Crash Course on Basic Statistics - CBMM
Crash Course on Basic Statistics
Marina Wahl, marina.w4hl@ University of New York at Stony Brook
November 6, 2013
2
Contents
1 Basic Probability
5
1.1 Basic Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 Probability of Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3 Bayes' Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Basic Definitions
7
2.1 Types of Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Reliability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.4 Validity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.5 Probability Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.6 Population and Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.7 Bias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.8 Questions on Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.9 Central Tendency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3 The Normal Distribution
11
4 The Binomial Distribution
13
5 Confidence Intervals
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6 Hypothesis Testing
17
7 The t-Test
19
8 Regression
23
9 Logistic Regression
25
10 Other Topics
27
11 Some Related Questions
29
3
4
CONTENTS
Chapter 1
Basic Probability
1.1 Basic Definitions
Trials
Probability is concerned with the outcome of trials.
The probability of an event is always between 0 and 1.
The probability of an event and its complement is always 1.
Trials are also called experiments or observations (multiple trials).
Trials refers to an event whose outcome is unknown.
Several Events
The union of several simple events creates a compound event that occurs if one or more of the events occur.
Sample Space (S)
Set of all possible elementary outcomes of a trial.
If the trial consists of flipping a coin twice, the sample space is S = (h, h), (h, t), (t, h), (t, t).
The probability of the sample space is always 1.
The intersection of two or more simple events creates a compound event that occurs only if all the simple events occurs.
If events cannot occur together, they are mutually exclusive.
If two trials are independent, the outcome of one trial does not influence the outcome of another.
Events (E)
An event is the specification of the outcome of a trial.
An event can consist of a single outcome or a set of outcomes.
The complement of an event is everything in the sample space that is not that event (not E or E).
Permutations
Permutations are all the possible ways elements in a set can be arranged, where the order is important.
The number of permutations of subsets of size k drawn from a set of size n is given by:
n! nP k =
(n - k)!
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