5.06 Sampling distribution proportion

Loading...

University of Amsterdam 提供のコース

Basic Statistics

2117件の評価

University of Amsterdam

Basic Statistics

2117件の評価

Specialization Methods and Statistics in Social Sciences における 5 の 3 コース

Understanding statistics is essential to understand research in the social and behavioral sciences. In this course you will learn the basics of statistics; not just how to calculate them, but also how to evaluate them. This course will also prepare you for the next course in the specialization - the course Inferential Statistics. In the first part of the course we will discuss methods of descriptive statistics. You will learn what cases and variables are and how you can compute measures of central tendency (mean, median and mode) and dispersion (standard deviation and variance). Next, we discuss how to assess relationships between variables, and we introduce the concepts correlation and regression. The second part of the course is concerned with the basics of probability: calculating probabilities, probability distributions and sampling distributions. You need to know about these things in order to understand how inferential statistics work. The third part of the course consists of an introduction to methods of inferential statistics - methods that help us decide whether the patterns we see in our data are strong enough to draw conclusions about the underlying population we are interested in. We will discuss confidence intervals and significance tests. You will not only learn about all these statistical concepts, you will also be trained to calculate and generate these statistics yourself using freely available statistical software.

レッスンから

Sampling Distributions

Methods for summarizing sample data are called descriptive statistics. However, in most studies we’re not interested in samples, but in underlying populations. If we employ data obtained from a sample to draw conclusions about a wider population, we are using methods of inferential statistics. It is therefore of essential importance that you know how you should draw samples. In this module we’ll pay attention to good sampling methods as well as some poor practices. To draw conclusions about the population a sample is from, researchers make use of a probability distribution that is very important in the world of statistics: the sampling distribution. We’ll discuss sampling distributions in great detail and compare them to data distributions and population distributions. We’ll look at the sampling distribution of the sample mean and the sampling distribution of the sample proportion.

5.06 Sampling distribution proportion5:01

5.07 Example6:48

コースの提供者

Matthijs Rooduijn
Dr.
Department of Political Science
Emiel van Loon
Assistant Professor
Institute for Biodiversity and Ecosystem Dynamics

Okay.

Imagine you're living in Paris, and

you know that a proportion of 0.10 of all students identifies as a hipster.

You would like to know what the sampling distribution of this proportion

looks like.

Note that it doesn't make much sense to compute the population mean here.

Your variable of interest is a binary nominal variable.

Students can choose if they identify as a hipster or not.

Means are not relevant with such a binary variable.

In this video, I'll explain what the sampling distribution of

a population proportion looks like.

You know that 10% of the students in Paris identifies as a hipster,

this means that the population proportion, which is symbolized by pi, equals 0.10.

Now imagine that we draw a sample of n equals 200 from this population.

The sample proportion, which is symbolized by p, will be a number close to 0.10.

It could be for instance 0.09 or 0.12.

If you would draw five sample,

the sample proportions might look something like this.

A histogram of these sample proportions would look like this.

There are five values and they all occur once so

they all have a probability of 0.2.

Now, if you would draw 25 samples,

the distribution would look something like this.

And if you would draw 50 samples, something like this.

And when an infinite number of samples, your distribution would look like this.

This is the sampling distribution of the sample proportion, and

the mean of this distribution will be 0.10 which equals the population proportion.

To show that we are dealing with the mean of a sampling distribution,

the mean is symbolized by mu p.

We add the p to show that we are dealing with the sampling distribution of

the sample proportion in which the scores are not scores of individuals but

sample proportions.

As you can see the exact same logic applies as in the case of the sampling

distribution of the sample mean.

In the case of the sampling distribution of the sample mean,

the distribution is approximately bell-shaped if the population

itself is normally distributed or if the sample size is sufficiently large.

Usually 30 is taken as a minimum.

In the case of the sampling distribution for

the sample proportion, you can only be sure that the distribution is bell-shaped

if you have at least fifteen positive cases and fifteen negative cases.

So, at least fifteen hipsters and fifteen non-hipsters.

You can express this formula as follows.

n multiplied with pi is equal or larger than 15 and

n multiplied with 1 minus pi is equal or larger than 15.

What does that mean for our example?

First the product of the sample size and

the population proportion should be 15 or more.

In our case that's 200 multiplied with 0.10.

That equals 20 hipsters, and 20 is larger than 15.

Second, the product of the population proportion and 1- pi should be 15 or more.

In our case, that's 200 times 1 minus 0.10

equals 200 times 0.90 equals 180.

So 180 non hipsters.

We can conclude that the sampling distribution will be bell-shaped

because 20 and 180 are both larger than 15.

There is also a pretty straightforward formula to compute the standard deviation

of the sampling distribution of the sample proportion.

We symbolize the standard deviation by sigma p.

You know that sigma stands for the standard deviation, and

p is added to show that we are talking about a sampling distribution

in which the cases are sample proportions, and not individual subjects.

To compute the standard deviation, we have to multiply the population proportion

with 1 minus the population proportion.

Next we have to divide the outcome by the sample size n and

take the square root of this outcome.

In our case this boils down to the square root of 0.10 multiplied

with 1 minus 0.10 divided by 200.

That equals 0.02.

The standard deviation of the sampling distribution is 0.02.

So to conclude, when it comes to binary categorical variables

it doesn't make sense to compute the population mean or standard deviation.

Instead, we compute proportions when we are dealing with categorical variables.

So when it comes to binary variables, we only have the population proportion pi.

A similar logic holds for the sample.

We only have the sample proportion p.

Yet when it comes to the sampling distribution of the sample proportion

we do have a mean and a standard deviation.

These values can easily be computed as long as we know the value of

the population proportion.

コース一覧で検討

サインアップは無料です。今すぐサインアップして、パーソナライズされたお勧め、更新、サービスを利用しましょう。

コーセラは、世界トップクラスの教育を世界中に配信しています。最高峰の大学や組織とのパートナーシップに基づくオンラインコースが提供されています。

© 2019 Coursera (株)すべての権利予約します。

App Storeからダウンロード

Google Playで取得