Confidence intervals & statistical testing Flashcards

1
Q

Sampling distribution

A

Under random sampling, sample mean good estimate of population mean.
When sampled from Gaussian distribution, sample mean also has Gaussian distribution.

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2
Q

Squared standard error of the mean

A

Variance of the sample mean

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3
Q

Standard error of the mean

A

Square root of the sample variance

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4
Q

Confidence interval

A
An interval (based on observed data) that contains an unknown population parameter with some specified probability.
Statement about the likelihood that true parameter value occurs between two bounds. 
NOT probability a value falls between 2 points.
NOT amount of certainty that an estimate takes a certain value.
NOT variability in an estimate.
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5
Q

Critical value

A
Value of a distribution that occurs with a certain level of probability. 
Normal distribution:
-1 to 1 = 68% of density
-1.96 to 1.96 = 95% of density
-2.58 to 2.58 = 99% of density
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6
Q

α

A

Probability of making a mistake.

P(-c

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7
Q

t distribution

A

T = (Xbar - mu)/((s/SQRT(n))

Distribution only depends on size of sample or degrees of freedom (n-1).

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8
Q

Two forms of error

A

Type 1 error: Reject the null when it’s in fact true. Probability is equal to alpha level.
Type 2 error: Fail to reject the null when it’s in fact false. Called beta, & speak in terms of power to reject the null when it is false (1-beta).

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9
Q

Test for normality

A

Shapiro-Wilk test.
Compares the quantiles of your distribution to those of a normal distribution.
Generates a test statistic, W, & a p-value which tell us if data “normal” or not.

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10
Q

Hypothesis testing

A

z-test for the mean, test a sample mean vs. a hypothesized mean value.

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11
Q

p-values

A

p-values are probabilities.
Probability of seeing a test statistic as large ast he one we calculate, then test doesn’t negate null hypothesis.
If test statistics like ours occur very rarely, then have small p value & conclude support for research hypothesis.

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