Stat 217 – Day 7 Tests of Significance

Last Time Using observed sample data to evaluate a claim about the general process Is this convincing evidence that, in general, students tend to put Tim on the left? Idea: Look at results that do happen “by chance alone” to see whether our observed data are consistent with that pattern

Example 1: Helper/Hinderer Trying to decide between 1. Infants do evaluate individuals as appealing or aversive based on their actions 2. Infants don’t have a genuine preference and these 16 just happened to pick the helper toy more often

If infants are picking at random Meaning choose equally between the two toys in the long run “could have been results”

Conclusions Small p-value : It would be very unlikely to have 14 (or more) picking the helper toy if all 16 infants were picking blindly between the two toys Conclusion: Strong evidence against the null hypothesis in favor of the alternative Strong evidence these infants (in the long run) have a genuine preference for the helper toy

Follow-up study Video

Example 2: Bottled water vs. Tap water Let p represent the probability that some one picks tap water as their favorite Null hypothesis: p = .25 (people pick the tap cup equally among the four cups) Alternative hypothesis: p < .25 (people are less likely to prefer tap water than non-tap)

Tap water What are typical values for the proportion of successes (tap water) if people are choosing equally?

Tap water If people pick tap water 25% of the time in the long run, then we would expect to see 11.1% or fewer picking water in about 5% of repetitions of 27 water tasters by chance alone. A p-value of .05 is some evidence that the long-run probability of picking tap water is less than .25. Tap water is “statistically significantly” less preferred.

“Survey” A campus legend tells the story of two friends who told their professor that they got a flat tire returning to town and missed the exam. The professor agreed to give them a make-up exam. The first question (worth 5 points) was easy, but the second question worth 95 points, asked “Which tire was it?”

Data Collection If you have to choose a hypothetically flat tire, which of the four tires would you say went flat? Left front Right front Left rear Right rear

To Do Submit Lab 1 by beginning of next class Finish reading Section 1.2