beginning, we briefly go through what inferential statistics is and then I'll explain the six key components to you.

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So, what is inferential statistics?

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Inferential statistics allows us to make a conclusion or inference about a population based on data from a sample.

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What is the population and what is the sample?

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The population is the whole group we're interested in.

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If you want to study the average height of all adults in the United States, then the population would be all adults in the United States.

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The sample is the smaller group we actually study, chosen from the population.

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For example, 150 adults were selected from the United States.

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And now we want to use the sample to make a statement about the population.

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And here are the six steps how to do that: 1.

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Hypothesis.

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First, we need a statement, a hypothesis, that we want to test. For example,

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you want to know whether a drug will have a positive effect on blood pressure in people with high blood pressure.

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But what's next?

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In our hypothesis, we stated that we would like to study people with high blood pressure.

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So, our population is all people with high blood pressure in, for example, the US.

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Obviously, we cannot collect data from the whole population.

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So, we take a sample from the population.

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Now, we use this sample to make a statement about the population.

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But how do we do that?

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For this, we need a hypothesis test.

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Hypothesis testing is a method for testing a claim about a parameter in a population, using data measured in a sample.

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Great, that's exactly what we need.

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There are many different hypothesis tests.

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And at the end of this video I will give you a guide on how to find the right test.

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And of course you can find videos about many more hypothesis tests on our channel.

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But how does a hypothesis test work?

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When we conduct a hypothesis test, we start with a research hypothesis, also called alternative hypothesis.

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This is the hypothesis we are trying to find evidence for.

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In our case, the research hypothesis is: the drug has an effect on blood pressure.

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But we cannot test this hypothesis directly with a classical hypothesis test,

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So, we test the opposite hypothesis: that the drug has no effect on blood pressure.

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But what does that mean?

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First, we assume that the drug has no effect in a population.

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We therefore assume that in general, people who take the drug and people who don't take the drug have the same blood pressure on average.

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If we now take a random sample and it turns out that the drug has a large effect in a sample,

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then we can ask: how likely it is to draw such a sample

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or one that deviates even more if the drug actually has no effect?

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So, in reality, on average, there is no difference in the population.

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If this probability is very low, we can ask ourselves: maybe the drug has an effect in the population?

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have enough evidence to reject the null hypothesis that the drug has no effect.

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And it is this probability that is called the p -value.

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Let's summarize this in three simple steps: 1.

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The null hypothesis states that there is no difference in the population.

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2. The hypothesis test calculates how much the sample deviates from the null hypothesis.

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3. The p -value indicates the probability of getting a sample

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that deviates as much as our sample or one that even deviates more than our sample, is true.

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But at what point is the p -value small enough for us to reject the nile hypothesis?

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This brings us to the next point: statistical significance.

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If the p -value is less than a predetermined threshold, the result is considered statistically significant.

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This means that the result is unlikely to have occurred by chance alone

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and that we have enough evidence to reject the null hypothesis.

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This threshold is often 0 .05.

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Therefore, a small p -value suggests that the consistent with the null hypothesis.

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This leads us to reject the null hypothesis in favor of the alternative hypothesis.

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A large p -value suggests that the observed data is consistent with the null hypothesis and we will not reject it.

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But note: there is always a risk of making an error.

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A small p -value does not prove that the alternative hypothesis is true.

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It is only saying that it is unlikely to get such a result

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or a more extreme when the null hypothesis is true.

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And again, if the null hypothesis is true, there is no difference in a population.

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And the other way around,

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a large p -value does not prove that the null hypothesis to get such a result or a more extreme,

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when the null hypothesis is true.

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So, there are two types of errors which are called type 1 and type 2 error.

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Let's start with the type 1 error.

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In hypothesis testing, a type 1 error occurs when a true null hypothesis is rejected.

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So, in reality, the null hypothesis is true, but we make the decision to reject the null hypothesis.

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In our example, it means that the drug actually had no difference in blood pressure whether the drug is taken or not,

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the blood pressure remains the same in both cases.

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But our sample happened to be so far off the true value that we mistakenly thought the drug was working.

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And a type 2 error occurs when a false null hypothesis is not rejected.

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So, in reality, the null hypothesis is false, But we make the decision not to reject the null hypothesis.

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In our example, this means: the drug actually did work, there is a difference between those who have taken the drug and those who have not,

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but it was just a coincidence that the sample taken did not show much difference

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and we mistakenly thought the drug was not working.

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And now I'll show you how Datadap helps you to find a suitable hypothesis test and, of course, calculates it and interprets the results for you.

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data .net and copy your own data in here.

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We will just use this example dataset.

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After copying your data into the table, the variables appear down here.

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DataTab automatically tries to determine the correct level of measurement, but you can also change it up here.

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Now we just click on "Hypothesis testing" and select the variables we want to use for the calculation of a hypothesis test.

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Datadab will then suggest a suitable test.

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For example, in this case, a chi -square test or, in that case, an analysis of variance.

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Then you will see the hypotheses and the results.

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If you're not sure how to interpret the results, click on "Summary in words".

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Further, you can check the assumptions and decide whether you want to calculate a parametric or a non -parametric test.

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You can find out the difference between parametric and non -parametric tests in my next video.

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Thank you for watching and I hope you enjoyed the video!

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