psyc011 week 3

chapter 9

part 1

  • null hypothesis significance testing (NHST) - process producing probabilities that are accurate when the null hypothesis is true

  • effect size index (ex1)

    • doritos claims 269.3 g in package

      • what does that mean?

        • perhaps that the minimum amount you’ll get in a pack is that many grams

      • how does one test it?

        • weigh each bag to get the following results⬇

    • Checking up on Frito-Lay

      • buy 8 bags

        • mean weight = 270.675

        • standard dev = 0.523

      • how large is difference between 270.675 and 269.300?

        • 1.375g how else could that be represented

    • 1.375g in raw units - how about relative to standard dev?

    • **work in Notability

  • hypothesis of equality - mu1 = mu0

  • hypothesis of difference - mu1 NOT= mu0

  • NHST can show strong support for hypothesis of difference (if data allows)

  • NHST does not show support for hypothesis of equality (no matter outcome of data

  • if hypothesis of equality is not credible, the only hypothesis left is hypothesis of difference

    • credibility lost if sample mean found is far away from sample mean given

  • null hypothesis (H0) - hypothesis about population or relationship among populations

    • used to produce sampling distribution of differences

  • alternative hypothesis (H1) - hypothesis about population parameters accepted if null hypothesis is rejected

  • how to determine if results are unlikely enough under H1 to reject H0

    • SET AN ALPHA (significance level)

    • if results are less than or equal to alpha, H0 is rejected

  • alpha - probability of a type 1 error

  • significance level - probability (alpha) chosen as criterion for rejecting the null hypothesis

  • statistically significant - difference so large that chance is not a plausible explanation for the difference

  • NS - difference that is not statistically significant

  • rejection region - area of sampling distribution that corresponds to test statistic values that lead to rejection of null hypothesis

  • critical values - number from sampling distribution that determines whether null hypothesis is rejected

  • the one sample t-test - statistical test of hypothesis that a sample with a given mean came from a population with a mean mu0

  • type 1 error (probability alpha) - rejection of null hypothesis that is true

    • Reject H0, H0 true

  • type 2 error (probability beta) - failure to reject a null hypothesis that is false

    • retain H0, H0 false

  • correct decision

    • reject H0, H0 false

    • retain H0, H0 true

  • under NHST, p is probability of obtained statistical test value WHEN H0 IS TRUE

  • if p<0.05, results obtained or results more extreme are rare, occurring fewer than 5 times in 100 when null hypothesis is true

    • p is not probability that H0 is true

    • p is not probability of a Type 1 error

    • p is not probability that data are due to chance

    • p is not probability of making wrong decision

    • complement of p, (1 - p), is not probability that alternative hypothesis is true

  • two tailed test: actual population is different from null hypothesis - greater or less than

    • H1: mu1 not equal to mu0

  • one tailed test:

    •   EITHER

      • actual population mean is less than null hypothesis

        • H1: mu1 < mu0

      • OR

      • actual population mean is greater than null hypothesis

        • H1: mu1 > mu0

chapter 10

  • logic of an experiment

    • 1) start with 2 equivalent groups

    • 2) treat them exactly alike except for one thing

    • 3) measure both groups

    • 4) determine size of difference between groups

    • 5) if difference cannot reasonably be attributed to chance factors, conclude difference is due to one way in which groups were treated different

  • experimental group - group receiving treatment

  • control group - group not receiving treatment

  • treatment - one value/level of independent variable

  • paired-samples design

    • natural pairs - paired samples design in which pairing occurs without intervention by the researcher (ex. father, son)

    • matched pairs - paired-samples design in which two individuals are paired by the researcher before the experiment (ex. two siblings)

      • key difference - in natural pairs, group membership is predetermined; in matched pairs, individuals can be randomly assigned two groups

    • repeated measures - experimental design in which each subject contributes to more than one treatment (ex. before and after)

  • independent samples design

    • two groups randomly assigned from overall sample

    • no clear way to line up participants from one group with the other

      • ex) sample of 20 participants

        • random 10 selected for control group, remaining 10 in experimental group

  • hints

    • if 2 groups have different sample sizes → independent

    • if sample sizes are equal, see if top row of numbers are there for a reason (natural pairs, matches, or repeated), if yes → paired; if no → independent

  • degrees of freedom

    • denny’s analogy

      • 3 people, 2 plates set down, where is the 3rd?

        • df = N - 1; df = 3 - 1 = 2

    • one-sample t-test: N scores, if N - 1 are determined, what is Nth?

      • t test relies on estimate of population mean from sample

      • df = N - 1

    • test of r: N pairs (points), if N-2 are determined, what are the last two?

      • r relies on formula for a line with 2 parameters estimated

      • df = N - 2

part 2

  • in paired sample design

    • analysis performed on difference between each participant’s two scores

    • steps

      • calculate descriptive stats and effect size index

      • calculate confidence interval about mean difference in 2 populations

      • apply NHST logic to data

      • write conclusion