interpretions in statistics

Standard deviation

On average, the values are (blank) units away from the mean

Percentile

Percentile% of (context) are less than or equal to (value)

Z-score

(Specific value with context) is (z-score) standard deviations above/below the mean

Describe a distribution

Address the SOCS

Shape

Outliers

Center

Spread

Correlation

The linear/non-linear association between (x-context) and (y-context) is (weak/moderate/strong —> strength) and positive/negative (direction)

Residual

The actual (y-context) was residual above/below the predicted value when (x-context = #)

Y-intercept

The predicted y value is (blank) units when x = zero

Slope

The slope tells us for every additional (x unit), the predicted (y units) will increase/decrease by (blank)

Standard deviation of residuals

When using the LSRL with (x units) to predict (y units), we will typically by off by ( blank y units)

Coefficient of determination

(Blank)% of the variation in (y units) is explained by the linear model relating ( y units) to (x units)

Describe the relationship

Address strength, direction, form and unusual features (outliers, gaps, clusters) in context

Probability P(A)

After many, many (context), the proportion of times that (context A) will occur is about P(A)

Conditional probability P(A/B)

Given (context B), there is a P(A/B) probability of (context A)

Expected value mean

If the random process of (context) is repeated many, many times, the average number of (x context) we can expect is (expected value)

Binomial mean

After many, many trails the average number of (success context) out of n is mean

Binomial standard deviation

The number of (success context) out of n typically varies by (standard deviation) from the true proportion of p

Confidence interval

We are % confident that the interval from A to B chapters the true (parameter in context)

Confidence level

If we take many, many samples of the same size and calculate a confidence interval for each, about (confidence level %) of them will capture the true (parameter in context)

P-value

Assuming (null in context), there is a (p-value) probability of getting the (observed result) or less/greater/more extreme, by chance alone

Significance test

Because our p-value is less/greater than alpha, we reject/ fail to reject the null hypothesis. We do/do not have convincing evidence for the alternative hypothesis

Type 1 error

The (null hypothesis context) is true, but we find convincing evidence for the alternative hypothesis

Type 2 error

The (alternative hypothesis context) is true, but we don’t find convincing evidence for the alternative hypothesis

Power

If (alternative hypothesis is true at a specific value) there is a (power) probability the significance test will correctly reject the null hypothesis

Standard error of the slope

The slope of the sample LSRL for (x context) and (y context) typically varies from the slope of the population LSRL by about (standard error of b)