POLS285 Test 2 P.2 Flashcards
What is alternative and null hypothesis?
-Alternative hypothesis: What we expect to see if our theory is true; usually, it’s that the parameter isn’t 0, e.g., μ 6 = 0.
-Null hypothesis: What we expect to see if our theory is false; usually, it’s that the parameter is 0, e.g., μ = 0.
What is the basic logic of null hypothesis and what does it mean?
-Always performed on null, the purpose of the test is to see whether we can reject the null.
-Does not mean: theory is proven, alternative hypothesis is true or that the null hypothesis is false.
-It means: the null hypothesis (e.g, the parameter is 0) is unlikely and we favour the alternative hypothesis (e.g, parameter is something other than 0).
What is sampling distribution and null sampling distribution?
-Null sampling distribution is the distribution of a sample statistics in the event the null hypothesis is true.
-Sampling distribution is the distribution of sample statistics from an infinite number of samples of the same size.
What is a P-value?
-P-values measure the lack of fit between our null hypothesis and our sample data; it’s the probability of observing our results or something less likely in the event the null is true.
-If p is sufficiently low, the null hypothesis is likely false.
what is the t-value and df?
-t is the number of standard errors and value is above or below
-df refers to degrees of freedom (sample size)
-as df increases, t decreases, and the non-rejection region narrows.
What are the limits of p-values?
-P-values are only valid if we’re working with random or probability samples.
-Low p-values don’t necessarily imply causation.
-Stastical significance is often conflated with substantive significance.
How is t-distribution different from normal distribution?
-Like normal ones, they are bell-shaped, unimodal and symmetric but they:
-Have heavier tails and more observations further from the mean.
-Dont represent any one distribution but a family of them.
-Get taller, and thinner, and converge on a normal distribution with higher degrees or freedom (which is closely linked to sample size).
What is the population regression model?
-The true model whose parameters we can never know with certainty.
Yi = α + βXi + ui
-Captures the actual relationship of X and Y, although we cannot see it
What is the sample regression model?
The model we estimate from sample data
Yi = ˆα + ˆβXi + ˆui
We distinguish between population parameters and parameter estimates by placing hats (^) over each parameter estimate.
What is OLS and significance of b (hat) equation?
-Ordinary least squares regression: fitting a line that minimizes sum of squared errors or residuals.
-Significance: Top is covariance equation and denominator is the difference between X values. Smaller difference between X will result in a smaller denominator resulting in larger slope.
What is the difference between causal effects and causal mechanisms?
-Causal effects aren’t causal mechanisms: The former
refers to the effects of a change in X on Y (as represented byˆβ); the latter to the causal process linking the variables.
What is the average causal and treatment effects and its relationship with probabilistic and deterministic understandings of causality?
-We often interpret ˆβ as the average effect; average treatment effect; or average causal effect.
-The language is probabilistic. If the effects were
deterministic, we wouldn’t refer to average effects - just the
effect.
