**Instructions:**

The instructions for this assignment are what they were for previous assignments which included a mix of short answer, calculations, and SPSS. A quick summary of those instructions:

- You may complete the assignment individually or with one partner.

- If at all possible, PLEASE save the document as a Word file and submit it to me in that format, or otherwise saved and submitted as a PDF.

- You must show your work for any requested calculations (Section 1 of this assignment) in order to receive any credit.

- When you are to complete calculations, do so on a separate sheet of paper by hand, take a photo of your work, and insert it into your assignment document.

- When completing analyses using SPSS (Section 2 of this assignment) you must provide the syntax and those parts of the output which you used in answering the various questions.

- Use copy and paste functions in order to copy the syntax or relevant SPSS output tables from SPSS into your assignment document.

- Continue to provide typed answers to short-answer sorts of questions.

Formulas are provided at the end of this document, and the t-table is available on Moodle.

__Section 1: Hypothesis Testing with t-tests & Confidence Intervals__

- A drug is being evaluated regarding a specific side-effect risk. While the medication has been shown to be effective for its intended purpose, there have been concerns that it may also result in increases in “bad” cholesterol levels (LDL, low-density lipoprotein). A very small preliminary study is created to look for this specific risk (thus, test directionally). Each participant has his or her LDL checked at the beginning of the study and after one month on the experimental medication, and the data is presented in the table below.

Answer all of the questions about this study (parts a-e, on this page and the next)

**[11 points total]**

a. What is the independent variable? | ___________________ | ||||||

How many levels are there of the IV? | ___________________ | ||||||

Is the IV being manipulated between- or within-subjects? | ___________________ | ||||||

What is the dependent variable? | ___________________ | ||||||

What is the appropriate statistical test: | ___________________ | ||||||

LDL cholesterol | |||||||

Participant # | Pre-test | Post-test | |||||

1 | 185 | 188 | |||||

2 | 114 | 119 | |||||

3 | 145 | 142 | |||||

4 | 168 | 165 | |||||

5 | 97 | 99 | |||||

6 | 144 | 146 | |||||

7 | 152 | 153 | |||||

8 | 95 | 97 | |||||

9 | 160 | 160 | |||||

10 | 129 | 134 | |||||

- What are the null and alternative hypotheses? Null:

Alternative:

- Within the context of this research, what would be a Type I error? (one sentence) Within the context of this research, what would be a Type II error? (one sentence)

Page 2 of 10

- Wanting to make sure that this possible side effect is detected if it in fact exists, test the hypotheses at α = 0.10 [note, this is “zero point one” (10%) not “zero point
*zero*one” (1%)].

Run the appropriate test showing your formulas and computations. Keep your work organized. Be sure to report:

- Your obtained test statistic (t-obtained = ?)
- The critical value(s) used to evaluate the obtained test statistic.

- Provide a properly formatted/complete conclusion. (one sentence)

Page 3 of 10

- Catherine has randomly assign rats to two treatment groups; one group contains animals which receive lesions of the amygdala (a brain structure) while animals in the other group undergo a sham surgery (no actual damage to brain structures). One of her sham animals died during surgery.

After recovery from surgery, animals are presented with a convincing cat puppet that looks and smells like a cat. The table below shows the amount of time that elapsed before each animal approached and explored the puppet. In theory, if an animal was less fearful then it would take less time to approach the very convincing cat puppet. Is the amygdala involved in fear responding? Test non-directional, α = .05

Answer all of the questions about this experiment (parts a-c) | [8 points total] | ||

Lesion | Sham | ||

7.1 | 8.2 | ||

6.8 | 7.5 | ||

6.7 | 7.7 | ||

7.3 | 7.8 | ||

7.5 | 8.0 | ||

6.2 | 7.4 | ||

6.9 | 7.3 | ||

6.5 | 6.5 | ||

7.2 | |||

_{1} = 1.349 | _{2} = 1.900 | ||

a. What is the independent variable? | ___________________ | ||

How many levels does the IV have? | ___________________ | ||

Is the IV being manipulated between- or within-subjects? | ___________________ | ||

What is the dependent variable? | ___________________ | ||

What is the appropriate statistical test: | ___________________ |

Here are the hypotheses which you are to test below:

**H****0****: The animals in the sham and lesion conditions will on average take equal amounts of time to approach the puppet.**

**H****A****: The animals in the sham and lesion conditions will on average take different amounts of time to approach the puppet.**

b. Run the appropriate test showing your formulas and computations. Keep your work organized.

Be sure to report:

- Your obtained test statistic (t-obtained = ?)
- The critical value(s) used to evaluate the obtained test statistic.

- Provide a conclusion related to what was learned about the amygdala’s role in fear responding

(therefore, this won’t take the same exact form as the hypotheses). (1-2 sentences)

Page 4 of 10

- A
*dependent t-test*was run for an experiment with 30 participants and the resulting mean difference was 8.350 with a standard error of 1.467. Compute and report the 95% confidence interval associated with this analysis.**[3 points]**

- An
*independent t-test*was run comparing the mean performance of participants in one condition to the mean performance of other participants in a different condition. The test resulted in the following statistics:**[5 points total]**

= ^{2.4−7.5}_{2.222} = −2.295 [ t(40) = –2.295, p < 0.05, two-tailed ]

- Compute and report the 98% confidence interval.

- Provide a one-sentence explanation of what the confidence interval in part b means and/or shows the reader (hint: remember the “fill in the blanks” way of explaining what it means – see class notes and/or study guide).

- The information provided at the start of this problem shows us that the difference was significant at α = .05 (i.e., because the bracket reports “p < .05,” we know that a significant difference exists).

Using the 98% confidence interval you reported in part a, explain whether the difference between 2.4 and 7.5 is statistically significant at α = .02, and explain why. *Provide enough detail* *so that it is an effective explanation of how to use the confidence interval to make the determination*. (2 sentences max.)

- Thus the question is
**NOT**about how to use t and t-critical, it is about how to use the confidence interval to decide retain or reject.

Page 5 of 10

__Section 2: Hypothesis Testing with SPSS__

__The data related to the experiments described below (problems 5–7) is provided after question 7__*.*

Depending on the test you need to run, decide how to organize the data in SPSS and then use SPSS to analyze the data and respond to the questions below.

- A drug designed to reduce pain associated with migraine headaches is being evaluated. Participants experiencing migraine pain are randomly assigned one of two doses of the medication and their self-assessed level of pain is measured 30 minutes after the drug is administered (Note: this is the only time a measurement of pain is taken (this is not a pre/post design), & higher scores reflect greater pain).
**[7 points total]**

a. What is the independent variable? ___________________

How many levels does the IV have? ___________________

Is the IV being manipulated between- or within-subjects? ___________________

What is the dependent variable? ___________________

What is the appropriate statistical test: ___________________

- Conduct the test, and provide the answers/numbers for each of the following (just fill in the blanks).
**Also, make sure to provide your syntax for this analysis, and provide any parts of the****output which you are using to answer questions in part b or c of this question.**

From your output, report the following here:

The obtained test statistic: _________________

The probability value used to evaluate the obtained test statistic: _________________

The confidence interval: _________________

- Provide a properly formatted conclusion. (i.e.,
*as always*, make sure to include one or two sentences explaining what you found in terms of the specific problem, and also include the bracketed statistical statement which supports that conclusion.)

Page 6 of 10

- A researcher is trying to understand if environment plays a role in the level of critical thinking a person is able to do. If a person has a challenging task to perform, should she isolate herself in a small room with no distractions, should she work in a room with more space but still minimal distractions, should she work in a busy environment with lots of stimulation, etc.?

For the actual experiment, the researcher chooses two particular environments (A and B) and looks to see if they have different effects on scores of critical thinking. *Treat the data as being provided by*

__within-subjects manipulation__*of the environment variable*.**[6 points total]**

- What is the appropriate statistical test: ______________________

- Conduct the test, and provide the answers/numbers for each of the following.
**Again, make****sure to provide your syntax for this analysis, and provide any parts of the output which you are using to answer questions in part b or c of this question.**

From your output, report the following here: | |

The obtained test statistic: | _________________ |

The probability value used to evaluate the obtained test statistic: _________________ | |

The confidence interval: | _________________ |

- Provide a properly formatted conclusion.

- Using the exact same data as used in question 6, this time,
*treat the data as being provided by*__a__.__between-subjects manipulation__of the environment variable**[6 points total]**

- What is the appropriate statistical test: ______________________

- Conduct the test, and provide the answers/numbers for each of the following.
**Again, make****sure to provide your syntax for this analysis, and provide any parts of the output which you are using to answer questions in part b or c of this question.**

From your output, report the following here: | |

The obtained test statistic: | _________________ |

The probability value used to evaluate the obtained test statistic: _________________ | |

The confidence interval: | _________________ |

c. Provide a properly formatted conclusion.

Page 7 of 10

__Data for SPSS Problems 5, 6, and 7__

Data for Problem 5

Participant # | low dose (10mg) | Participant # | high dose (50mg) | |

1 | 6.954 | 13 | 7.234 | |

2 | 6.845 | 14 | 7.101 | |

3 | 7.196 | 15 | 8.109 | |

4 | 6.854 | 16 | 7.892 | |

5 | 7.205 | 17 | 7.567 | |

6 | 6.698 | 18 | 7.001 | |

7 | 7.451 | 19 | 6.985 | |

8 | 7.023 | 20 | 7.541 | |

9 | 6.809 | 21 | 7.453 | |

10 | 6.753 | 22 | 7.228 | |

11 | 6.987 | 23 | 7.109 | |

12 | 6.991 | 24 | 7.469 |

Data for Problems 6 & 7

Depending on the nature of the problem (6 vs. 7), this data should be read as either data from two different groups of participants (group A, group B), or with each row showing the two scores for a given individual.

Environment A | Environment B |

12.43 | 12.09 |

10.54 | 10.43 |

8.76 | 8.52 |

15.23 | 14.32 |

10.2 | 9.91 |

5.78 | 5.52 |

16.78 | 15.08 |

12.09 | 11.98 |

5.87 | 5.76 |

19.03 | 18.54 |

17.23 | 16.11 |

7.89 | 7.54 |

19.32 | 18.12 |

20.54 | 18.76 |

4.44 | 4.41 |

8.76 | 8.74 |

Page 8 of 10

Central Tendency:

- =

^{̅}=

+ 1

Z-score Analysis:

= | − | |

̅ | ||

= | − | |

Single –Sample t-test:

. =

Variability:

2

_{=}^{̅−} ^{̅}

̅

= ∑( − )^{2}

2 _{=}

= √ ^{2}

= ∑( − ^{̅})^{2}

^{2}= _{−1}

= √ ^{2}^{}

̅ =

= − 1

=^{̅}± ∗̅

Dependent t-test:

_{=}^{̅−} ^{̅}

̅

̅ =

√

= − 1

=^{̅}± ∗̅

Page 9 of 10

Independent t-test:

̅ | ̅ | ̅ | |||||

− − ̅ | |||||||

= | 1 | 2 | _{1}− _{2} | ||||

̅ | ̅ | ||||||

_{1}− _{2} | |||||||

̅ ̅ | = √ ^{2} | ( | 1 | + | 1 | ) | |

_{1}− _{2} | _{1} | _{2} | |||||

1 + 2

^{2 }^{=}

_{1}_{+} _{2}_{−2}

= _{1}+ _{2}−2

= ( ^{̅}_{1} − ^{̅}_{2}) ± ∗ ̅_{1}_{− }̅_{2}_{}

Page 10 of 10