6.07 Example

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En provenance du cours de University of Amsterdam

Basic Statistics

1923 notes

University of Amsterdam

Basic Statistics

1923 notes

Cours 3 sur 5 dans Specialization Methods and Statistics in Social Sciences

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.

À partir de la leçon

Confidence Intervals

We can distinguish two types of statistical inference methods. We can: (1) estimate population parameters; and (2) test hypotheses about these parameters. In this module we’ll talk about the first type of inferential statistics: estimation by means of a confidence interval. A confidence interval is a range of numbers, which, most likely, contains the actual population value. The probability that the interval actually contains the population value is what we call the confidence level. In this module we’ll show you how you can construct confidence intervals for means and proportions and how you should interpret them. We’ll also pay attention to how you can decide how large your sample size should be.

6.06 Choosing the sample size5:54

6.07 Example4:20

Rencontrer les enseignants

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

Warning, this is a pretty dirty video.

So for those of you who can't handle that, it might be a good idea to skip it.

Okay, five weeks ago my daughter Lois was born.

A couple of days after her birth, I was changing her diaper.

And just after I removed her old one and before I put on a new one,

I saw her gaze become blurry.

And one second later I heard a strange sound coming from her bottom.

Oh no! But there was nothing.

Strange.

A couple of hours later when I was changing her diaper again,

by coincidence I looked at the wall next to the place where the diaper changing

process takes place.

And suddenly I realized what had happened before.

My daughter had repainted the freshly painted wall with a couple of brown

streaks.

Apparently the defecation process of little babies can be pretty explosive.

Of course, this made me curious about other babies.

How far are babies able to spurt their poo?

What is the maximum shooting distance?

Suppose I asked a simple random sample of 150 new parents

to measure how far their babies poo and to report to me the personal records.

Let's say that it turns out that the mean pooing distance is 28 centimeters,

the standard deviation is 21 centimeters.

I would like to construct a 90% confidence interval to estimate the population mean.

Let's first look at the step by step plan for constructing a confidence interval.

We already know the confidence level, it's 90%, and

that we are dealing with a mean instead of a proportion.

So, the next step is to look up the relevant t score.

To do that we should first know the degrees of freedom,

that's n minus 1 equals 150 minus 1 equals 149.

So in the t table, we look in the column of the 90% confidence level and

in the row of 100 degrees of freedom.

After all, 149 is not in the table, and 100 is the closest lower value.

The relevant t score is 1.66.

We can now complete the formula.

The lower endpoint is 28 minus 1.66 times 21 divided by the square root of 150.

That makes about 25.2.

The higher endpoint is 28 plus 1.66 times 21 divided by the square root of 150.

That is about 30.8.

The 90% confidence level thus ranges from 25.2 to 30.8.

We can be 90% confident that this interval contains the actual population mean.

More precisely, if we would draw an infinite number of samples with

n equals 150 from our population, and for every sample we

would compute the confidence interval with this margin of error, in 90% of the cases,

the population value would fall within the confidence interval.

Now imagine, I was not interested in the population mean of the pooing distance,

but in the percentage of babies that have a personal poo-spurting distance record

of over 50 centimeters.

Suppose that 18% of the babies spurt further than the 50 centimeters, and

that I would like to construct a 97% confidence interval.

Now, we're not interested in a population mean anymore, but

in a population proportion.

So this is formula we are working with.

First we have to look at the relevant z score in the z table.

That we employed a 97% confidence level

means that we are interested in these set scores.

That means that we have to look up in the Z table to scores that correspond to

a cumulative probability of respectively 0.015 and 0.985.

We find them here and here.

That's -2.17 and 2.17.

So, if you go back to the formula, that makes 0.18 plus and

minus 2.17 times the square root of 0.18 times 1 minus 0.18 divided by 150.

That leads to an interval from 0.11 to 0.25.

We can be 97% confident that this interval contains the actual

population proportion of babies that can spurt further than 50 centimeters.

So, my advice to new parents, never paint the walls of your baby's room before your

son or daughter is toilet trained.

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