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PSYC512: Research Methods Lecture 19

PSYC512: Research Methods Lecture 19. Brian P. Dyre University of Idaho. Lecture 19 Outline. Inferential Statistics Testing for differences vs. relationships Analyzing frequencies Analyzing differences between means. Using Inferential Statistics. Which Statistic?

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PSYC512: Research Methods Lecture 19

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  1. PSYC512: Research MethodsLecture 19 Brian P. Dyre University of Idaho PSYC512: Research Methods

  2. Lecture 19 Outline • Inferential Statistics • Testing for differences vs. relationships • Analyzing frequencies • Analyzing differences between means PSYC512: Research Methods

  3. Using Inferential Statistics • Which Statistic? • The statistical decision tree Howell Figure 1.1 • Testing for relationships vs. differences (a false distinction) • Relationships: assessing the strength of relationship between measured (dependent) variables • Differences: comparing different groups or treatments on some measurement • But what causes those differences? The relationship between the independent variable defining the groups or treatment and the dependent variable • Hence, testing for differences is really testing the relationship between the IV and DV PSYC512: Research Methods

  4. Analyzing Differences Between Treatments • Nominal and Ordinal Frequency Data • “Success vs. Failure” - Binomial Distribution and The Sign Test • Multiple categories (> 2) Multinomial distribution and Chi-square • Multidimensional categories: Chi-square contingency tables • Integral and Ratio Data • 2 treatments or groups – t-test • Comparing two independent samples  HW3 • Comparing two correlated (or paired samples)  HW4 • More than 2 treatments or groups – ANOVA • More than 2 independent variables – multifactor ANOVA– HW5 • 2 or more dependent variables (or repeated measures) – MANOVA • Covariate  ANCOVA – HW5 • Relations between measures • Correlation or Regression PSYC512: Research Methods

  5. Analyzing Frequencies (Howell, Chapter 5) • Bernoulli Trials: series of independent trials that result in one of two mutually exclusive outcomes • E.g. coin flips, gender of babies born, increase of decrease in a measure after application of a treatment • The Binomial Distribution PSYC512: Research Methods

  6. Analyzing Frequencies (Howell, Chapter 5) • Using the binomial distribution • Mean number of successes = Np • Variance in number of successes = Npq • Testing Hypotheses using the binomial distribution: The Sign Test • Ho is typically p= q = .50 (50-50 chance of success of failure), but that doesn’t have to be the case • H1 is typically p ≠q • Plug in values for N, X, p, and q and p(X) directly provides the probability that the pattern of data could result given the null hypothesis is true • Sum the probabilities p(X) for all number >= X to get the total probability of finding p(>=X) • Important: The sign test takes into account direction of differences but not magnitude PSYC512: Research Methods

  7. Analyzing Frequencies (Howell, Chapter 5) • What about multiple (more than 2) possible outcomes? • Multinomial distribution PSYC512: Research Methods

  8. Analyzing Frequencies (Howell, Chapter 5) • Using the multinomial distribution • Mean Xk = NpXk • Variance in Xk = NpXk (1-pXk) • Testing Hypotheses using the multinomial distribution: • Ho is typically pX1= pX2 … = pXk = 1/k (each outcome has the same chance), but that doesn’t have to be the case • H1 is typically pX1 ≠ pX2 …≠ pXk • Plug in values for N, X, and pX, and p(X1, X2…Xk) directly provides the probability that this particular pattern of data could result given the null hypothesis is true • Must sum the probabilities for all patterns that deviate equal to or more to get the total probability – time consuming! PSYC512: Research Methods

  9. Analyzing Frequencies (Howell, Chapter 6) • Easier Alternative to Multinomial distribution: Chi-square (c2) test • Compare computed value of c2 to value of c2 distribution with df=k-1 • Expected frequencies for the null hypothesis typically = N/k, where N is the total number of observations k is the number of categories in the variable O is the observed frequency for each category E is the expected frequency for each category i is the category index PSYC512: Research Methods

  10. Analyzing Frequencies (Howell, Chapter 6) • Using c2 with multiple dimensions: contingency tables—frequencies of one dimension are contingent on the other dimension • Eij = RiCj/N • N is the total number of observations • Compare computed value of c2 to value of c2 distribution with df=(R-1)(C-1) R is the number of categories in the dimension defined by the rows of the table C is the number of categories in the dimension defined by the columns of the table O is the observed frequency for each category E is the expected frequency for each category i and j are category indices PSYC512: Research Methods

  11. Analyzing Frequencies (Howell, Chapter 6) • Assumptions of the c2test • Each observation is independent • Inclusion of non-occurrences PSYC512: Research Methods

  12. z-tests, t-tests • s of population is known: z • s of population is estimated as s: t • df = N-1 • Comparing 2 paired (or correlated) samples • Difference scores • Df = N -1 • Comparing 2 independent samples • df = n1 + n2 – 2 • Unequal sample sizes, heterogeneity of variance, and pooled variances PSYC512: Research Methods

  13. ANOVA (F Statistic) • Used when comparing more than 2 means or 2 or more factors • Assumptions • Homogeneity of variance • Normality • Independence of observations • Between Groups comparisons • k = number of means compared • n = number of Ss in group • Repeated Measures • Error term is interaction of error with subject random variable PSYC512: Research Methods

  14. Interpreting SPSS output PSYC512: Research Methods

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