S519: Evaluation of Information Systems

1
S519 Evaluation of Information Systems

• Social Statistics
• Inferential Statistics
• Chapter 10 t test

2
T test for dependent

• A repeated-measures study (a.k.a dependent study)
  is one in which a single sample of individuals is
  measured more than once on the same dependent
  variable.
• Main benefit two sets of data are from the same
  subjects.

3
Example

• Three professors at University of Alabama studied
  the effects of resource and regular classrooms on
  the reading achievement of learning-disabled
  children. A group of children was test before
  they take the 1-year daily instruction and after
  they took the 1-year daily instruction.
• Which statistical test we should use?

4
T test for dependent
the sum of all the difference between
groups the sum of the differences squared
between groups n the number of pairs of
observations
5
T test for dependent
Pre-test Post-test D D2
3 7 4 16
5 8 3 9
4 6 2 4
6 7 1 1
5 8 3 9
5 9 4 16
4 6 2 4
5 6 1 1
3 7 4 16
6 8 2 4
7 8 1 1
8 7 -1 1
7 9 2 4
6 10 4 16
7 9 2 4
8 9 1 1
8 8 0 0
9 8 -1 1
9 4 -5 25
8 4 -4 16
7 5 -2 4
7 6 -1 1
6 9 3 9
7 8 1 1
8 12 4 16
6
T test for dependent

• Step1 A statement of the null and research
  hypotheses

7
T test for dependent

• Step2 setting the level of risk (or the level of
  significance or Type I error) associated with
  null hypothesis
• 0.05

8
T test for dependent

• Step3 selection of the appropriate test
  statistics
• Following Figure 10.1
• T test for dependent t test for paired samples
  t test for correlated samples

9
T test for dependent

• Step4 computation of the test statistic value
• t2.45

10
T test for dependent

• Step5 determination of the value needed for
  rejection of the null hypothesis
• Table B2
• dfn-125-124
• One tailed because research hypothesis is
  directed

11
T test for dependent

• Step6 a comparison of the t value and the
  critical value
• 2.45gt1.711
• Reject the null hypothesis

12
T test for dependent

• Step7 and 8 time for a decision
• There is the difference between pre-test and
  post-test the post-test scores are higher than
  the pre-test scores.

13
Excel TTEST function

• TTEST (array1, array2, tails, type)
• array1 the cell address for the first set of
  data
• array2 the cell address for the second set of
  data
• tails 1 one-tailed, 2 two-tailed
• type 1 a paired t test 2 a two-sample test
  (independent with equal variances) 3 a
  two-sample test with unequal variances

14
Excel TTEST()

• It does not computer the t value
• It returns the likelihood that the resulting t
  value is due to chance
• Less than 1 of the possibility that two tests
  are different due to chance ? the two tests are
  difference due to other reasons than chance.

15
Excel ToolPak

• T test paired two sample for means option

t-Test Paired Two Sample for Means t-Test Paired Two Sample for Means

  pretest posttest
Mean 6.32 7.52
Variance 2.976666667 3.343333333
Observations 25 25
Pearson Correlation 0.050718341
Hypothesized Mean Difference 0
df 24
t Stat -2.449489743
P(Tltt) one-tail 0.010991498
t Critical one-tail 1.710882067
P(Tltt) two-tail 0.021982997
t Critical two-tail 2.063898547  

16
Advantages of theRepeated-Samples Design

• Repeated-measures design reduces or limits the
  variance, by eliminating the individual
  differences between samples.

17
Problems With theRepeated-Samples Design

• Carryover effect (specifically associated with
  repeated-measures design) subjects score in
  second measurement is altered by a lingering
  aftereffect from the first measurement.

18
Types of t test
19
Example I

• A researcher is interested in a new technique to
  improve SAT verbal scores. It is known that SAT
  verbal scores have µ500 s100.
• She randomly selects n30 students from this
  population, and has them undergo her training
  technique. Students are given analogy questions,
  and are shocked each time they get an answer
  wrong.
• The sample then writes the SAT, and gets M 560.

20
Example II

• A social psychologist is interested in whether
  people feel more or less hopeful following a
  devastating flood in a small rural community. He
  randomly selects n10 people and asks them to
  report how hopeful the feel using a 7-point scale
  from extremely hopeful (1) to neutral (4) to
  extremely unhopeful (7)
• The researcher is interested in whether the
  responses are consistently above or below the
  midpoint (4) on the scale, but has no hypothesis
  about what direction they are likely to go.
• His sample reports M4.7, s 1.89.

21
Example III

• To test the hypothesis that people give out more
  candy to kids in cute costumes than scary ones, I
  hire 20 kids to work for me. Ten are randomly
  assigned to wear cute bunny costumes, and the
  other ten wear Darth Vader costumes.
• I drop the kids off in random parts of the city,
  and count the total pieces of candy each has
  after 1 hour of trick-or-treat.
• Cute bunnies M 120, s 10
• Darth Vaders M 112, s 12

22
Example IV

• We are testing the effects of moderate amounts of
  alcohol on driving performance. We make the
  hypothesis that even a small amount of beer will
  degrade driving performance (an increase in
  obstacles hit).
• To test our hypothesis, we have n5 subjects
  drive around a course on Big Wheels covered with
  cardboard cutouts of children and furry animals,
  and we record the number of cutouts they hit.
  Then, they drink one beer, and do the course
  again again we record the number of cutouts hit.
• What is a potential confound with this experiment?

23
Example V

• We want to determine if IU SLIS faculty publish
  more than the national average of 4 papers per
  year (per person). We take a random sample of
  n12 IU SLIS profs and survey the number of
  papers each has published, obtaining M6.3,
  s1.13.

24
Example VI

• I want to know which dog is responsible for the
  holes in my yard. I buy 10 German Shepherds, 10
  Beagles, and randomly assign each dog to its own
  yard. At the end of the day, the Beagles have dug
  M11.3 holes, s2.1, and the Shepherds have dug
  M5.4 holes, s1.9. Test my hypothesis that
  Beagles dig more holes than German Shepherds.

25
Example VII

• We want to know if noise affects surgery
  performance. We randomly select a sample of 9
  surgeons, and have them perform a hand-eye
  coordination task (not while performing surgery,
  of course). The surgeons first perform the task
  in a quiet condition, and then we have them
  perform the same task under a noisy condition.
  Test the hypothesis that noise will cause poorer
  performance on the task.

26
Example VIII

• ETS reports that GRE quantitative scores for
  people who have not taken a training course are
  µ555, s139. We take a sample of 10 people from
  this population and give them a new preparation
  course. Test the hypothesis that their test
  scores differ from the population.