STAT1008 Lecture Notes - Lecture 14: Statistical Significance, Zener Cards, Null Hypothesis
STAT1008 Week 5 Lecture B
● Extrasensory Perception:
○ One way to test for ESP is with Zener cards
○ Subjects draw a card at random and telepathically communicate this to someone
who then guesses the symbol
○ E.g. There are five cards with five different symbols, so if there is no such thing
as esp, P = ⅕ of all guesses should be correct
○ Stats vary from sample to sample; even if the population proportion is ⅕, not
every sample proportion will be exactly ⅕
○ Statistical Test:
■ A statistical test uses data from a sample to assess a claim about a
population
■ E.g. In the ESP experiment, we want to use sample data to determine
whether or not the sample of correct guesses is really over
⅕
.
● Statistical hypotheses:
○ Statistical tests are framed formally in terms of two competing hypotheses:
■ Null Hypothesis (H0): Claim that there is no effect or difference in the thing
we are trying to test
■ Alternative Hypothesis (Ha): Claim for which we seek evidence. Normally
set it up first
■ Both compete with each other about a population
○ The alternative hypothesis is established by observing evidence (data) that
contradicts the null hypothesis and supports the alternative hypothesis
○ Hypotheses are always about population parameters.
○ Usually the null is a very specific statement thus use the alternative hypothesis to
find statements to reject the null
○ E.g. For the ESP experiment:
■ Ho: P = ⅕ <- no “effect” or no “difference”
■ Ha: P > ⅕ <- claim we seek “evidence” for
■ Hints:
● Ho usually includes =
● Ha usually includes >, <, or doesn’t =
● The inequality in Ha depends on the question
○ E.g. Sleep vs Caffeine
■ Students were given words to memorize, then randomly assigned to take
either a 90 min nap, or a caffeine pill.
■ Let mus and muc be the mean number of words recalled after sleeping
and after caffeine.
● Ho: mus = muc
● HA: mus doesn’t = muc
■ The following hypotheses are equivalent, and either set can be used:
● H0: mus - muc = 0
● HA: mus - muc doesn’t = 0
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Document Summary
One way to test for esp is with zener cards. Subjects draw a card at random and telepathically communicate this to someone. Statistical hypotheses: who then guesses the symbol. There are five cards with five different symbols, so if there is no such thing as esp, p = of all guesses should be correct. Stats vary from sample to sample; even if the population proportion is , not every sample proportion will be exactly whether or not the sample of correct guesses is really over . A statistical test uses data from a sample to assess a claim about a. In the esp experiment, we want to use sample data to determine population. Statistical tests are framed formally in terms of two competing hypotheses: Null hypothesis (h0): claim that there is no effect or difference in the thing we are trying to test. Alternative hypothesis (ha): claim for which we seek evidence. Both compete with each other about a population.
