Inferential Stats for Two-Group Designs

1
Inferential Stats for Two-Group Designs
2
Inferential Statistics

• Used to infer conclusions about the population
  based on data collected from sample
• Do the results occur frequently or rarely by
  chance?
• Two-group designs
• one control group vs. experimental group
• two experimental groups
• Two samples representing two populations

3
Inferential Statistics

• Null hypothesis differences between groups are
  due to chance (i.e., not due to the manipulation
  of IV).
• Results are not significant
• Results are Significant results would occur
  rarely by chance alone. Therefore, likely due to
  the manipulation of the IV.
• plt .05 or p lt .01

4
Single samples t-test

• Compared single sample with a population
• Given population mean
• Derived sample mean, standard deviation and
  standard error of the mean
• Conducted t-test
• Determined critical t value (one-tailed vs.
  two-tailed) based on df
• Reject H0 the sample comes from a population
  that is different from the comparison population.
  
• Sustain H0 the sample and comparison population
  come from the same population.

5
T-test (Difference between Means)

• t-test Inferential statistical test used to
  evaluate the difference between two groups or
  samples.
• Two types
• t-test for independent samples (between-subjects
  design)
• t-test for paired samples (within-subjects
  design)

6
T-test for independent samples

• Compares means of 2 different samples of
  participants.
• Assesses the differences between these 2 samples.
  
• Do participants in each sample perform so
  similarly so that they are likely to come from
  the same population?
• Do participants in each sample perform so
  differently so that they are likely to represent
  2 different populations?

7
Assumptions of independent samples t-test

• Data are interval-ratio scale
• Normally distributed (bell shaped)
• Observations of one group are independent of
  other group.
• Homogeneity of variance
• Variance shows spread the scores are from the
  mean (standard deviation squared)
• The variance of 2 populations represented by each
  sample should be equal.

8
Independent samples t-test

• Two groups of 8 salesclerks, each tested only
  once.
• IV dress style of customers
• levels
• Sloppy Clothing customers
• Dressy Clothing customers
• DV response time of clerks to help customers

9
Reaction time (seconds)
10
Degrees of freedom for independent groups df N
- 2
11
Independent samples t-test

• Formula pg 198
• Numerator difference between 2 sample means
• Denominator standard error of the difference
  between means of independent samples.
• Rationale according to H0, µ1 µ2, so the
  difference between population means is zero.
• according to H1, µ1 ? µ2, and their difference
  should be large enough to be significant.

12
Independent samples t-test

• Rationale continued
• If we took an infinite number of samples from
  each population, calculated their means,
  subtracted the means from each other, and plotted
  the difference, we would get a distribution of
  differences between sample means.
• When we take the standard deviation of this new
  distribution, we get the standard error of the
  difference between means of independent samples.

13
Independent samples t-test

• Steps
• 1) calculate means of each sample.
• 2) calculate the variance of each sample.
• 3) determine the std error of difference between
  means.
• 4) calculate independent samples t-test
• 5) determine t critical (based on df N-2 alpha
  level, one vs two-tailed)
• 6) make decision reject or do not reject null
  hypothesis

14
Factors that Increase power

• To increase power in independent samples
• Increase differences between the means (i.e.,
  choose an IV that will produce greater
  differences between groups)
• Reduce variability of raw scores in each
  condition (variance will be smaller)
• Increase sample size

15
Textbook example pg. 197
16
Hw problem 1
17
Correlated-groups t-test or paired samples t-test

• One sample where each participant is tested twice
  (within-subjects design).
• Measures whether there is a difference in the
  sample means and if this difference is greater
  than expected by chance.
• H0 there is no difference between the scores of
  person A in condition 1 and condition 2.
• H1 person A performs differently in condition 1
  than condition 2.
• Determine difference scores difference between
  participants performance in condition 1 and
  performance in condition 2.

18
Correlated-samples t-test

• Difference scores pg 204, table 9.3
• Formula pg. 204
• Numerator mean of difference scores minus zero
• Denominator standard error of difference scores
• Standard deviation of the difference scores
  divided by vN
• Degrees of freedom N - 1

19
Paired-samples t-test textbook pg. 204
20
Paired samples t-test

• Steps
• 1) calculate the difference scores for each
  participant.
• 2) calculate the mean of difference scores.
• 3) determine the std deviation of difference
  scores.
• 4) calculate the std error of the difference
  scores divide 3 by square root of N
• 5) calculate paired samples t-test
• 6) determine t critical (based on df N-1 alpha
  level, one vs two-tailed)
• 7) make decision reject or do not reject null
  hypothesis

21
Assumptions of paired samples t-test

• Data are interval-ratio scale
• Normally distributed (bell shaped)
• Observations are correlated dependent on each
  other
• Homogeneity of variance
• Variance shows spread the scores are from the
  mean (standard deviation squared)
• The variance of 2 populations represented by each
  condition should be equal.

22
Hw prob. 3