# ATHK1001 Assignment 1

ATHK1001 Assignment 1

1

# Assignment 1

• Word length: 750 words across all questions (except references in Question 12). Penalties will apply to papers that exceed this limit by more than 10%.
• Total marks: 60 (17.5% of total grade for class)

2

# Background to Assignment 1

• Sometimes we aren’t just presented with data to analyse, instead we have to estimate or predict data that we don’t know for certain.
• Tversky & Kahneman (1974) argued that we have biases and heurstics that can help us make these estimates.
• They pointed out these biases and heuristics can be important because they can affect the decisions we make based on estimates.
• One such bias they called “anchoring”.

3

# Anchoring

• When people make estimates, they have a starting point that they then adjust.
• These adjustments may be insufficient, so the starting point biases the eventual answer, thus the starting point metaphorically “anchors” the estimate.
• We can demonstrate anchoring by giving people a starting point and seeing how it affects the final answer.
• Strongest pure demonstrations of anchoring are when the anchor is clearly arbitrary.

4

# Demonstration

• Tversky & Kahneman (1974) asked people the percentage of African countries in the United Nations (UN)
• First a number between 0 and 100 was generated by spinning a wheel.
• Participants then indicated whether wheel’s number was higher of lower than the answer to the UN question.

– This ensured they were thinking about the number

• Then they answered the UN question.

5

# Result

• If wheel said “65”, median estimate for UN was 45
• If wheel said “10”, median estimate for UN was 25
• So, a number that the participants knew was random and had nothing to do with the UN biased their answer to the UN question.

6

 Our experiment •     We followed up Tversky and Kahneman’s (1974) demonstration with two tasks. •     Phone task –   Maybe in the UN task the participants did not believe the anchor number really was random, so they saw it as potentially meaningful. –   So make the anchor number based on their own phone number. •     Paired task –   Can any number we encounter be an anchor –   Test if number has to be presented in a similar context by giving pairs of questions and varying their similarity.

7

• Every participants was first asked a sequence of three questions:
• “Think of the last 3 digits of your telephone number, now add 100 to its value, then write the answer in the box below” [adding 100 was a way to make participants focus on the number].
• “Looking at the number you created above did the following event occur before or after this date AD: Attila the Hun was defeated at the Battle of Chalons”

8

 Hypotheses for Phone task • If even a completely random number that participants know cannot possibly have anything to do with the Battle of Chalons can anchor their answers, then we would expect to find support for the following hypotheses: –    Hypothesis 1: Participants with phone numbers above the median produced higher Battle of Chalons estimates than those with phone number below the median. –    Hypothesis 2: Participants’ phone numbers and their estimates for the Battle of Chalons will have a positive correlation. • How we test such hypotheses will be covered in lectures in Week 4 and 5.

9

 Paired task • We first presented the anchor as part of one question in which participants were asked if the number was above or below the anchor. – E.g., “Please indicate whether you think the true answer for the quantity is higher or lower than the random number in blue. The population of New York City in 2019 was [anchor number in blue]”. • Then gave an estimate for the same question: – “What was the population of New York City in 2019?” • Of gave an estimate for a different question: – “What was the number of babies born in the USA in 2018?”

10

 Materials for the Paired task • Participants given nine such pairs. • We manipulated two independent variables: • Question condition –    Participants in the Same Question condition received the same question for the nine estimates. –    Participants in the Different Question condition received a different question for the nine estimates. • Anchor condition. [e.g., New York population in 2019 was 8,419,000] –    Participants in the high anchor condition received a random anchor that had a magnitude one greater than the true answer [e.g., 70,336,817] –    Participants in the low anchor condition received a random anchor that had a magnitude one less than the true answer [e.g., 736,817] • For both conditions participants were randomly assigned to a

level

11

Design
Every participant was randomly assigned to one of four cells of the following table and received the materials specified for that cell:

 Same question Different question High anchor Low anchor

12

 Hypotheses for the Paired task • If the influence of anchors depends on how similar the context of the anchor is to the estimation question, then we would expect support for the following hypotheses: –    Hypothesis 3: In the Paired task, participants in the High anchor condition will produce higher aggregated estimates if they were also in the same question condition than if they were in the different question condition. –    Hypothesis 4: In the Paired task, participants in the Low anchor condition will produce lower aggregated estimates if they were also in the same question condition than if they were in the different question condition.

13

 Results • Data file “Assignment1_dataset.xls” has been put on our Canvas website. Each line represents a participant with an arbitrary ID number. • 294 participants based on those submitting data and giving consent for its use. • Two columns for Phone task: • phone_number: the number participants entered as their phone numbers (plus 100), – [To preserve participants’ anonymity we added a random number between 0 and 100 to their number. This did not change the analyses in any important way] • Chalons_estimate: participants’ estimates for the year of the Battle of Chalons.

14

 Results • Three columns in the data file for the Paired task: • Anchor_condition: whether the participant was given high or low anchors • Question_condition: whether the participant received the same question or a different question to that used to present the anchor. • Aggregated_estimates: represents how close overall a participant’s estimate was to the mean estimate, with negative numbers indicating they tended to be below the mean of everyone’s estimates and positive numbers indicating they tended to be above the mean. – How this was calculated is complicated, but it is described in the assignment. You don’t have to understand this.

15

 Your task • Use Excel (or similar program) to analyse this data and determine if the hypotheses have been supported. • There are 12 questions to answer, each with a certain number of marks. • Answer these questions with complete sentences (except where a graph is requested), but do not repeat the questions themselves. Don’t use tables. • Some questions ask you to give interpretations, just try to use your judgement and the tools you have been given in the course to answer as well as you can. – There are not necessarily single correct answers to such questions.

16

 Readings •      You will need to read at least the part of Tversky and Kahneman (1974) that discusses anchoring (p. 1128) •      This will be available on the “Reading list” accessible from ATHK1001’s Canvas page. •      You do not need to read anything else on anchoring in order to be able to write a perfect assignment. –    So although there is a large literature on anchoring effects you do not need to read any of it. –    You can read more widely if you wish. However, if you use words or ideas from something you read then you must properly cite it.

17

 Formatting recommendations •     Our preference is that you use the font “Times New Roman”, 12-point size, and double-space all the lines. – Indent the beginning of each paragraph using one tab space. •     You should use APA style referencing and citations, but we will accept other styles.

18