Statistics Review Flashcards

Flashcards for reviewing statistics concepts and sentence interpretations.

Standard Deviation

Typically, the context will vary from the mean in context by about SD value in context.

Slope (b) of LSRL (𝑦^ = 𝑎 + 𝑏𝑥)

For every additional x in context, the predicted y in context will in/decrease by about b.

Standard Deviation of Residuals

Typically, the observed y in context will vary from predicted y in context by about s when using the least-squares regression line relating x and y.

Coefficient of Determination 𝑟²

r²% of the variation in y in context can be explained using the least-squares regression line relating x and y.

Least-Squares Regression Line (LSRL)

The line that minimizes the sum of the squared differences between the observed and predicted y in context when relating x and y is the least-squares regressing line.

Confidence Interval

We are C% confident that the population/true parameter in context lies between (lower, upper).

Confidence Level

If we take many random samples of n in context, about C% of the resulting intervals will capture the parameter in context.

Standard Error (one sample)

If we take many random samples of n in context, typically the sample mean or proportion in context will vary from the population/true parameter in context by about standard error value.

Standard Error (two sample)

If we take many random samples of 𝑛" in context and 𝑛! in context, typically the difference in sample means or proportions in context will vary from the difference in population/true means or proportions in context by about standard error value.

P-value in context (ONE sample with 𝒙 bar or 𝒑^ or b) Ha: __ < __

Assuming null in context, the probability of obtaining a sample statistic in context of value of statistic or less by random chance is about p-value.

P-value in context (ONE sample with 𝒙 bar or 𝒑^ or b) Ha: __ > __

Assuming null in context, the probability of obtaining a sample statistic in context of value of statistic or higher by random chance is about p-value.

P-value in context (ONE sample with 𝒙 bar or 𝒑^ or b) Ha: __ ≠ __

Assuming null in context, the probability of obtaining a sample statistic in context of less than or equal to NEGATIVE abs. value of statistic below null value or greater than or equal to POSITIVE abs. value of statistic above null value by random chance is about p-value.

P-value in context (TWO sample with 𝒙bar𝟏 − 𝒙bar2 or 𝒑^𝟏 − 𝒑^𝟐) Ha: __ < __

Assuming null in context, the probability of obtaining a difference in sample statistic in context of value of statistic or less by random chance is about p-value.

P-value in context (TWO sample with 𝒙bar𝟏 − 𝒙bar2 or 𝒑^𝟏 − 𝒑^𝟐) Ha: __ > __

Assuming null in context, the probability of obtaining a difference in sample statistic in context of value of statistic or higher by random chance is about p-value.

P-value in context (TWO sample with 𝒙bar𝟏 − 𝒙bar2 or 𝒑^𝟏 − 𝒑^𝟐) Ha: __ ≠ __

Assuming null in context, the probability of obtaining a difference in sample statistics in context of less than or equal to NEGATIVE abs. value of difference below null value or greater than or equal to POSITIVE abs. value of statistic above null value by random chance is about p-value.

Significance Level or Alpha Level

If we were to conduct many tests, we would expect to reject null in context and conclude alternative in context about alpha-level% of the time by random chance alone.

Type I Error (in context)

A Type I error would be rejecting the null and concluding alternative in context when parameter in context is actually null value in context. (null is true)

Type II Error (in context)

A Type II error would be failing to reject the null and not concluding alternative in context when actually alternative in context. (alternative is true)

Power (in context)

The probability we reject null in context at the alpha-level% and conclude it’s original alternative in context when it’s actually NEW alternative in context is probability of power.

Decision to Reject Null (𝒑 − 𝒗𝒂𝒍𝒖𝒆 = ≤ 𝜶 = )

With 𝑝 − value = ≤ 𝛼 = , we reject the null. We have convincing evidence to conclude alternative in context.

Decision to Fail to Reject Null (𝐩 − 𝐯𝐚𝐥𝐮𝐞 = > 𝛂 = )

With p − value = > α = , we do not reject the null. We do not have convincing evidence to conclude alternative in context.