Exploring 1 variable data
CSOCS - Context, Shape, Outliers, Center, Spread
How do you describe a distribution?
Describe a correlation
The linear association between x-context and y-context is weak/moderate/strong (strength) and positive/negative (direction).
We are % confident that the interval from A to B captures the true parameter context.
Interpret the Confidence Interval
After many many context, the proportion of times that context A will occur is about P(A)
The Ha context is true, but we donβt find convincing evidence for Ha context.
What is a Type 2 Error?
Interpret the Z-Score.
Specific value with context is z-score standard deviations above/below the mean.
Interpret the Residual
The actual y-context was residual above/below the predicted value when x-context = #.
Interpret the Slope
The predicted y-context increases/decreases by slope for each additional x-context.
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.
Interpret the Expected Value.
Conclusion for a Significance Test
Because p-value p-value < / > significance level we reject / fail to reject H0. We do / do not have convincing evidence for Ha in context.
Describe a Distribution
CSOCS - Context, shape, outliers, center, spread
Describe the relationship
DUFS - Direction, Unusual Points, Form, Strength
Interpret the 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
Interpret the conditional probability
Given context B, there is a P(A|B) probability of context A
Interpret a P-value
Assuming Ho in context , there is a p-value probability of getting the observed result or less/greater/more extreme, purely by chance.
Interpret a Percentile.
percentile % of context are less than or equal to value.
The actual SAT score is typically about 14.3 points away from the value predicted by the LSRL.
Standard Deviation of Residuals
The sample proportion of success context typically varies by πp from the true proportion of π
Standard Deviation of Sample Proportions
Interpret the Binomial Standard Deviation
The number of success context out of n typically varies by πx from the mean of πx
Type 1 Error
The Ho context is true, but we find convincing evidence for Ha context.
Interpret the Standard Deviation.
The context typically varies by SD from the mean of mean.
Interpret the Coefficient of Determination
About π2% of the variation in y-context can be explained by the linear relationship with x-context.
The sample mean amount of x-context typically varies by πx from the true mean of πx.
Standard Deviation of Sample Means
Interpret the Binomial Mean
After many, many trials the average # of success context out of n is πx.
Standard Error of the Slope (SEb)
The slope of the sample LSRL for x-context and y-context typically varies from the slope of the population LSRL by about SEb context.