Chapter 1 - Significance Flashcards
Parameter
Long-run numerical property of a random process (it is also the numerical summary, analogous to the sample statistics, if we were to gather the entire population)
What does it mean for a result to be statistically significant?
A result is statistically significant if it is unlikely to occur just by random chance. If our observed result appears to be consistent with the chance model, we sat that the chance model is plausible or believable
Hypothesis
A statement about the numerical value or condition of a population parameter
Rare event rule for inferential statistics
Given a particular assumption, if the probability of a particular observed event is extremely rare, we conclude that the initial assumption is probably not correct
p-value
The p-value is the proportion of the simulated statistics in the null distribution that are at least as extreme (in the direction of the alternative hypothesis) as the value of the statistic actually observed in the research study
What is the equation for a general z-score?
z= (observation - mean of observation)/ standard deviation of the observation
- negative score shows that observation is below the mean
- positive shows that its above the mean
- score of 0 shows that the observation is equal to the mean
What does the z-score indicate?
z-scores show how many standard deviations the observation is above or below the mean
Equation or standardized statistic
z = (statistic - mean of null distribution)/standard deviation of null distribution
- also known as the test statistic
What happens as the standardized statistic is farther from 0?
*if statistic is 0 then our observed statistic is equal to the value we would expect under the null hypothesis
- if stat is farther from 0, then
Are large values of the standardized statistic evidence against the null hypothesis?
YES
What happens to variability as sample size increases?
As sample size increases, the variability decreases
(so as the sample size increases, the evidence against the null hypothesis increases)
What is the law of large numbers?
As the number of observations drawn increases, in general, the sample statistic of the observed values gets closer and closer to the population parameter.
Type I error (with probability alpha)
rejecting the null hypothesis when it is in fact true
What is the significance level?
The probability of making a type I error. So this is the probability of rejecting the null hypothesis when it is true
What happens when one type of error (I or II) decreases?
Decreasing one type of error causes the other to increase
What is the central limit theorem?
Consider a ransom sample of n observations selected from a qualitative variable. If the sample size is large enough, the distribution of sample proportions will be bell-shaped (or normally distributed) with the following properties:
1. will be centered at the long run proportion pi
2. the distribution will have a sd of sqrt((pi(1-pi))/n)
the approximation becomes better as the sample size increases
