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Chapter 12: Problem 31

Can people tell the difference between a female nose and a male nose? This important (?) research question was examined in the article "You Can Tell by the Nose: Judging Sex from an Isolated Facial Feature" (Perception [1995]: 969-973). Eight Caucasian males and eight Caucasian females posed for nose photos. The article states that none of the volunteers wore nose studs or had prominent nasal hair. Each person placed a black Lycra tube over his or her head in such a way that only the nose protruded through a hole in the material. Photos were then taken from three different angles: front view, three-quarter view, and profile. These photos were shown to a sample of undergraduate students. Each student in the sample was shown one of the nose photos and asked whether it was a photo of a male or a female; and the response was classified as either correct or incorrect. The accompanying table was constructed using summary values reported in the article. Is there evidence that the proportion of correct sex identifications differs for the three different nose views? $$ \begin{array}{l|ccc} & & \text { View } \\ \hline & & & \text { Three- } \\ \text { Sex ID } & \text { Front } & \text { Profile } & \text { Quarter } \\ \hline \text { Correct } & 23 & 26 & 29 \\ \text { Incorrect } & 17 & 14 & 11 \\ \hline \end{array} $$

Short Answer

Expert verified
The chi-square test will provide a p-value based on the calculated chi-square and degrees of freedom. The conclusion to the question depends on this p-value. If it is below 0.05, then there is a significant difference between the proportions. If it is above 0.05, then there is no significant difference.

Step by step solution

01

Calculate the proportions

Firstly, the proportions of correct identifications for each view must be calculated. For this, add up the correct and incorrect identifications for each view. Then, divide the correct identifications with this total for each view. The proportions for Front view \(p_{f}\), Profile view \(p_{p}\), and Three-quarter view \(p_{tq}\) needs to be calculated.
02

Chi-Square Test

Secondly, perform a chi-square test on the proportions \(p_{f}\), \(p_{p}\), and \(p_{tq}\) to see if there's a significant difference between them. Use a chi-square 3x2 table, with the calculated proportions for correct and incorrect identifications in each view, and perform the chi-square test.
03

Interpret the result

Lastly, base on the chi-square test, the p-value will be determined. If the p-value is less than 0.05, we reject the null hypothesis and conclude that view affects identification. If the p-value is greater than 0.05, we fail to reject the null hypothesis, thus, conclude there is no difference in the proportions across the different nose views.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Proportions
Proportions are a mathematical way to express a part of a whole. In the context of this exercise, we're looking at proportions to determine how well undergraduate students can successfully identify the sex of an individual based on a nose photograph. To calculate a proportion, you'll divide the number of successful identifications (the "correct" identifications) by the total number of identifications (both correct and incorrect). For example:
  • For the front view, we have 23 correct identifications and 17 incorrect ones, giving a total of 40. The proportion of correct identifications would be calculated as \( \frac{23}{40} \).
  • Similarly, for the profile and three-quarter views, you'll follow the same method.
Understanding these proportions is crucial because they allow us to see if there is a different level of identification success depending on the nose view shown to the students. It sets the stage for applying the Chi-Square Test to see if these differences are statistically significant.
Sex Identification
Sex identification by visual features like the nose is a fascinating aspect of human perception. In this context, students are tasked with identifying the sex of individuals based solely on images of noses. The underlying question is whether certain nose views鈥攆ront, profile, and three-quarter鈥攎ake it easier or harder for students to correctly guess the sex of the individual. This is explored through the proportions of correct identifications. What's interesting is the psychological and biological factors at play. Even though a nose isn't typically considered as distinctive in gender identification as other features like eyes or mouth, small differences can still significantly impact perception. While not a foolproof method, understanding the nuances in sex identification based on seemingly minor features can shed light on how nuanced and detailed human perception is.
Undergraduate Students
Undergraduate students play an important role in psychological and perception research due to their availability and diversity. In this study, they serve as the sample group tasked with identifying the sex from isolated facial features. Choosing undergraduates offers several benefits:
  • They are usually more willing to participate in studies for course credit or monetary compensation.
  • Students represent a widely diverse demographic, making findings more generalizable.
However, one must also consider potential biases. For example, students may have different levels of experience and ability to perceive subtle facial differences, potentially affecting results. Being aware of who is participating in the study allows for a better understanding and interpretation of results, ensuring that the conclusions drawn are insightful and applicable to broader contexts.

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Most popular questions from this chapter

The authors of the article "A Survey of Parent Attitudes and Practices Regarding Underage Drinking" (Journal of youth and Adolescence [1995]: 315-334) conducted a telephone survey of parents with preteen and teenage children. One of the questions asked was "How effective do you think you are in talking to your children about drinking?" Responses are summarized in the accompanying \(3 \times 2\) table. Using a significance level of \(.05\), carry out a test to determine whether there is an association between age of children and parental response. $$ \begin{array}{l|cc} & \text { Age of Children } \\ \hline \text { Response } & \text { Preteen } & \text { Teen } \\ \hline \text { Very Effective } & 126 & 149 \\ \text { Somewhat Effective } & 44 & 41 \\ \text { Not at All Effective or Don't Know } & 51 & 26 \\ \hline \end{array} $$

The authors of the paper "Movie Character Smoking and Adolescent Smoking: Who Matters More, Good Guys or Bad Guys?" (Pediatrics [2009]: 135-141) classified characters who were depicted smoking in movies released between 2000 and \(2005 .\) The smoking characters were classified according to sex and whether the character type was positive, negative or neutral. The resulting data is given in the accompanying table. Assume that it is reasonable to consider this sample of smoking movie characters as representative of smoking movie characters. Do the data provide evidence of an association between sex and character type for movie characters who smoke? Use \(\alpha=.05\). $$ \begin{array}{lccc} & & \text { Character Type } \\ \hline \text { Sex } & \text { Positive } & \text { Negative } & \text { Neutral } \\ \hline \text { Male } & 255 & 106 & 130 \\ \text { Female } & 85 & 12 & 49 \\ \hline \end{array} $$

The polling organization Ipsos conducted telephone surveys in March of 2004,2005, and 2006 . In each year, 1001 people age 18 or older were asked about whether they planned to use a credit card to pay federal income taxes that year. The data given in the accompanying table are from the report "Fees Keeping Taxpayers from Using Credit Cards to Make Tax Payments" (IPSOS Insight, March 24, 2006 ). Is there evidence that the proportion falling in the three credit card response categories is not the same for all three years? Test the relevant hypotheses using a .05 significance level. $$ \begin{array}{l|rrr} & 2004 & 2005 & 2006 \\ \hline \text { Definitely/Probably Will } & 40 & 50 & 40 \\ \text { Might/Might Not/Probably Not } & 180 & 190 & 160 \\ \text { Definitely Will Not } & 781 & 761 & 801 \\ \hline \end{array} $$

The paper referenced in the previous exercise also gave the accompanying data on the age at which smoking started for a sample of 1031 men who smoked low- tar cigarettes. $$ \begin{array}{cc} \text { Age } & \text { Frequency } \\ \hline<16 & 237 \\ 16-17 & 258 \\ 18-20 & 320 \\ \geq 21 & 216 \\ \hline \end{array} $$ a. Use a chi-square goodness-of-fit test to test the null hypothesis \(H_{0}: p_{1}=.25, p_{2}=.2, p_{3}=.3, p_{4}=.25\) where \(p_{1}=\) proportion of male low-tar cigarette smokers who started smoking before age 16, and \(p_{2}\), \(p_{3}\), and \(p_{4}\) are defined in a similar way for the other three age groups. b. The null hypothesis from Part (a) specifies that half of male smokers of low-tar cigarettes began smoking between the ages of 16 and \(20 .\) Explain why \(p_{2}=.2\) and \(p_{3}=.3\) is consistent with the ages between 16 and 20 being equally likely to be when smoking started.

The color vision of birds plays a role in their foraging behavior: Birds use color to select and avoid certain types of food. The authors of the article "Colour Avoidance in Northern Bobwhites: Effects of Age, Sex, and Previous Experience" (Animal Behaviour [1995]: \(519-526\) ) studied the pecking behavior of 1 -day-old bobwhites. In an area painted white, they inserted four pins with different colored heads. The color of the pin chosen on the bird's first peck was noted for each of 33 bobwhites, resulting in the accompanying table. $$ \begin{array}{lc} \text { Color } & \text { First Peck Frequency } \\ \hline \text { Blue } & 16 \\ \text { Green } & 8 \\ \text { Yellow } & 6 \\ \text { Red } & 3 \\ \hline \end{array} $$ Do the data provide evidence of a color preference? Test using \(\alpha=.01\).
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