A social psychologist wants to investigate a well-known phenomenon concerning he

Question

A social psychologist wants to investigate a well-known phenomenon concerning helping behavior. She wants to investigate how long it will take someone to help when they are alone, or when they are with two other people. She also wants to know whether being on time or whether being in a hurry affects whether someone will help. She has an experiment set up where people fill out questionnaires that are short enough so that students can get to their class on time or long enough so they will be in a hurry if they look to get help for someone. During the time they arc filling out the questionnaire, a student fakes an epileptic seizure in an adjacent room. The researcher records how long it takes participants to try to help or to go get help. The data for the study are shown below. Perform the appropriate analysis by hand. Please write up the results as you would in a scientific paper. For any significant main effects, please report the effect size.

Explanation / Answer

Solution

A two-way ANOVA with equal number of observations per cell would be the analysis tool,

treating available time as row effect and company status (single or with 2 others) as column effect.

Back-up Theory

Suppose we have data of a 2-way classification ANOVA, with r rows, c columns and n observations per cell.

Let xijk represent the kth observation in the ith row-jth column, k = 1,2,…,n; i = 1,2,……,r ; j = 1,2,…..,c.

Then the ANOVA model is: xijk = µ + i + j + ij + ijk, where µ = common effect, i = effect of ith row, j = effect of jth column, ij = row-column interaction and ijk is the error component which is assumed to be Normally Distributed with mean 0 and variance 2.

Now, to work out the solution,

Terminology:

Cell total = xij. = sum over k of xijk

Row total = xi..= sum over j of xij.

Column total = x.j. = sum over i of xij.

Grand total = G = sum over i of xi.. = sum over j of x.j.

Correction Factor = C = G2/N, where N = total number of observations = r x c x n =

Total Sum of Squares: SST = (sum over i,j and k of xijk2) – C

Row Sum of Squares: SSR = {(sum over i of xi..2)/(cxn)} – C

Column Sum of Squares: SSC = {(sum over j of x.j.2)/(rxn)} – C

Between Sum of Squares: SSB = {(sum over i and jof xij.2)/n} – C

Interaction Sum of Squares: SSI = SSB – SSR – SSC

Error Sum of Squares: SSE = SST – SSB

Mean Sum of Squares = Sum of squares/Degrees of Freedom

Degrees of Freedom:

Total: N (i.e., rcn) – 1;

Between: rc – 1;

Within(Error): DF for Total – DF for Between;

Rows: (r - 1);

Columns: (c - 1);

Interaction: DF for Between – DF for Rows – DF for Columns;

Fobs:

for Rows: MSSR/MSSE;

for Columns: MSSC/MSSE;

for Interaction: MSSI/MSSE

Fcrit: upper % point of F-Distribution with degrees of freedom n1 and n2, where n1 is the DF for the numerator MSS and n2 is the DF for the denominator MSS of Fobs

Significance: Fobs is significant if Fobs > Fcrit

Calculations:

We have r = 2, c = 2, n = 10, N = 40. x2 = 640, x11. = 40, x12. = 10, x21. = 50, x22. = 20,

G = 120 and hence C = 360

SST = 640 – 360 = 280 = SST

SSB = {(402 + 102 + 502 + 202)/10} – C = 460 – 360 = 100 = SSB

SSR = [{(40 + 10)2/20} + {(50 + 20)2/20}] – C = 370 – 360 = 10 = SSR

SSC = [{(40 + 50)2/20} + {(10 + 20)2/20}] – C = 450 – 360 = 90 = SSC

SSW(SSE) = SST – SSB = 280 – 100 = 180 = SSE

SSI = SSB – SSR – SSC = 100 – 10 – 90 = 0 = SSI

ANOVA TABLE [level of significance is taken to be 5%]

Source

DF

SS

MS

FCAL

FCRIT

Significance

Row

1

10

10

2.06

4.11

Not sig

Column

1

90

90

18.52

4.11

Sig

Interaction

0

0

*

*

Between

2

100

-

Error

37

180

4.86

Total

39

280

-

Note: * Since for Interaction both SS and DF are zero, it is not pursued further.

Conclusion

Evidence is not sufficient enough to suggest that availability of time has effect on response time. But, being alone or with two others does impact the response time. When with two others, people tend to take longer time to offer help.,

DONE

A minor point: under Alone-In a hurry category, T is given as 20 and M is given as 1, which are not compatible. T = 20 is taken as correct entry.

Source

DF

SS

MS

FCAL

FCRIT

Significance

Row

1

10

10

2.06

4.11

Not sig

Column

1

90

90

18.52

4.11

Sig

Interaction

0

0

*

*

Between

2

100

-

Error

37

180

4.86

Total

39

280

-

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