Eric, Kawthar

&nb= sp;

AP Stati= stics Project:

Effect of Order on Random Answer Selection

(Q or M?)

Eric Schlic= h

Kawthar Suleiman

May 16, 200= 6

AP Stati= stics Project:

Effect o= f Order on Random Answer Selection

(Q or M?)

Eric Schlic= h

Kawthar Suleiman

Disclaimer

This study= was done in an AP Statistics course with relatively small sample sizes. The validity of such studies must always be questioned. Please keep this in min= d if you use or report the results of this study.

Abstract<= /p>
Purpose: The purpose= of this study is to determine whether order has any effect on a random selection of= two unbiased letters (Q or M) by a simple random sample of = Sophomore students at Tates Creek High School.

There exis= t two psychological phenomena that influences this stu= dy:

            Primacy Effect*- items presented at the beginning of the list are easier to remember than

those in the middle and may be a preference choice for the test subjects.

            = Recency Effect*- items presented at the end of a = list (most recent) are easier to remember

than those in the middle and may be a preference choice for the test subjects.
Research Question: I= f a subject is asked to choose between two unbiased choices (the letters Q or M) are they more likely to choose the one presented first or second?

Hypothesis: The recency effect is more influential in choosing between the first or second letter. Therefore, the proportion of subjects who choose the second letter will be larger than those who choose = the first.

Population: 438 Tates Creek High School Sophomore students

Test: Two-Proportion= Z-test, Significance Level- alpha =3D .05

Methodology

Introduction<= /b>

This surve= y was designed to determine whether the order of choices presented to a person affects his/her choice. For instance, if a subject is surveyed about which politician he/she would be more likely to vote for in the upcoming election: Politician A or Politician B, which would they choose, given they are not predisposed to one or the other? If a company wishes to randomly survey peo= ple about whether they would choose their product or a different brand, is it m= ore advantageous for the company to ask the question stating their product firs= t or second? Studying the choices of two SRS’s= of 20 Sophomores at Tates Creek High School between two unbiased letters, Q or M (M or Q), may offer an analysis of this topic.

Sampling<= /p>
            Two Simple Random Samples (SRS’s) of 20 Tates Creek High School Sophomore students were gathe= red from the population of 438 total Sophomores in t= he school. This was accomplished by assigning each student a random number from 1-438 and using a random number generator to select each group of 20. The groups were then randomly assigned treatments (order of letters they would = be asked) by using the number generator and the following assignment of letter order:

1 =3D Q or M

2 =3D M or Q

A final list was compiled o= f both sets of 20 names divided according to allocated treatment.

NOTE: As improbable as it m= ay seem in a list of 438, two random numbers were generated twice (48 and 362). To complete the samples of 20, two other random numbers were generated to sele= ct the students to replace the duplicates.

Surveying=

            To reduce bias each subject was surveyed in the same manner. The surveyor stat= ed the following to each subject:

            “This is a short one-question interview conducted by an AP Statistics course. You have been selected to participate in a random sample. Your name will not be used. Please sign below to indicate you give your permission to take part in the study. Thank you.”

The surveyor then asked:

            “Choose between the letters Q or M.”

After the subject gives the= ir response, it is recorded, and the subject signs the release form.

Exploratory Data Analysis<= /o:p>

Data Table

Letter Order

Proportion

(First Letter)<= /o:p>

Proportion

(Second Letter)=

Q or M

0.2

0.8

M or Q

0.7

0.3

Bar Graph

Analysis<= /p>
Inference=

2-Sample Proportion Z-te= st

p1 =3D proportion= of students who selected Q when it was asked FIRST (Q or M= )- 0.2

p2 =3D proportion of students who selected Q when it was asked S= ECOND (M or Q)- 0.3

n1 =3D sample siz= e of SRS of Q or M treatment- 20

n2 =3D sample siz= e of SRS of M or Q treatment- 20

Assumptions:<= /b>

ü      Proportions are derived from two independent= SRS’s.

The ch= oice made by each individual subject does not affect any choices made by any oth= er subjects in the study.

ü      Populations are ≥ 10 times the respect= ive sample size.

            438 ≥ 10 (20) =3D 200

ü    n1 p1 ≥ 5        &= nbsp;           &nbs= p;             = n2 p2 ≥ 5<= /span>

          n1 (1-p= 1) = 805; 5                &= nbsp;         n2 (1-p= 2) = 805; 5

        &= nbsp; 20 (0.2) =3D 4    &nbs= p;            &= nbsp;          20 (0.3) =3D 6 ≥ 5

        &= nbsp; 20 (0.8) =3D 16 ≥ 5   &nb= sp;            =    20 (0.7) =3D 14 ≥ 5

Note: Because 20 (0.2) =3D 4 is not ≥ 5 t= he sample size of this study should be INCREASED.

PROCEED WITH CAUTION.

Significance Tests

The hypothesis of the study= stated that the proportion of those selecting the SECOND choice would be greater t= han those selecting the FIRST:

            Ho : p1 =3D = p2        &= nbsp;           &nbs= p;            &= nbsp;           &nbs= p;    Ha : p1 <= p2=

        &= nbsp;           &nbs= p;            &= nbsp;

Conclusion

Because the significance test yields a p-value of 0.2326 the data is NOT statistically significant at the α =3D 0.05 level. Therefo= re, we FAIL to reject Ho in favor of Ha. This means we fail to reject the hypothesis that there is no difference between = the proportion of students selecting Q when it is asked FIRST and than when it = is asked SECOND, in favor of the hypothesis that there is (and the proportion selecting Q when it is asked SECOND is larger than the proportion when Q is asked FIRST.)

            The main reason this study was ineffective in determining the effect of order on selection is the presence of major bias observed in the preference of the letter M over the letter Q. In both SRS’s= the letter M was chosen much more than the letter Q by test subjects. The fault lies with letter selection. M is a much more common letter than Q in the English language. There exists a third psychological phenomena known as the= Mere Exposure Effect* in which people subconsciously tend to prefer stimuli = they are most repeatedly subjected under over stimuli less present in their live= s. This may have caused more students to choose the M “randomly” over the Q despite letter order.

            It is difficult to think of a survey with a selection LESS biased than two sim= ple letters such as Q and M. Subj= ects should not feel partial toward either letter, yet the data reveals M is most chosen. An appropriate conclusion would be that order CANNOT be a major fac= tor in selection because the two items being selected will incorporate some for= m of bias that affects the results MORE than order. For instance, in the example= of two politicians, the influence of their names, sexes, political parties, or even the tone of voice of the interviewer would have more effect on selecti= on than order. If a company really wished to influence subjects who do not know their product or competitor’s product, creating a popular name, or lo= go would be more effective than the order of the question.

In conclus= ion, because it is so DIFFICULT to limit the bias inherent in the two items being selected, the effect of order is DIFFICULT to analyze. The key is finding t= wo completely non-preferable items to select from. In this study it is easy to RANDOMIZE and REPLICATE. It is the CONTROL of this bias that requires furth= er attention in subsequent studies.

Resource<= /p>
*Barron’s AP Psycholo= gy, Robert McEntarffer and Allyson Wesely, Copyright 2000;

Barron’s Educational = Series, Inc.