Deciding which inferential test to use'

1
Deciding which inferential test to use.
2
Deciding which inferential test to use.

• Expanded office hours for specific questions
  only!
• Toms foolproof test-choosing chart.
• Examples for practice in choosing the right test.
• What you will want to be especially familiar with
  for the final.

3
Toms foolproof test-choosing chart.
1) Is s known?
No
Yes
2) How many samples?
One-sample z
One
Two
More than two
One-sample t, df N-1
3) What type of samples?
Correlated
3) What type of samples?
Independent
Correlated
Correlated t df N - 1
Independent
Independent t df N1 N2 - 2
Correlated ANOVA F(dfnum,dfdenom )
Independent ANOVA F(dfnum,dfdenom )
N number of pairs of scores.
4
Example 1 Potato bags
The local grocery store sells potatoes in 5 pound
bags. Because potatoes come in unpredictable
sizes, it is almost impossible to get a bag that
weighs exactly 5 pounds. Therefore, the store
advertises that the bags average 5 pounds. To
determine if the bags differ from the advertised
average, a sample of 25 bags was randomly
selected and weighed. Tell me 1) The correct
inferential test (and why it is the correct
one). 2) The critical value if a .05 3) H0
and HA
5
Example 2 Handedness and pitch perception.
Several studies indicate that handedness is
related to differences in brain function.
Because different parts of the brain are
specialized for specific behaviors, this means
that left- and right-handed people might show
different skills or talents. To test this
hypothesis, a psychologist tested pitch
discrimination (a component of musical ability)
for three groups of subjects left-handed (n10),
right-handed (n10), and ambidextrous (n10).
1) The correct inferential test (and why it
is the correct one). 2) The critical value if a
.05 3) H0 and HA
6
Example 3 Less homework.
In 1985, an extensive survey indicated that
fifth-grade students in the city school district
spent an average of µ 5.5 hours per week doing
homework. The distribution of homework times was
approximately normal, with s 2. Last year, a
sample of n 100 fifth-grade students produced a
mean of X 5.1 hours of homework each week.
Complete a standard 10-step hypothesis test to
determine if last years students really spent
less time on homework than students in 1985 or
whether the difference simply reflected chance
variation.
7
Decision-making steps

• 1. Define problem
• 2. Define hypotheses with respect to known
  population mean, m
• H0
• HA
• 3. Define experiment
• 4. Define statistic
• 5. Define acceptable probability of Type I error
• 6. Define value of statistic upon which decision
  hinges
• 7. Perform experiment/collect data
• 8. Compare observed statistic to critical value.
• 9. Decide
• 10. Draw conclusion using at least one complete
  sentence

8
Example 4 Light cigarettes.
Many people who are trying to quit smoking will
switch to a lighter brand of cigarettes to reduce
their intake of tar and nicotine. However, there
is some evidence that switching to a lighter
brand simply results in people smoking more
cigarettes. A researcher examining this
phenomenon recorded the number of cigarettes
smoked each day for 16 smokers before and after
they switched to lighter brand. On average, the
subjects smoked D 3.2 more cigarettes after
switching, with SSD 375 (D after before).
Do these data indicate a significant change in
the number of cigarettes smoked per day? Test at
the .05 level of significance.
9
Decision-making steps

• 1. Define problem Do smokers who switch to
  light cigarettes change the number of
  cigarettes that they smoke?
• 2. Define hypotheses with respect to mD,
• H0 mD 0
• HA mD 0
• 3. Define experiment 16 smokers, count cigs
  smoked before and after.
• 4. Define statistic
• 5. Define acceptable probability of Type I error
• 6. Define value of statistic upon which decision
  hinges
• 7. Perform experiment/collect data
• 8. Compare observed statistic to critical value.
• 9. Decide
• 10. Draw conclusion using at least one complete
  sentence

10
Example 5 Memory
New information going into memory is assumed to
interfere with the information that is already
there. One demonstration of interference
examines the process of forgetting while people
are asleep versus while they are awake. Because
there should be less interference during sleep,
there also should be less forgetting. The data
to the right are results from an experiment
examining 4 groups of 10 subjects. All subjects
were given a list of words to remember. Then
half went to sleep, and the others stayed awake.
Within both the asleep and the awake groups, half
of the subjects were tested after 2 hours, and
the rest were tested after 8 hours. The
dependent variable is the number of words
correctly recalled. Graph the data and say if
you think an ANOVA would likely show a
significant interaction between delay and the
sleep/wakefulness condition. If so, use one
sentence to explain the interaction.
11
Significant interaction?
Delay (columns)
2 hours
8 hours
4.5
4.9
4.7
Asleep
Wakefulness (rows)
Means
3.2
0.9
2.1
Awake
3.9
2.9
12
Effects?
Delay (columns)
Asleep
2 hours
8 hours
Awake
4.5
4.9
4.7
5
Asleep
Wakefulness (rows)
Words recalled
2.5
3.2
0.9
2.1
Awake
0
3.9
2.9
2 hours
8 hours
Delay
13
Example 6 SATs
An educator wants to determine if SAT scores
improve following an intensive review course.
Two samples of 15 each are selected. The first
group takes the review course, and the second
receives no treatment. SAT scores are
subsequently measured for both groups. Tell
me 1) The correct inferential test (and why
it is the correct one). 2) The critical value
if a .05 3) H0 and HA 4) A more powerful
way to design this experiment. 5) The critical
value in your more powerful design.
14
Be especially familiar with

• Standard deviation (and variance)
• In your own words, what is s?
• Why does s (and s2) not change when you add a
  constant to each score in a group.
• What does your answer to that question have to do
  with ANOVA?
• Why use x to help you predict y when rxy gt 0
  (draw a diagram)?
• What is the relationship between the one sample t
  and the correlated sample t?
• What are z scores and how do you use them to find
  area/probability?
• Tukeys HSD How and when to do it.
• How to fill in and interpret ANOVA tables.