11_Binomial_Sp08_BB_nocolor

11_Binomial_Sp08_BB_nocolor - Probability & the Binomial...

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1 Probability & the Binomial Test Non-Parametric Statistics Outline • Probability • Binomial Distribution • Z-Approximation to the binomial • The Sign Test The Binomial Distribution Non-parametric statistics: – No assumptions about the shape of the population. Nominal & ordinal data This class will only cover Χ 2 , Binomial, Sign Test - - all use nominal data. The Binomial Distribution • There is only one Z- distribution. – This is the null hypothesis distribution for the Z-distribution. • There are INFINITE binomial distributions. – We can set up these different null hypothesis distributions using three different methods.

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2 The Binomial Distribution • Assumptions for the Binomial: – Events are dichotomous. – Events are mutually exclusive, independent, and randomly selected. – The number of observations/trials (N) is fixed. – The probability of success (p) is the same for each outcome. The Binomial Distribution • Assumptions for the Binomial: – Events are dichotomous. – Events are mutually exclusive, independent, and randomly selected. – The number of observations/trials (N) is fixed. – The probability of success (p) is the same for each outcome. Setting up the Null Hypothesis Distribution • Normal distribution – Continuous Distribution – Defined by mean and standard deviation • Special case - - Standard Normal distribution (0,+/- 1) • One Sample Z-test – Mean of the null = 0 – Standard deviation = +/-1 – Critical Regions with alpha = 0.05: +/-1.96 Setting up the Null Hypothesis Distribution 0 +1.96 -1.96
3 Setting up the Null Hypothesis Distribution • Binomial distribution: – Discrete distribution – Defined by the mean and standard deviation The Binomial Distribution N = # of Trials p = probability (P) of a success q = probability (P) of a failure (or 1-p) Mean Np = SD Npq = The Binomial Distribution • What’s the probability of getting a “heads” on a single coin flip? – Bernoulli Trial p = 0.50 q = 0.50 (or 1- p ) Binomial Distribution - N=20, p=0.50 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 01234567891 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 N p H 0

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4 Method 1: Setting up Null for The Binomial Distribution • The number of ways a particular outcome can occur and the probability of that outcome. ! !( )! x Nx N pq xN x = •W h e r e : – N = number of independent trials – x = number of outcomes (successes) out of N trials – p = probability that the event occurs (success) – q = probability that the event does not occur (~success) Combinations The Binomial Distribution • Let’s say we we’re to flip a fair coin 20 times. What would the binomial distribution look like?
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This note was uploaded on 04/07/2008 for the course PSY 031 taught by Professor Dicorcia during the Spring '08 term at Tufts.

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11_Binomial_Sp08_BB_nocolor - Probability & the Binomial...

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