Stat

Stats Medic Ultimate Interpretations Guide

CED Unit 1: Exploring One-Variable Data

Standard Deviation: The context typically varies by SD from the mean of mean.

Example: The height of power forwards in the NBA typically varies by 1.52 inches from the

mean of 80.1 inches.

Percentile: percentile % of context are less than or equal to value.

Example: 75% of high school student SAT scores are less than or equal to 1200. z-score: Specific value with context is z-score standard deviations above/below the mean.

Example: A quiz score of 71 is 1.43 standard deviations below the mean. (z = -1.43)

Describe a distribution: Be sure to address shape, center, variability, and outliers (in context).

Example: The distribution of student height is unimodal and roughly symmetric. The mean

height is 65.3 inches with a standard deviation of 8.2 inches. There is a potential upper outlier at 79 inches and a gap between 60 and 62 inches.

CED Unit 2: Exploring Two-Variable Data

Correlation (r): The linear association between x-context and y-context is weak/moderate/strong (strength) and positive/negative (direction).

Example: The linear association between student absences and final grades is fairly strong

and negative. (r = -0.93)

Residual: The actual y-context was residual above/below the predicted value when x-context = #.

Example: The actual heart rate was 4.5 beats per minute above the number predicted when

Matt ran for 5 minutes.

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

Example: The predicted time to checkout at the grocery store when there are O customers in

line is 72.95 seconds.

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

Example: The predicted heart rate increases by 4.3 beats per minute for each additional

minute jogged.

Standard Deviation of Residuals (s): The actual y-context is typically about s away from the value predicted by the LSRL.

Example: The actual SAT score is typically about 14.3 points away from the value predicted

by the LSRL.

Coefficient of Determination (r): About r2% of the variation in y-context can be explained by the linear relationship with x-context.

Example: About 87.3% of variation in electricity production is explained by the linear

relationship with wind speed.

Describe the relationship: Be sure to address strength, direction, form and unusual features (in context).

Example: The scatterplot reveals a moderately strong, positive, linear association between the weight and length of rattlesnakes. The point at (24.1, 35,7) is a potential outlier.

CED Unit 4: Probability, Random Variables and Probability Distributions

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

Example: P(heads) = 0.5.

0.5.

After many many coin flips, the proportion of times that heads will occur is about

Conditional Probability P(A|B): Given context B, there is a P(AIB) probability of context A

Example: P(red car I pulled over) = 0.48.

Given that a car is pulled over, there is a 0.48 probability of the car being red.

Expected Value (Mean, p: 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. (decimals OK).

Example: If the random process of asking a student how many movies they watched this week is repeated for a very large number of times, the average number of movies we can expect is 3.23 movies.

Binomial Mean (Mx): After many, many trials the average # of success context out of n is ux.

Example: After many, many trials the average # of property crimes that go unsolved out of

100 is 80.

Binomial Standard Deviation (ox): The number of success context out of n typically varies by ex from the mean of ux.

Example: The number of property crimes that go unsolved out of 100 typically varies by 1.6

crimes from the mean of 80 crimes.

CED Unit 5: Sampling Distributions

Standard Deviation of Sample Proportions (p): The sample proportion of success context typically varies by of from the true proportion of p.

Example: The sample proportion of students that did their AP Stats homework last night

typically varies by 0.12 from the true proportion of 0.73.

Standard Deviation of Sample Means (0x): The sample mean amount of x-context typically varies by Or from the true mean of ux.

Example: The sample mean amount of defective parts typically varies by 5.6 parts from the

true mean of 23.2 parts.

CED Unit 6, 7, 8 & 9: Inference for Proportions, Means, and Slope Confidence Interval (A, B): We are % confident that the interval from A to B captures the true parameter context.

Example: We are 95% confident that the interval from 0.23 to 0.27 captures the true proportion of flowers that will be red after cross-fertilizing red and white.

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

Example: If we take many, many samples of size 20 and calculate a confidence interval for each, about 90% of them will capture the true mean weight of a soda case.

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

Example: Assuming the mean body temperature is 98.6 °F (Ho: 4 = 98.6), there is a 0.023 probability of getting a sample mean of 97.9°For less, purely by

chance.

Conclusion for a Significance Test: Because p-value p-value < / ≥ a we reject / fail to reject Ho. We do / do not have convincing evidence for Ha in context

Example: Because the p-value 0.023 ≤ 0.05, we reject Ho. We do have convincing evidence that the mean body temperature is less than 98.6 °E(Ha: (Ha: < <98.6).

Type 1 Error: The Ho context is true, but we find convincing evidence for Ha context

Example: The mean body temperature is actually 98.6°F, but we find convincing evidence the mean body temperature is less than 98.6 °F.

Type II Error: The Ha context is true, but we don't find convincing evidence for H, context.

Example: The mean body temperature is actually less than 98.6 °F, but we don't find convincing evidence that the mean body temperature is less than 98.6°F.

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

Example: If the true mean body temperature is 97.5°E, there is a 0.73 probability the

significance test will correctly reject Ho: u = 98.6

Standard Error of the Slope (SE): The slope of the sample LSRL for x-context and y-context typically varies from the slope of the population LSRL by about SEp.

Example: The slope of the sample LSRL for absences and final grades typically varies from the slope of the population LSRL by about 1.2 points/absence.