chapter 6.2 Flashcards
null hypothesis
a kind of default assumption - a reasonable expectation about how the world is
alternative hypothesis
since it is posited as an alternative to the default assumption and is the speculative hypothesis of focal interest. This will be a bold and risky conjecture, the value of which we have periodically emphasized.
the nulll hypothesis and alternative hypothesis are related in this way in the hopes of performing the follwing kind of inference
the null hypothesis - the default expectation - leads one to expect a certain range of possible outcomes. When the actual data collected are pretty far outside that range, scientists can reason that such data would be overwhelmingly unlikely if the null hypothesis were ture. And so, the data provide grounds for rejecting the null hypothesis. The data instead support the alternative hypothesis - the bold conjecture
summary of statistical hypothesis testing and its relationship to general hypothesis testing
Hypothesis: formulate alternative hypothesis and corresponding null hypothesis
Expectations: Determine probability distribution for the range of outcomes expected if the null hypothesis is true
Observation: By experiment or observational study, determine one or more actual outcomes
Conclusion: evaluate whether the actual outcome is unlikely enough given expectations from the null hypothesis to provide grounds for rejecting the null hypothesis
mean formula
mean = #trials x Pr(0=success)
standard deviation for the probability distribution can be calculated like
sd = sqr(mean x (1-PR(0=success))
significance level
a decision about how improbable, given the null hypothesis, an experimental result must be to warrant rejecting the null hypothesis
p-value
the probability of the obsvered data assuming the null hypothesis is true. The smaller the P-value the more unlikely the data if the null hypothesis is true
whether one should reject the null hypothesis is determined by comparing the p-value and the significance level selected in step 2
the precise p value can be calculated (eg) from the probability of guessing all eight cups correctly. This is easy 0.5^8 = 0.0039
the p value the probability of your friend guessing correctly on all eight cups by random guesswork is only 0.0039 which means 0.39% chance of this happening –> statistically significant
type 1 error
The risk of erroneously rejecting the null hypothesis when it is true
type 2 error
the risk of erroneously failing to reject the null hypothesis when it is false
effect size
the magnitued of difference some variables make
Effect size can be reflected in different measurements, such as the mean difference in some feature between two groups of the correlation between two variables. The important point here is that a statistically significant finding may nonetheless identify a factor with only a small effect size
statistical tests may vary in their
power, that is, in the probability that they will enable the rejection of a null hypothesis
more powerful tests increase the chance of
rejecting false null hypothesis and thus decreasing chance of type 2 errors. Power increases with sample size
increasing sample size to increase the power of a statistical test can be a good thing, tea tasting experiment. but it also has a downside:
this increases the chance of making a type 1 error. Studying very large sample of individuals makes it relatively easy to uncover statistical significant findings, but also makes it relatively easy to erroneously reject the null - that is to declare incorrect findings
