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Statistically Significant

Unlikely to occur by random chance

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Strength of Evidence

How sure we are it's not chance

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Sample

The set of our observational units

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Sample Size

Number of observational units (n)

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Statistic

Summary of the sample (p-hat)

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Parameter

The long-run proportion (π or p)

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Test of Significance

Measuring the strength of evidence against the chance model (3-S Strategy)

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Null Hypothesis

Random chance explanation

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Alternative Hypothesis

Special situation explanation

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Null distribution

Distribution of simulated statistics from simulating the null hypothesis

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3-S Strategy

Statistic, simulate, strength of evidence

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Steps of a statistical investigation

Research question, collect data, explore data, draw inferences, conlusions, look back and ahead

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Data

Recorded from observational units

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Variables

Recorded characteristics of the observational units

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Quantitative Variables

Numerical values

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Categorical Variables

Category designations

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Distribution

The pattern of the data

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Random Process

A process that can be repeated an infinite amount of times with predicted outcomes

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Simulation

Artificially re-creating a random process to estimate the probability

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Anecdotal Evidence

Personal experience or striking example

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Dot Plot

Each dot is a statistic

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Standardized statistic

(statistic - mean) / (standard deviation)

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P-hat

The summary number of the sample - what you really saw - statistic

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π

Your prediction for the whole population - not just your sample

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P-value

Evidence against the prediction (π) - how unusual was it? - probability

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Too unusual to be random (%)

< 5% (p-value)

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Binary Variable

only two outcomes

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Distribution

how often it happens

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Statistic

summary number

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Strength of evidence

against random chance

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Two-Sided Test

looking for a difference, bigger or smaller

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When do we use the two-sided hypothesis?

When there is no prior assumption of the study

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What does the standardized statistic specifically measure?

It measures how many standard deviations it is away from the mean

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What EXACTLY is the p-value

proportion of statistics in null distribution as extreme as the statistic.

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