Question

A social psychologist conducted a study to see if sales approach made a difference in the number of raffle tickets sold. Using the norm of reciprocity (giving buyers a free gift), 3, 1, and 2 tickets were sold; using the foot-in-the-door approach (getting buyers to agree to buy one ticket first, then more), 3, 3, and 3 tickets were sold; and using no special technique, 1, 0, 1, and 2 tickets were sold. Using the .05 level, does sales technique make a difference in the number of tickets sold? a. Carry out a complete hypothesis testing and make a complete analysis of variance table with α = .05. b. IF NECESSARY perform the appropriate post hoc tests. Remember: state your hypothesis, identify the critical region, do your test, make a decision and state the results in the conventional manner.

Answer 1

SOL:

Norm of reciprocity - Mean is 3 tickets
Standard deviation is 1

Foot-in-door approach - Mean is 3 tickets
Standard deviation is 0

No special technique- Mean is 1.33 tickets
Standard deviation is 0.816

a).

State the Hypotheses -
Null Hypothesis - The mean tickets sold is same for Norm of reciprocity, Foot-in-door and no special technique
Alternative hypothesis - The mean tickets sold is not same for Norm of reciprocity, Foot-in-door and no special t

Formulate an Analysis Plan - The significance level is 0.05. Use two-sample t-test to determine whether the difference between means.

Analyze Sample Data - Standard error, SE = sqrt[ (s₁²/n₁) + (s₂²/n₂) ]

SE for Norm of reciprocity and Foot-in-door approach = sqrt[ (1²/3) + (0²/3) ] = 0.5773

SE for No special technique and Foot-in-door approach = sqrt[ (0.816²/4) + (0²/3) ] = 0.408

SE for Norm of reciprocity and No special technique = sqrt[ (1²/3) + (0.816²/4) ] = 0.707

Degree of freedom, DF = (s₁²/n₁ + s₂²/n₂)² / { [ (s₁² / n₁)² / (n₁ - 1) ] + [ (s₂² / n₂)² / (n₂ - 1) ] }

DF for Norm of reciprocity and Foot-in-door approach = 2

DF for No special technique and Foot-in-door approach = 3

DF for Norm of reciprocity and No special technique = 4

t for Norm of reciprocity and Foot-in-door approach = (3-3)/0.5773 = 0

t for No special technique and Foot-in-door approach = (3-1.33)/0.408 = 4.09

t for Norm of reciprocity and No special technique = (3-1.33)/0.707 = 2.36

p-value for Norm of reciprocity and Foot-in-door approach at t = 0 and df =2 is 0.5

p-value for No special technique and Foot-in-door approach at t = 4.09 and df =3 is 0.013

p-value for Norm of reciprocity and No special technique at t = 2.36 and df =4 is 0.039

Interpret Results - Reject the null hypothesis for mean difference in No special technique and Foot-in-door approach and Norm of reciprocity and No special technique. Fail to reject the null hypothesis for Norm of reciprocity and Foot-in-door approach.

Conclusion - The ticket sale is same for Norm of reciprocity and Foot-in-door approach. The ticket sale is different for No special technique when compared with Norm of reciprocity and Foot-in-door approach.

(b).

Already ran in part (a), We conclude that the ticket sale is different for No special technique when compared with Foot-in-door approach.

Effect size is given as,

Mean difference of Norm of reciprocity and Foot-in-door approach = 3 -3 = 0

Mean difference of No special technique and Foot-in-door approach = 3 - 1.33 = 1.67

Mean difference of Norm of reciprocity and No special technique = 3 - 1.33  = 1.67

SDpooled of Norm of reciprocity and Foot-in-door approach = 0.707

SDpooled of No special technique and Foot-in-door approach = 3 - 1.33 = 0.577

SDpooled of  Norm of reciprocity and No special technique = 3 - 1.33  = 0.913

Effect size of Norm of reciprocity and Foot-in-door approach = 0 (Small)

Effect size of No special technique and Foot-in-door approach = 3 - 1.33 = 2.89

Effect size of  Norm of reciprocity and No special technique = 3 - 1.33  = 1.83

It looks that the tickets sale are same for Norm of reciprocity and Foot-in-door approach. As the effect size of  Norm of reciprocity and No special technique is lesser than effect size of No special technique and Foot-in-door approach, tickets sale in No special technique is more cloaser to Norm of reciprocity than Foot-in-door approach.