Psychology Statistics Problems (College)

Formulae:

Independent samples t-test:

1) Pooled Variance: 𝑠𝑝 2 =

(𝑛1 −1)𝑠1 2+(𝑛2 −1)𝑠2

2

𝑛1+ 𝑛2 − 2

2) Standard Error: 𝑆�̅�1− �̅�2 = √ 𝑠𝑝 2

𝑛1 +

𝑠𝑝 2

𝑛2

3) T-Statistic: 𝑡 = (�̅�1− �̅�2)

𝑆�̅�1− �̅�2

Correlation:

1) Do the 7-column table to find SSX, SSY, and SP.

2) Pearson’s r: 𝑟 = 𝑆𝑃

√𝑆𝑆𝑋 ∗𝑆𝑆𝑌

Chi-Squared:

1) E = N / C (one variable) or E = R*C / N (two variables)

2) Chi-Square: χ2 = ∑ (𝑶 −𝑬)𝟐

𝑬

Note: For critical values, you can find all of them here:

https://www.socscistatistics.com/tests/criticalvalues/default.aspx

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Hypothesis Test Examples:

For each hypothesis test listed, explain who that test would be used on and describe a unique

study you could run that would use that test. Be sure to mention the groups or variables being

compared and what the dependent variable would be. Be specific to avoid accidently providing

an example for a different type of test!

For example, if the prompt said “Z-Test” then I would provide an example, such as “Z-Tests

compare one sample mean to the population mean. For example, I could compare a sample of 10

local basketball players to the population of all NBA league players on their 3-point shot ratio.

This would let me see if the team of basketball players are better, or worse, than NBA players.”

1) One Sample T-Test:

One sample t-tests compare data from a sample to a population with the known value.

2) A One-Way ANOVA with 4 Groups:

3) Chi-Squared with 2 Independent Variables:

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Smoking Program:

1. You oversee an experimental anti-smoking program. You are worried that participant

attrition (i.e., drop-outing out a study) is causing your treatment group to bias against

heavy-smokers. You run a chi-squared to check the participant distribution.

Control Treatment Total

Light Smokers 100 80 180

Heavy Smokers 90 50 140

Total 190 130 320

a. What is the expected value for each cell?

Control-Light:

Control-Heavy:

Treatment-Light:

Treatment-Heavy:

b. Calculate the chi squared. Using a critical value of 3.84, is it significant? What does

this mean for your treatment?

c. In this study, why might attrition be cause for concern? Explain your reasoning by

tying this question back to concepts of internal validity.

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Study-Time Focus

2. You are studying the impact of three popular Twitch influencers on brand recognition.

Your survey gives you a score based on how much the fan follows the influencer. Higher

scores means more positive opinion of the brand.

Use this data to answer the following questions.

Be sure to show your work and round all

numbers to two decimals (i.e. x.xx) when

applicable.

a. What hypothesis test would we use to compare all three influencer audiences at the same

time? How would you describe the null hypothesis in this case?

For b, c, and d, be sure to show your work (e.g. at least the pooled variance and standard error)

b. Find the t-statistic for ‘K.K.’ vs. ‘P.C.’ and the critical value for this comparison

c. Find the t-statistic for ‘K.K.’ vs. ‘D.J.’ and the critical value for this comparison:

d. Find the t-statistic for ‘P.C.’ vs. ‘D.J.’ and the critical value for this comparison:

𝒏 �̅� 𝒔

Influencer K.K. 20 9 2

Influencer P.C. 25 4 4

Influencer D.J. 15 7 1

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e. Compare the t-statistics to each critical value. In your own words, what do your findings

say about these influencers and brand they represent?

f. What would you need to add to this study to turn it into a factorial ANOVA? Give me a

unique example.

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Age and Income

3. You are looking for a correlation between age

and income (in thousands):

Use this data to answer the following questions. Be

sure to show your work and round final answers to two

decimals (i.e. x.xx).

a. State in words and formulas the null and

alternative hypotheses

H0:

Ha:

b. Use the 7-column method to find SSX, SSY and SP (4pt):

X Y

SSX =

SSY =

SP =

c. Calculate r using your numbers above

r =

d. How would you describe this correlation’s strength and direction?

Name Age Income

Maria 20 10

Marco 23 20

Melody 23 10

Markus 27 40

Maxwell 33 70

Martin 40 50

Minnie 44 80

Mary 68 100

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e. Given a critical value of 0.582, is there a significant relationship between age and

income? Describe this relationship in your own words.

f. Does this correlation alone provide evidence to show that one variable causes the other?

Explain your answer.

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ANOVA Interpretation

4. Your pharmacy is testing the impact of an anti-anxiety medication. So far experiments

have failed, but you decide to run a 2x2 ANOVA using gender as an additional variable.

SPSS provides you with the following table of means (higher is better) and F-test results:

SUMMARY Control Experiment Total

Men 40.0 35.0 37.5

Women 60.0 40.0 50.0

Total 50.0 37.5

ANOVA

Source of Variation Sum of Squares df

Mean Squares F Sig

Gender 562.5 1 562.5 3.551 0.030

Treatment 622.5 1 622.5 4.502 0.025

Gender * Treatment 3062.5 1 3062.5 24.775 0.000

Within 4450 36 123.611 Total 8137.5 39

a. Describe the tables above. What does each column indicate about the row?

b. Use the sig to determine significance at a 0.05 and 0.01 confidence level. What do you

conclude about the three different ANOVA hypotheses? Be extra careful not to confuse

the main effect of a factor and the interaction effect of those factors.

i. The main effect of treatment

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ii. The main effect of gender

iii. The interaction

c. Name and describe the tests you need to run when following up on a significant ANOVA