What's the difference?
Hypothesis Testing
Confidence Intervals
Errors and Power
Flashback Friday
100
What's the difference between sigma and standard error?
Sigma is the population standard deviation and standard error is the sample standard deviation. -or- Standard error is sigma divided by the square root of the sample size (n).
100
Do you make decisions about what to do with the null hypothesis or the alternative hypothesis?
What is THE NULL. Either you decide to reject the null or you fail to reject the null. We never phrase it in terms of the alternative hypothesis.
100
Which one of these things varies in confidence intervals: the confidence intervals or the population mean?
The population mean is fixed. The confidence intervals are what varies.
100
When you reject the null hypothesis, but the null hypothesis is true, you have made this type of error
What is Type I Error
100
This tells us the deviation of a score from the mean measured in standard deviation units
What is z-score
200
What's the difference between an interval estimate and a point estimate?
The point estimate is a single value from the sample used to estimate a population parameter. The interval estimate is not a single number but a range of values to estimate the population parameter.
200
What is the rejection region?
The rejection region is the area in the tail(s) has an area exactly equal to alpha.
200
What is the value that you add and subtract the margin of error from?
The margin of error is added and subtracted from the point estimate.
200
This is the probability of a Type II error
What is beta
200
If "feeling good about math" and "math ability" are positively correlated, what are the 3 possible explanations of this?
3 possible explanations: 1.) Feeling good about math causes math ability 2.) Math ability causes feeling good about math 3.) Something else, a third variable, is mediating (or explaining) the relationships between feeling good about math and math ability.
300
What's the difference between standard error of the sampling distribution and standard error of the estimate?
Standard error of the sampling distribution is the sd (sigma divided by sqrt(sample size)) of the sampling distribution. Standard error of the estimate is the average distance between your actual data points and your predicted regression line.
300
What is the term for the probability of finding a test statistic more extreme than the one obtained?
The p-value.
300
Calculate a margin of error if alpha = .05 (two-tailed), the population sd is 15, and the sample size is 100.
Margin of error = critical value X standard error Critical value = 1.96 Standard error = 15/sqrt(100) = 15/10=1.5 Margin of error = 1.96 X 1.5 = 2.94
300
The probability of rejecting the null hypothesis given that the null is false
What is power
300
R^2 tell us
What is the variance in X explained by Y
400
What is the difference between alpha and beta?
Alpha is the probability of a Type I error, beta is the probability of a Type II error
400
What is the term for the area in the null distribution we define to be unlikely?
Alpha (Rejection region is also acceptable)
400
What 3 things affect the width of the confidence interval? Explain how each of these 3 things affects the width of the confidence interval (CI)
1. standard error (more variability means wider CI) 2. sample size (bigger sample size means narrower CI) 3. confidence level (higher confidence level means wider CI)
400
The center of the alternative hypothesis distribution
What is the non-centrality parameter
400
A probability of one event OR another event occurring
What is additive probability
500
What's the difference between saying "the confidence interval contains the population mean" or "the population mean falls within the confidence interval"?
These statements express opposite relationships between what is changing and what is fixed. The population parameter is fixed and the confidence interval varies. So we talk about whether the CI includes the mean, not whether the mean is in the CI.
500
Calculate a z-score: Pop mean = 100; Pop sd = 15; Sample mean = 110; n = 36. Then decide whether this z-score can be used as evidence to reject the null or fail to reject the null (alpha = .05; two-tailed).
z = (110-100)/(15/sqrt(36)) = 10/(15/6) = 10/2.5 = 4 A z-score of 4 is much higher than the 1.96 cutoff value. This provides evidence to reject the null hypothesis.
500
Why do people bother with hypothesis testing when they could use confidence intervals instead?
We don't know. Maybe because of tradition. Most statisticians like confidence intervals better. Confidence intervals, like hypothesis testing, allow us to make decisions about the null, but they also give us an interval estimate, which tells us about the precision of our point value by providing a range.
500
The precision of your estimate decreases as this increases
What is confidence interval
500
From a study of children’s internalizing problems and quality of parenting received: R = -0.24 To predict internalizing problems from parenting quality, b = -.34 and a = 28 Write the complete regression equation
What is Y ̂=28 -.34X Y ̂ = predicted internalizing problems score X = known parenting quality score
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