100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
logo-home
Previously searched by you
Previously searched by you
logo
Summary Statistics I - Exam and Class Notes - GRADE 8.5 CA$8.38   Add to cart
Quickly navigate to
Preview
  2.  
  3. Universiteit Leiden (UL)
  4.  
  5. Statistics I (6441HST1Y)

Summary

Summary Statistics I - Exam and Class Notes - GRADE 8.5

1 review
 74 views  2 purchases
  • Course
  • Statistics I (6441HST1Y)
  • Institution
  • Universiteit Leiden (UL)

Extensive notes and exam revision for Statistics I, IRO 1st year, Bloc 4. This is just for the exam, not for the seminars. I have a weekly overview of the content, with some examples of exercises which are useful for the exam. It is the same statistics professor, with the same exam format. My grad...

[Show more]

Preview 4 out of 47  pages

Document information

  • April 18, 2024
  • 47
  • 2022/2023
  • Summary

Subjects

  • statistics
  • statistics i
  • iro
  • stats
  • iro stats
  • iro stats 1
  • iro year 1
  • iro 1st year
  • 2024
  • 2023
  • statistics 1
  • international relations and organisations
  • international relations and organizations

Written for

  • Universiteit Leiden (UL)
  • International Relations and Organizations
  • Statistics I (6441HST1Y)
All documents for this subject (2)

1  review

review-writer-avatar

By: matthiasb1 • 6 months ago

Seller

avatar-seller
lauragfsilva

Reviews received

Content preview

Statistics I
Exam Revision




Week 1
Variables – anything that differs (across entities or across time) and can be measured over time.




(Categorical)
- Nominal: two or more exclusive categories. The data in categories has no order or
ranking (eye color, marital status, hair color, political party affiliation).
- Ordinal: categories have a real ordering/ranking. Often used for subjective data
(opinions, attitudes, education levels, political interests, performance ratings, agreement
to a statement). The spacing between the variables is not the same across variables.
(Numerical) – real numbers
- Continuous: can take on any value within a range. Can be decimals, fractions – an infinite
number of values (height, weight, temperature, time) (some can be measured as discrete,
by rounding them).
- Discrete: can only take countable values – usually whole numbers (international conflicts,
number of pets owned, number of car accidents).


Alternative levels of measurement (Stevens):

,Interval: the zero is arbitrary/meaningless (temperature, like 0C does not mean an absence of
anything, pH (pH=0 does not mean absence of anything), IQ scores
Ratio: the zero is meaningful (salary, 0K, number of international conflicts)




Independent variable: causes, x, has an effect on the DV
Dependent variable: outcomes, y




Measures of central tendency
When we collect data, we can show ow the data is distributed in comparison to other values.
This is frequency distribution, it shows all the intervals, and how often they occur.




Uniform – every outcome has a roughly equal chance of happening
Multimodal – more than 2 likely values


Skewness: a distribution can skew to the right or left, positive of negative skew, respectively.
This depends on where the mass “tail” is longest. Long tail on the right = skewed right.


Measure of central tendency: single value that attempts to describe a set of data by identifying
the central position within that set. For example, mean, median and mode.
Measures of dispersion: give an indication of how stretched the data set is.

, - Mode: most frequent score in a data set, that with most frequencies. There can be several
modes, when the frequencies for two categories are the same.
- Median: the middle score for a data set, arranged in order of magnitude. Then, we find
the value in the middle, in the order. With an even number of scores, we just add the two
in middle, and divide them by two: constructing a new middle point.
- Mean: the mean is calculated by adding up every value in a variable, and divide by the
number of observations (n). When there are extreme values, the median may be more
useful, because the mean is sensitive to extreme values, and the median isn’t.


How to calculate the standard deviation given the sum of all squared errors?
First, we calculate the sum of all squared errors by taking each individual observation and
subtracting it from the mean. Then, squaring each of the differences, and adding them all up.
(mean = 11.44. X1 = 3
11.44 – 3 = -8.44
-8.44^2 = 71.2336.
Do this for each X, and then add everything up.)


Once we have the sum of squared errors, we calculate the standard deviation using




This is similar to calculating the variance – the variance, s^2, is the same calculating without the
squared root. (The formula for standard deviation in the formula sheet is just s = sqrt(s^2) –
confusing)


Measures of dispersion

, An indicator to the extent which a distribution is stretched or squeezed.




The range is the difference between the lowest and the highest values. The highest – lower is the
range.
We can divide this into “chunks” called “quantile”. The more common quantiles are: percentiles,
deciles, quintiles, quartiles. The common range to use here is the interquartile range. This is the
range of the middle 50% of the data.
How to calculate the IQR? Calculate the median – calculate the median of the lower half
(when there is none, we calculate the sum of the two middle values/2) – do the same for the
upper half – then we can lay out the quartiles, by calculating the difference between the upper
half quartile and the lower half. The same is done with even numbers, except we do not need to
calculate the man of the middle values.
When calculating this, the IQR uses only a selection of the data. It is resistance against outliers –
a “robust” statistic.
- The deviance is used to calculate how such easy value deviates from the mean
- To calculate it, we find out how much each of the frequency deviate from the mean
- So, we need the mean
- Then, we do this for each observation: subtract the mean from the frequency
- Then we add the sum of each of these of deviances = total deviance
The total deviance is not a useful measure of spread – it usually totals to zero. We fix this by
squaring the differences.
So, we square the deviances, and we add these up. This makes every value positive (which as the
prob before, positive and negative.



Week 2
Introduction Graphs and Visualizations
The goal of data visualization to make it easier to identify patterns, data and find relations. A
good visualization shows the important features of the data.

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

Quick and easy check-out

You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.

Focus on what matters

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.

Who am I buying these notes from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller lauragfsilva. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy these notes for CA$8.38. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

75323 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy study notes for 14 years now

Start selling
CA$8.38  2x  sold
  • (1)
  Add to cart