Probability Cheat Sheet printable pdf download

Probability Cheat Sheet

Probabilities... (A.K.A. Chance)

Definitions

How likely something (an event) is to happen

Coefficient – Basically just a static numerical value that

is used in a calculation

Kinds of Probabilities

Linear – Like, or in shape of, a line

Conditional Probabilities – Probability of an event

happening based on whether or not something else

Variable – Something we take into account in our

happened

analysis

Remember! Probabilities are always

Joint Probabilities – Probability of two events

Ordinal Data – Data that is ordered so that its values

between 0 and 1, if you get a probability

happening at the same time

indicate rank

outside this range there is something wrong

with calculation.

Marginal Probabilities – A.K.A. Unconditional

Dichotomous Data – Data that takes on two values only

Probabilities, are just the summation of all

(e.g. 1 or 0, True or False, Yes or No)

0 = Not gonna happen

probabilities

1 = Definitely gonna happen

How many times event happened

Probability

Big Takeaway

Logical Fallacies to Avoid...

Total Outcomes

...to make better arguments

Probabilities can give you an indication of what is

Kinds of Events

likely to happen, but they CANNOT tell you what

will happen.

Fallacy – An error in reasoning that will undermine your

Mutually Exclusive – Events that can’t happen at

argument

same time

Here’s an example… probability tells us that when

you flip a coin you have a 50% chance of hitting

Slippery Slope – Saying that if A happens, and B-Y

Non-Mutually Exclusive – Events that can happen at

either heads or tails, so if you flip the coin 100 times

happen, then Z will happen, so basically A = Z

same time

you would expect to get 50 heads and 50 tails… but

that isn’t always what will happen!

Hasty Generalizations – Just what it sounds like, you

Independent – When an event’s probability isn’t

come to a conclusion about something before you have

affected by anything else happening or not happening

All that probability is telling us is that most of the

sufficient information

(e.g. a coin toss isn’t affected by previous coin toss)

time you’ll get a number somewhere close to 50

heads and 50 tails, not that you absolutely will get

Post hoc ergo propter hoc – Basically saying that if B

Dependent – Events whose probabilities change

that exact number each and every time you run the

happens after A, then A caused B

based on each other happening or not happening

“100 coin flip test.”

Genetic – Saying that the origin of a person or a thing

dictates its character or worth

Begging the Question - When you try to validate your

Correlation

conclusion within the question that you are asking

When there is some relationship between two things

Circular Arguments – Stating a conclusion that just

Correlations always take values between -1 and 1

restates itself as proof (ex. My car is awesome because

it’s so cool)

-1 is a perfect negative correlation, which means as one thing gets bigger the other thing gets smaller

Either-Or – Oversimplifying a conclusion by assuming

0 is no correlation at all, basically there is no relationship between these things

that it must be either one thing or the other

1 is a perfect positive correlation, which means that when one thing gets bigger so does the other

The closer the correlation value is to -1 or 1, the tighter (more linear) the relationship will be on a scatter plot

Caution Hazard

(see below on Pearson’s coefficient)

Perfect

High

Low

Positive

Positve

Correlation

Correlation DOES NOT prove

Correlation

Causation!

Beware temptation to say that a correlation

between two things means one causes the other.

For example…

There may be a correlation between sweater and

0.9

0.5

snow-shovel sales. However, that does not mean

that sweaters make people buy snow-shovels.

Low

High

Perfect

Negative

All that we can say with a correlation is that there is

Correlation

a relationship/link between sweater sales and

snow-shovel sales.

Multiple & Conditional Probability

Make sure that you account for ALL possible events

when calculating probability.

Same is true for conditional vs. unconditional

-0.5

-0.9

-1

probabilities, be sure you understand all

relationships.

Some different correlation

Here’s how we calculate

calculations...

correlation (Pearson’s way):

Real life is never as simple as a coin toss.

Probabilities ARE NOT Guarantees!

In this example we have two things to compare, X

There are different correlation calculations (called

coefficients) for different kinds of data:

and Y.

Probability tells you that over the long run there is

Pearson’s Coefficient – Measures linear

First calculate Mean (average) of X

a certain chance of something happening. Not that

relationship between two variables

Calculate Mean (average) of Y

something will or will not happen at a specific time.

Subtract Mean of X from each of X values (we’ll

Spearman’s Rank Coefficient – Measures

call these A), and subtract Mean of Y from each

In other words, probabilities are great for general

relationship between two ordinal variables

of Y values (we’ll call these B)

predictions about long term events, but they

Phi Coefficient – Measures relationship

Square A’s (we’ll call these C

’s)

cannot and do not predict specific events.

between two dichotomous variables

Square B’s (we’ll call these D

’s)

Multiply all A’s by B’s (we’ll call these AB’s)

Over Generalization of Results

Pearson’s Coefficient is most popular and what

Add up all AB’s

analytical tools use.

Add up all C

’s

Add up all D

’s

If you calculate a correlation on a specific

population, you cannot then say that correlation is

10.

Now perform calculation below…

same for general population.

Sum of all AB’s

Correlation =

(Sum of C2’s) x (Sum of D2’s)

Make sure to review

Hazards! section regarding correlation and causation!

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