Statistics for People Who (Think They) Hate Statistics - International Student Edition
I wrote this summary based on all lectures, additional video lectures and the book of Salkind. It provides you a good fundament for quantitative research with hypothesis testing.
Blok 4, Quantitative Methods
Samenvatting Salkind, hoorcolleges en video’s
Linn Luijerink
Inhoud
Video’s ..................................................................................................................................................... 3
Video’s lecture 1 .................................................................................................................................. 3
Video’s lecture 2 .................................................................................................................................. 4
Video’s lecture 3 .................................................................................................................................. 4
Video’s lecture 4 .................................................................................................................................. 5
Video’s Lecture 5 ................................................................................................................................. 7
Video’s Lecture 6 ................................................................................................................................. 8
Video’s Lecture 7 ............................................................................................................................... 10
Lectures ................................................................................................................................................. 12
Lecture 1, 4-1-2021 ........................................................................................................................... 12
Lecture 2, 6-1-2021 ........................................................................................................................... 13
Lecture 3, 11-1-2021 ......................................................................................................................... 15
Lecture 4, 13-1-2021 ......................................................................................................................... 17
Lecture 5, 18-1-2021 ......................................................................................................................... 20
Lecture 6, 20-1-2021 ......................................................................................................................... 23
Lecture 7, 25-1-2021 ......................................................................................................................... 25
Lecture 8, 29-1-2021 ......................................................................................................................... 27
Lecture 9, 3-2-2021 ........................................................................................................................... 29
Chapters Salkind .................................................................................................................................... 33
Part 1, Yippee! I’m in Statistics .......................................................................................................... 33
Chapter 1, Statistics or sadistic?.................................................................................................... 33
Part 2, ∑igma, Freud and Descriptive Statistics ................................................................................. 33
Chapter 2, Means to an End: Computing and Understanding Averages....................................... 33
Chapter 3, Vive La Différence, Understanding Variability ............................................................. 34
Chapter 4, A Picture Really Is Worth a Thousand Words .............................................................. 35
Chapter 5, Computing Correlation Coefficients ............................................................................ 38
Chapter 6, An Introduction to Understanding Reliability and Validity.......................................... 40
Part 3, Taking Changes for Fun and Profit ......................................................................................... 41
Chapter 7, Hypotheticals and You ................................................................................................. 41
Chapter 8, Are Your Curves Normal? Probability and Why it Counts ........................................... 43
Part 4, Significantly Different Using Inferential Statistics ................................................................. 47
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, Chapter 9, Significantly Significant ................................................................................................ 47
Chapter 11, t(EA) for two .............................................................................................................. 48
Chapter 15, Testing Relationships using the Correlation Coefficient............................................ 50
Part 5, More Statistics! More Tools! More Fun! ............................................................................... 50
Chapter 16, Using Linear Regression ............................................................................................. 50
Chapter 17, Chi-Squared ............................................................................................................... 52
Chapter 18, Some Other (Important) Statistical Procedures ........................................................ 53
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,Video’s
Video’s lecture 1
Video 0, Pro-Tips!
Orders of operations
BODMAS:
1. Brackets: 4(4) → 4 X 4
2. Orders
3. Division and multiplication (from left to right)
4. Addition and subtraction (from left to right)
Tips for calculator
- Brackets
- Formulate the whole sum and not just a part
- Make use of ‘ANS’
Decimal places and rounding
Use the same number of decimal places in your answer as given in the question. Be careful with
rounding.
Standard notation
The subscript ‘i‘ usually means individual
The subscript ‘X-bar’ this means the mean
Greek letters
∏ (PI) → is not related to a circle, but it represents a proportion (always between 0 and 1).
∑ (sigma) → means just sum up all the values that come after a sigma.
% (percentage) → a proportion scaled up by 100 (always between 0 and 100).
Video 1, Key Definitions
Populations → for example the students from an university. It is impossible to speak to them all in a
research and that is why we make use of samples → is a group of people who have been drawn from
the population. Samples need to be chosen randomly, this is the gold standard. Nevertheless, most
of the time we have to make use of convenience samples.
Descriptive statistics → are the statistics that we produce, that summarize the data of a sample.
There are no uncertainties.
Inferential statistics → there is a little bit uncertainty, because we are making a guess about the
population and a sample is never a perfect representative of the population. We speak about
sampling error, which is the difference between the sample statistics and the population grammars
(which often is unknown).
Causation: A → B
You cannot have causation without correlation. Be aware of the spurious relationships.
Video 2, Levels of Measurement
Cases → can be individuals, companies or countries. The units of data in your samples.
Variables → the properties that differ between the cases. Distinction between two:
- Categorical (discrete) variables: measures where different cases can belong to one or several
categories. These categories are discrete so there is no overlap. A case cannot fit in more
categories (male or female).
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, - Continuous variables: a case can take any numerical value (temperature or age).
4 different levels of measurement (NOIR):
1. Nominal (categorical variable), there is no order.
2. Ordinal (categorical variable), there is some order.
3. Interval (continuous variable), there is no zero point.
4. Ratio (continuous variable), there is a true zero point which means the absent of what you
are measuring.
Video 3, Measures of Central Tendency
Another definition is measures of average. There are three levels:
1. Mean → the average as we use it the most. Add up all values and divide it by the number of
values. Mean for a sample is reported with a M or with an 𝑿̅ (X-Bar), to distinguish samples
from population we use the letter: µ.
2. Weighted Mean → sometimes we have to reconstruct sample meaning from different
samples.
3. Median → the middle value.
4. Mode → the most frequent value, the most common value.
Video’s lecture 2
Video 1, Variability
Measures of variability:
• Standard deviation → describes how spread out your data are. If SD is small, your data is
clustered, if SD is bigger, your data are more spread out. You can think of SD as the average
deviation, the distance of each observation from the mean. The average deviation of the
mean. Original data.
• Variance → the squared standard deviation. Data that is squared, so it can be more difficult
to analyse and understand.
• Range → distance between the smallest and the largest value of your data. Mostly used to
check if there are mistakes in the data.
Video 2, Normal Distribution
The normal distribution is basically a bell curve. It has interesting properties that make it easy to
calculated probabilities. It is described by two parameters:
1. Measure of central tendency: mean, the height of the normal distribution.
2. Measure of variability (spread): standard deviation, the width of the normal distribution.
Bigger standard deviation → short and wide.
Smaller standard deviation → skinny and tall.
The normal distribution is symmetrical, the mean, mode en median are the same.
The empirical rule → the area under the different parts of the distributions are always the same.
Video’s lecture 3
Video 1, Probabilities and Probability Distributions
A proportion and a probability have in common that they both fall between the numbers 0 and 1. A
percentage is the proportion multiplied by 100. You calculate a probability the same way as a
proportion, but you use different words to describe it.
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