Chapter 17, Problem 13P

1. In a classic study, Loftus and Palmer (1974) investigated the relationship between memory for eyewitnesses and the question they are asked.

In the study participants watched a film of an automobile accident and then were questioned about the accident. One group was asked how fast the cars were going when they “smashed into” each other.

A second group was asked about the speed when the cars “hit” each other, and a third group was not asked any question about the speed of the cars. A week later, the participants returned to answer additional questions about the accident, including whether they recalled. Seeing any broken glass. Although there was no broken glass in the film, several students claimed to remember seeing it. The following table shows the frequency distribution of response for each group.

Response to the Question

Did You See Any Broken Glass?

Verb Used to Ask About the Speed

Verb Used as Ask About the Speed

Smashed into Hit

Control (Not Asked)

Response About Broken Glass

Yes  No

1. Does the proportion of participants who claim to remember broken glass differ significantly from group to group? Test with a = .05.
2. Compute Cramer’s V to measure the size of the
treatment effect.

Describe how the phrasing of the question influenced

the participants’ memories.

Write a sentence demonstrating how the outcome of the hypothesis test and the p1easure of effect size would be reported in a journal article.

To determine

The relationship between memory for eyewitness and the questions they were asked.

Answer to Problem 13P

Solution:

a) The test statistic of 7.778 is greater that the critical value of 5.991, hence, we reject the null hypothesis.

b) The Cramer's V obtained is 0.228.

c) The influence of the phrasing of the question on the participant's memeories is explained

d) A sentence demonstrating the outcome of the hypothesis test and the measure of effect size to be reported in a journal article is provided.

Explanation of Solution

a) Null Hypothesis H₀: The memory for eyewitness and the question they were asked is independent. Alternate Hypothesis H_a: The memory for eyewitness and the question they asked is not independent.

Using the ${\chi }^2$ -test for independence.

The test statistic is

${\chi }^2={\displaystyle \sum _{i=1}^n\frac{{(O_i-E_i)}^2}{E_i}}$ Where, $O_i:$ observed frequency, $E_i:$ expected frequency, number of cells

The expected frequencies are calculated as

$E_i=\frac{R\times C}{Total}$ Where, & are the cell's corresponding row & column total.

	Response To	Broken Glass	Total
	Yes	No
Smashed Into	$O_1=16$	$O_2=34$	$50$	$E_1=9.67$	$E_2=40.33$
Hit	$O_3=7$	$O_4=43$	$50$	$E_3=9.67$	$E_4=40.33$
Control (Not asked)	$O_5=6$	$O_6=44$	$50$	$E_5=9.67$	$E_6=40.33$
Total	$\text{29}$	$121$	$150$

The observed value of the test statistic is:

${\chi }_{obs}^2={\displaystyle \sum _{i=1}^6\frac{{(O_i-E_i)}^2}{E_i}}=7.778$

The critical value from the ${\chi }^2$ -table is ${\chi }_{0.05;(3-1)(2-1)}^2={\chi }_{0.05;2}^2=5.991$ .

b) Cramer's V is calculated as

$V=\sqrt{\frac{{\chi }_{obs}^2/Total}{\min (k-1,r-1)}}$, where & are the number of columns and rows respectively.

$\therefore V=\sqrt{\frac{7.778/150}{1}}=0.228$

c) The phrasing of the question has a significant influence on the memory of the eyewitness. We can see this from both the Chi square test and Cramer's V that there is a moderately strong association between the eyewitness and the questions asked, and the way the question is phrased might change the way an eyewitness answers it.

d) From the result of the hypothesis testing, we can see that there is a significant relationship between the eyewitness and the question they were asked. We know this as the the test satstistic is greater than the critical value allowing us to reject null hypothesis. The measure of the relationship can be obtained from the result of the Cramer's V. We can also see from the Cramer's V of 0.228, that the association between the variables is moderately strong (0.20-0.25).

Conclusion:

We conclude that the memory for eyewitness and the question they were asked are dependent, i.e. the proportion of participants who claim to remember broken glass differ significantly from group to group at 5% level of significance.

Justification:

As the observed value of the test statistic is greater than the critical value, we reject $H_0$ at 5% level of significance.