Basic Quantitative Methods in the Social Sciences (AKA Intro Stats)

1
Basic Quantitative Methods in the Social
Sciences(AKA Intro Stats)

• 02-250-01
• Lecture 11 (Review Revised June 18 1015 PM)

2
A Few Things

• You need to be able to decide which hypothesis
  test statistic to use for the exam questions. We
  have covered (since the last midterm)
• z-test
• One-sample t-test
• Two sample t-tests
• Independent Sample t
• Dependent (Related) Samples t

3
A Few Hints

• z-test
• Comparing a sample mean with a population mean
• Sigma is known (so you calculate standard error)
• One-sample t-test
• Comparing a sample mean with a population mean
• Sigma is unknown (so you are given or need to
  calculate sample standard deviation to get
  estimated standard error)

4
A Few Hints

• Independent Sample t
• Comparing two sample means
• Two distinct (independent) groups
• Dependent (Related) Samples t
• Comparing two sample means
• Scores are pairs (e.g., pre-post test, couples,
  members of the same family, etc)

5
Question 1

• Researcher Q knows that regular Canadians spend
  an average of 50 per month on take-out food. She
  thinks that students probably spend more money on
  take out-food per month than regular Canadians.
  She asks 25 students how much money they spend on
  take-out food per month, and finds that they
  spend an average of 75 per month, with a
  standard deviation of 10.

6
Question 1

• A) State the null and alternative hypotheses
• B) What type of test should you use?
• C) Test the researchers hypothesis at the .01
  level of significance
• D) Test the researchers hypothesis at the .05
  level of significance using the Confidence
  Interval approach

7
Question 1

• A) State the null and alternative hypotheses
• Ho students spend the same amount of money on
  take-out food per month as regular Canadians
• Ha students spend more money on take-out food
  per month than regular Canadians
• B) What type of test should you use?
• We are comparing a sample mean with a population
  mean, but do not know sigma
• We use a ONE-SAMPLE T-TEST

8
Question 1

• C) Test the researchers hypothesis at the .01
  level of significance
• Alpha .01 (one-tailed), df 24, tcrit 2.492
• B/c tobs gt tcrit, we reject the Ho
• Conclusion students spend more money on take-out
  food each month than regular Canadians

9

• D) Test the researchers hypothesis at the .05
  level of significance using the Confidence
  Interval approach
• B/c is outside of the interval, we
  reject Ho
• Conclusion students spend more money on take-out
  food each month than regular Canadians

10
Question 2

• Dr. Smith thinks that pet owners are happier than
  people who do not own pets. She randomly samples
  5 dog owners and 6 people who do not own pets and
  asks them to rate their level of happiness on the
  Happy Scale (from 1 to 50). The pet owners have
  a mean Happy Scale rating of 35 with a standard
  deviation of 5, while the people who do not own
  pets have a mean Happy Scale rating of 30 with
  a standard deviation of 3.

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Question 2

• A) State the null and alternative hypotheses
• B) State the IV, levels of IV, and DV
• C) What type of test should you use?
• D) Test Dr. Smiths hypothesis at the .05 level
  of significance
• E) Test Dr. Smiths hypothesis at the .05 level
  of significance using the Confidence Interval
  approach

12

• A) State the null and alternative hypotheses
• Ho people who own pets are as happy as people
  who do not own pets
• Ha people who own pets are happier than people
  who do not own pets
• B) State the IV, levels of IV, and DV
• IV pet ownership (yes, no)
• DV Happy Scale rating (happiness)
• C) What type of test should you use?
• Independent Samples t-test

13

• D) Test Dr. Smiths hypothesis at the .05 level
  of significance

tcrit 1.833 lt tobs, reject Ho Conclusion pet
owners are happier than those who do not own pets
df (n1 n2) 2 11 - 2 9
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• E) Test Dr. Smiths hypothesis at the .05 level
  of significance using the Confidence Interval
  approach
• B/c 0 is within the interval, we retain the Ho
• Conclusion pet owners are as happy as people who
  do not own pets
• This is a good example of how changing from a
  one-tailed to a two-tailed test can affect your
  Ho decision

15
Question 3

• Dr. Bob has invented a new drug for treating
  insomnia. He hopes the drug works, but it may
  actually make peoples insomnia worse (it is so
  new that he isnt sure which way the drug will
  work). Dr. Bob asks 10 people with insomnia to
  record how many hours of sleep they get without
  the drug and then has them take the drug and
  record their number of hours of sleep again. Dr.
  Bobs data is on the next slide

16
Patient Hrs. sleep before drug Hrs. sleep after drug
1 3 5
2 4 4
3 2 5
4 2 3
5 4 4
6 5 3
7 1 6
8 0 3
9 3 5
10 2 6
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Question 3

• A) State the null and alternative hypotheses
• B) State the IV, levels of IV, and DV
• C) What type of test should you use?
• D) Test Dr. Bobs hypothesis at the .01 level of
  significance
• E) Test Dr. Bobs hypothesis at the .05 level of
  significance using the Confidence Interval
  approach

18

• A) State the null and alternative hypotheses
• Ho taking the drug will not change the number of
  hours of sleep that insomniacs get
• Ha taking the drug will make insomniacs sleep
  either more or less than before they took the
  drug
• B) State the IV, levels of IV, and DV
• IV insomnia drug (no drug, drug)
• DV number of hours of sleep per night
• C) What type of test should you use?
• These are pairs of scores, so use Related Samples
  t

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Patient Hrs. sleep before drug Hrs. sleep after drug
1 3 5
2 4 4
3 2 5
4 2 3
5 4 4
6 5 3
7 1 6
8 0 3
9 3 5
10 2 6

D
-2
0
-3
-1
0
2
-5
-3
-2
-4
SD-18
D2
4
0
9
1
0
4
25
9
4
16
SD272
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• D) Test Dr. Bobs hypothesis at the .01 level of
  significance
• Alpha .01 (two tail), df 9 ( of pairs 1)
• tcrit /-3.250 gt -2.714, retain Ho
• Conclusion the drug does not work it did not
  change how much sleep the insomniacs get

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• E) Test Dr. Bobs hypothesis at the .05 level of
  significance using the Confidence Interval
  approach
• Since 0 is outside the interval, we reject Ho
• Conclusion the drug affected the number of hours
  of sleep that insomniacs get (it actually
  increased their sleep we can tell this by
  looking at the sign of D, but you simply need to
  say that the drug changed hrs of sleep b/c this
  is a two-tailed test)

22
Question 4

• A telephone service provider has introduced a new
  long distance calling program. For a flat fee of
  25 per month, callers can place as many long
  distance telephone calls within Canada as they
  want each month. The phone company thinks that
  callers will spend more time on the phone each
  month if they use the new plan. They know that
  average customers spend 5 hours on the phone each
  month, with a standard deviation of 45 minutes. A
  sample of 30 customers using the new plan spend
  an average of 6 hours on the phone each month.

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Question 4

• A) State the null and alternative hypotheses
• B) What type of test should you use?
• C) Calculate the standard error
• D) Test the phone companys hypothesis at the .05
  level of significance

24

• A) State the null and alternative hypotheses
• Ho Customers using the new long distance phone
  plan will spend the same amount of time on the
  phone as regular phone customers
• Ha Customers using the new long distance phone
  plan will spend more time on the phone than
  regular phone customers
• B) What type of test should you use?
• Comparing a sample with a population, sigma is
  know, so use a Z-TEST

25

• C) Calculate the standard error
• D) Test the phone companys hypothesis at the .05
  level of significance
• Conclusion customers using the new long distance
  plan spend more time on the phone than regular
  customers

Note!! Sigma is given in minutes, so you need to
state it as hours (45 minutes .75 hours) the
level of measurement of the means and standard
deviation must be the same!
zcrit 1.64 lt 7.30, reject Ho
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Question 5

• Professor Z hypothesizes that there is
  relationship between the degree to which people
  believe in magic and their appreciation for Harry
  Potter Books. He gives a random sample of 5
  people a self-report measure of Belief in Magic
  that produces scores ranging from 1 (Dont
  believe in magic at all) to 10 (Believe very much
  in magic). He also asks them to rate their
  appreciation of Harry Potter books on scale from
  1 (Harry Potter books are awful) to 10 (Harry
  Potter books are fabulous). Is there a
  relationship between belief in magic and
  appreciation of Harry Potter books?

27
Belief
in Ratings of Magic scores Harry
Potter
28
Correlation Arithmetic
29
The Pearson r
(SC) (SU)
SCU
N
r
30
The Pearson r
(21) (31)
146
5
r
31
The Pearson r
651
146
5
r
32
The Pearson r
146
130.2
r
33
The Pearson r
15.8
r
34
The Pearson r
15.8
r
35
The Pearson r
15.8
r




115
192.2
207
88.2
36
The Pearson r
15.8
r




14.8
26.8
37
The Pearson r
15.8
r
396.64
38
The Pearson r
15.8
r
19.9158
39
The Pearson r
.7933 .793
r
40
The Pearson r
.793
r
See Table E.2 (p.440) for n - 2 df ( 5 - 2 3
df) and an alpha (a) of .05
41
The Pearson r
.793
r
The Critical r .878 r .793 Therefore, we
retain the Ho, belief in magic and appreciation
of Harry Potter books do not appear to be
significantly correlated.
42
Question 6

• Chi Square Goodness of Fit Test Example (see
  answer on next page)
• 1. Before an Ontario provincial election,
  political researchers thought that the Liberal
  Party would receive 45 of the votes, the Reform
  Party would receive 25, the NDP would receive
  20, and the PC party would receive 10 of the
  votes. After the election, they examined 500
  random votes and found that the political parties
  received the following number of votes
• Liberal Party 200
• Reform Party 100
• NDP 150
• PC Party 50

43
Question 6 continued

• 5. A) State the null and alternative hypotheses
• 5. B) Test the hypothesis at the .05 level of
  significance

44
Hypotheses

• Ho The votes in the election were as predicted
  by the political researchers (OE)
• Ha The votes in the election were distributed
  differently than as predicted (O does not equal E)

45
Chi Square Chart
Calculate expected frequencies (multiply each
by n 500)
Liberals Reform NDP PC
O 200 100 150 50
E 225 125 100 50
O - E -25 -25 50 0
(O E)2 625 625 2500 0
(O E)2/E 2.7778 5 25 0

Sum 32.7778 32.7778 32.7778 32.7778
46
Question 6 Continued

• Chi Square observed 32.78
• DF k-1 4-1 3, alpha .05
• Chi Square critical 7.82
• B/c Chi Square obs gt Chi Square crit, we reject
  the Ho.
• Conclusion The political researchers were
  wrong. The votes in the election were distributed
  differently than as predicted.

47
Question 7

• Researchers want to know if men and women get
  sick at different rates when they are exposed to
  the flu. They contact 100 men and 100 women who
  have been in contact with someone with the flu
  over the past week and record how many got sick
  and how many stayed well. The results are
  presented in the table below
• Men
  Women

55 45
45 55
Sick Stayed Well
48
Question 7 Continued

• A) State the hypotheses
• B) Test the hypothesis at the .01 level of
  significance

49
Hypotheses

• Ho Gender and getting sick when exposed to the
  flu are independent
• Ha Gender and getting sick when exposed to the
  flu are not independent (are dependent)

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Calculating Expected Frequencies and Chi-Square
Men Women
O 55 E 50 O 45 E 50
O 45 E 50 O 55 E 50
Sick Stayed Well
100 100

100 100 200
.5 .5 .5 .5 2.00
51
Question 7 Continued

• Chi Square crit, df 1, alpha .01 6.63, so
  retain Ho
• Conclusion Women and men get sick from the flu
  at the same rates (gender and getting sick when
  exposed to the flu are independent)

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Good Luck!!