Stat - Top Hat Questions
Confidence Level
How much margin of error we allow to accurately capture a parameter within a certain range of values
Statistical Inference
Moving from the statistical information we gather on a sample and generalizing this to the larger population
the larger a sample size is, the _____ error in estimation bc we are closer to capturing the ____________
smaller, total population
fail to reject a hypothesis
specificity
A characteristic that exhibits a large amount of variability in the population
decreases power
Having fewer individuals in your sample
decreases power
Larger Amount of Error in Estimation
decreases power
Lowering the chances you're willing to take to erroneously reject a null hypothesis
decreases power
Choose a one-tailed instead of a two-tailed alternative hypothesis
increases power
Greater difference between a sample statistic and the parameter value under the null hypothesis
increases power
Having fewer groups to compare between (i.e. conducting fewer hypothesis tests)
increases power
when the shape of the sampling distribution is _______, we know the principle is the _________
normal, central limit theorem
Mean of Sampling Distribution
A point estimate that gives the best estimate of a parameter; in other words our best guess at the true parameter value
Researchers wanted to assess if caffeine consumption in the afternoon would affect mean fatigue levels in the evening time. They randomly assigned individuals to two groups, one where they were given a caffeine pill at around 2pm and the other where they were given a placebo (i.e., "a fake, ineffective pill"), then fatigue levels were measured at 7pm. They conducted hypothesis testing to see if there were any differences in the mean fatigue scores between the two groups. Which of the following would best express their null and alternative hypotheses?
Alternative: Caffeine consumers will have different mean fatigue score than the placebo group; Null: Caffeine consumers will have the same mean fatigue score as the placebo group
Which of the following accurately depicts the relationship between a test statistic, p-value, and likelihood of rejecting the null hypothesis? (select all that apply)
As test statistic gets larger the p-value gets smaller and the likelihood of rejecting the null hypothesis increases AND As test statistic gets smaller the p-value gets larger and the likelihood of rejecting the null hypothesis decreases
The Confidence Interval becomes more wide. We lose precision because we are allowing a wider possible range of values but are more certain that the parameter is in our interval (e.g. it's a safer bet that average commute times are somewhere between 0 minutes and 600 minutes than between 20 and 30; indeed 20-30 is inside of 0-600). The error in estimation isn't altered just the level of confidence we have in capturing the true parameter value.
Choose confidence level of 99% instead of 95%
Standard Error of a Statistic
Error in estimation captured by the standard deviation of a sampling distribution
Sampling variability
If we took repeated random samples and estimated a parameter we would find some variability amongst those estimates from sample to sample
A study failed to detect any differences in blood pressure between a placebo group and a group who had been taking a new medication meant to reduce blood pressure. From lab studies, they are certain it must work. They decide to conduct the study again. What can they do to increase their ability to detect the effect they anticipate? (select all that apply)
Increase their sample size AND Up the dosage (if ethical or possible) to increase their effect size AND Raise the alpha level (so long as it is within reasonable range) AND Choose a less heterogenous population to decrease their population's variance (though this was limit the generalizability of their results to a broader population)
Probability
Proportion of samples producing parameter estimate values within a given range of a sampling distribution
The width of the interval would be unchanged; however the range of values in which we have confidence our parameter will be captured will be systematically lower; the error in estimation and confidence will be unaltered; only the range of possible values changes. Upper: 22+2.4*1.96=26.704. Lower: 22-2.4*1.96=17.296 Now we say we are 95% confident that our true parameter is between 17.296 and 26.704; instead of we are 95% confident that the true value is between 21.3 and 30.7
The Sample Mean acquired was 22 instead of 26
reject a true null
type 1 error
An individual had become infected with a virus; a lab test designed to detect this virus failed to do so.
type 2 error
false negative
type 2 error
From the familywise error question, we saw an example of inflated type 1 error across many comparisons. For comparing amongst 6 different groups with alpha level of 0.05, what would be the alpha level adjusting for the inflated type 1 error due to multiple comparisons?
0.0033
If we wanted to conduct hypotheses testing to compare mean differences amongst 6 different groups, what would be the likelihood that we would erroneously reject at least one null hypothesis by chance alone if we were using a type 1 error rate of 0.05?
0.5368
Under the null, it is hypothesized that the population mean difference between two groups will be zero. Which of the following is an accurate statement? (select all that apply)
As the mean difference between groups gets larger the effect size will increase AND As the mean difference between groups gets larger the test statistic will get larger
Of the following statements, which are accurate?(select all that apply)
If null were false increasing alpha would decrease type 2 error AND If null were false decreasing alpha would decrease power AND If null were true increasing alpha would decrease specificity
Researchers found that usage of an app for health monitoring encouraged people to participate in more physical activities but there had not really been any genuine changes in people's participation in physical activities.
Type 1 error
If we decided to use a significance level of 0.01 (α=0.01) instead of 0.05(α=0.05) as criteria for whether we reject the null hypothesis; what would happen to the type 1 error rate(α), type 2 error rate(β), power of the test (1-β), and specificity of the test(1-α) if we acquired a p-value of 0.02 ?
We would fail to reject the null hypothesis; type 1 error would decrease; type 2 error would increase; Power would decrease; and Specificity would increase
Choosing a lower value for the parameter under the null hypothesis
doesn't affect power
Less Variability on a characteristic amongst individuals in the Population
increases power
The Confidence interval decreases in width. A larger sample results in less error of estimation (i.e. smaller standard error); this means we are more precisely capturing the true parameter in our interval with the same level of confidence (95%).
Sample goes from n=25 to n=50
The confidence interval would be wider. Higher Standard Deviation in the population will result in more error in estimation (i.e. larger standard error); this means we will have less precision in capturing our true parameter with the same level of confidence.
The actual population standard deviation were 18 minutes instead of 12 minutes
A health advocacy group was planning a study, they expected that individuals undergoing a mini-course on health literacy, would increase their health literacy exam scores by an average of 0.5 standard deviations. Which of the following statements are accurate? (select all that apply)
The expected effect size would be considered medium
Sampling Distribution of a Statistic
The frequency distribution of the Parameter Estimates (i.e. Statistics) from different samples of the same size
Increased knowledge of an auto-immune condition does not influence levels of anxiety over health problems; researchers found no significant relationship between the two through statistical analysis.
specificity
A counseling program which utilizes recovered addicts to help current addicts to enter recovery is actually effective; researchers conducted statistical tests to evaluate this program. They found that indeed there was an effect.
statistical power
true positive
statistical power