Interpretations Flashcards
(26 cards)
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)
SOCS
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
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
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 0 customers in line is 72.95 seconds.
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
Slope
The predicted (y-context) inc/dec 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^2)
About r^2% 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
Address strength, direction, form, and unusual features + 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.
Probability P(A)
After many many (context), the proportion of time that (context A) will occur is about (P(A)).
Example: P(heads) = 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(A|B)) probability of (context A).
Example: P(red car | 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, µ)
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 (µ_x)
After many, many trials, the average # of (success context) out of (n) is (µ_x).
Example: After many, many trials, the average # of property crimes that go unsolved out of 100 is 80.
Binomial Standard Deviation (σ_x)
The number of (success context) out of (n) typically varies by (σ_x) from the mean of (µ_x).
Example: The number of property crimes that go unsolved out of 100 typically varies by 1.6 crimes from the mean of 80 crimes.
Standard Deviation of Sample Proportions (σ_p̂)
The sample proportion of (success context) typically varies by (σ_p̂) 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 (σ_x̄)
The sample mean amount of (x-context) typically varies by (σ_x̄) from the true mean of (µ_x).
Example: The sample mean amount of defective parts typically varies by 5.6 parts from the true mean of 23.3 parts.
Confidence Interval (A, B)
We are (%) confidence that the interval from (A) to (B) capture 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 (H_o in context), 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 deg F (H_o: µ = 98.6), there is a 0.023 probability of getting a sample mean of 97.9 deg F or less, purely by chance.
Conclusion for a Significance Test
Because (p-value) (</>) (⍺) we (reject/fail to reject) H_o. We do/do not have convincing evidence for (H_a in context).
Because the p-value 0.023 < 0.05, we reject H_o. We do have convincing evidence that the mean body temperature is less than 98.6F.
Type 1 Error
The (H_o context) is true, but we find convincing evidence for (H_a context).
Example: The mean body temperature is actually 98.6F, but we find convincing evidence the mean body temperature is less than 98.6F.
Type II Error
The (H_a context) is true, but we don’t find convincing evidence for (H_a context)
Example: The mean body temperature is actually less than 98.6F, but we don’t find convincing evidence that the mean body temperature is less than 98.6F.
