Study guide
Statistics 1 Summary for EXAM
- Course
- Institution
- Book
This document contains a detailed summary of my lecture notes from the Statistics I course. With this summary, I scored an 8.5 in my exam.
[Show more]
Connected book
Book Title:
Author(s):
- Edition:
- ISBN:
- Edition:
More summaries for
-
Exam Guide for Applied Multivariate Data Analysis – Get yourself a Wonderful Grade!
-
Summary of Statistics (IBC), Radboud University
-
Answers assignment 3 business research methods
2 reviews
By: veerleschurgers • 2 year ago
By: jjdwumfour • 1 year ago
Seller
Follow
polscinotes
Reviews received
Content preview
STATISTICS 1 – DESCRIPTION AND INFERENCEWEEK 1: Distributions, means and deviation
Variable: anything that can be measured and can differ across entities or across time
1. Independent variables: Cause (x)
2. Dependent variables: Outcome (y)
Levels of measurement (categorical)
Nature of information within values assigned to variables
1. Nominal
• Two or more exclusive categories
• No natural order
• No arithmetic operations possible (subtraction, “equal to”, “greater than”)
• Frequency (mode)
• Occupation, political party affiliation, favorite football club
2. Ordinal
• Clear ordering of the variables
• Low <-> high; little <-> much; small <-> large
• Spacing between values not the same across the levels of the variables
• Level of agreement, level of education, political interest, trust in government
3. Interval
• Difference between two values meaningful
• Arbitrary/meaningless zero
• Temperature, pH (more examples in natural sciences)
4. Ratio
• Like interval but meaningful zero
• Height, weight, salary, Kelvin, number of international conflicts
Continuous variables – interval and ratio
Continuous variables (interval-ratio) are continuous but can be discrete.
o Continuous interval-ratio variables
• Can be measured to any level of precision
• Height or weight: 75.329242… cm
o Discrete interval-ratio variables
• Can take only certain, countable values (usually whole numbers)
• Points in an exam or number of car accidents at an intersection
• Discrete variables can be measured in discrete terms (height in cm)
,What can you do?
Possible to… Nominal Ordinal Interval Ratio
Frequency distribution? YES YES YES YES
Median and percentiles? NO YES YES YES
Add or subtract? NO NO YES YES
Mean, standard NO NO YES YES
deviation, standard error
of the mean?
Ratio, or coefficient of NO NO NO YES
variation?
I. DISTRIBUTION
To show how data values are distributed in relation to other values.
> Frequency distribution: the distribution of a statistical data set to show all the possible
values (or intervals) of the data and how often they occur.
Measure of central tendency
A value that attempts to describe a set of data by identifying the central position within that
set of data
Level of measurement Measures of central tendency
Nominal Mode
Ordinal Median + Mode
Interval and ratio Mean + Median + Mode
MODE: the most frequent score in a data set (there can be several modes)
MEDIAN: the middle score for a set of data that has been arranged in order of magnitude
o Odd number of scores: Arrange by magnitude to find median.
o Even number of scores: Arrange by magnitude, add 2 middle scores, divide by 2
MEAN: the average of the numbers
1. Calculate the sum of all values of x
2. Divide by the total number of observations (n)
&
Σ ' = 1)*
!" =
&
Mean is sensitive to extreme values/outliers
When there are extreme values, the median may be more useful
,Measure of dispersion
How stretched or squeezed is the distribution?
Level of measurement Measures of dispersion
Nominal No measure of dispersion possible
Ordinal Range, inter-quartile range
Interval and ratio Range, inter-quartile range,
variance/standard variation
RANGE: maximum - minimum
INTERQUARTILE RANGE: The range of the middle 50% of the data.
Calculate by subtracting the first quartile from the third quartile.
Even set of numbers?
1. Split the data in two halves
2. Find the median of the lower half
3. Find the median of the upper half
4. Calculate IQR = 57 – 35 = 22
VARIANCE AND STANDARD DEVIATION
Measure the spread using all data
DEVIANCE: How much does each value deviate from the mean?
+,-'.&/, = )* − )̅
Total deviance (sum of all deviances) is always zero.
&
2 = 1()* − )̅ )
'
, EXAMPLE: Number of points of students in a test
Adam Abby Dan Elsa Isan Liz Max Pat Tom Uma Zev
14 35 45 55 55 56 57 65 87 89 92
Step 1. Calculate the MEAN (column 2)
∑6*78 )*
!" =
&
89:;<:9<:<<:<<:<=:<>:=<:?>:?@:@A =<B
!" = 88
= 88
= 59.09
Step 2. Calculate all DEVIANCES (column 3)
Step 3. Square all the deviances (errors) (column 4) – SQUARED ERRORS
Step 4. Add the squared deviances – SUM OF SQUARED ERRORS (SS)
6
∑ = 1()* − )̅ )A = 5650.91
*
x )̅ ()* − )̅ ) ()* − )̅ )A
14 59.09 14 - 59.09 = -45.09 (−45.09)A = 2033.19
35 59.09 35 - 59.09 = -24.09 (−24.09)A = 580.37
45 59.09 45 - 59.09 = -14.09 (−14.09)A = 198.55
55 59.09 55 - 59.09 = -4.09 (−4.09)A = 16.74
55 59.09 55 - 59.09 = -4.09 (−4.09)A = 16.74
56 59.09 56 - 59.09 = -3.09 (−3.09)A = 9.55
57 59.09 57 - 59.09 = -2.09 (−2.09)A = 4.37
65 59.09 65 - 59.09 = 5.91 (5.91)A = 34.92
87 59.09 87 - 59.09 = 27.91 (27.91)A = 778.92
89 59.09 89 - 59.09 = 29.91 (29.91)A = 894.55
92 59.09 92 - 59.09 = 32.91 (32.91)A = 1038.01
5650.91
Step 5. Calculate the VARIANCE (K A )
LL ∑6*78()* − )̅ )A
KA = =
M−1 M−1
LL 5650.91 5650.91
KA = = = = OPO. QR
M−1 11 − 1 10
Step 6. Calculate STANDARD DEVIATION (s)
K = SK A
K = SK A = √565.09 = UV. WW
The benefits of buying summaries with Stuvia:
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
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
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 polscinotes. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $6.08. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
82871 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now