Interpretations - AP Statistics

Standard Deviation

Standard Deviation

The context typically varies by SD from the mean of 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.

When describing a distribution, use

GSOCS: Gaps, shape, outliers, center, spread.

Correlation (r)

The 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 = value.

Y-intercept

The predicted y-context when x = 0 context is the y-intercept.

Slope

The predicted y-context increases/decreases by slope for each additional x-context.

Standard Deviation of Residuals (s)

The actual y-context is typically about s away from the value predicted by the LSRL.

Coefficient of Determination (r²)

About r²% of the variation in y-context can be explained by the linear relationship with x-context.

When describing the relationship, use

DUFS: Direction, unusual features, form, strength.

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, mew)

If the random process of context is repeated for a very large number of times, the average number of x-context we can expect is expected value.

Binomial Mean (mew subscript x)

After many, many trials the average # of success context out of n is sample mean.

Binomial Standard Deviation (sigma subscript x)

The number of success context out of n typically varies by sample std from the mean of sample mean.

Standard Deviation of Sample Proportions

The sample proportion of success context typically varies by proportion std from the true proportion of p.

Standard Deviation of Sample Means

The sample mean amount of x-context typically varies by mean std from the true mean of mean of x.

Confidence Interval

We are % confidence that the interval (A, B) captures P, the true parameter 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 Ho in context is true, there is a p-value probability of getting the observed result or less/greater/more extreme purely by chance.

Conclusion for a Significance Test

With a p-value of p-value, less than/greater than alpha, we reject/fail to reject Ho. We do/do not have convincing evidence that Ha in context.

Type 1 Error

The Ho context is true, but we find convincing evidence for Ha context.T

Type 2 Error

The Ha context is true, but we don’t find convincing evidence for Ha context.

Power

If Ha context is true at a specific value there is power probability the significant test will correctly reject Ho.

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 SE of slope.