Study effect of Smiling on Leniency in judicial matters.

Introdution

Many People believe that there is something magical in a smile. When you smile, people treat you differently. How true are these statements? Does smiling affects decision making of our brains? A smile makes a person more likeable and more approachable. According to some studies each time someone smile at you the brain coaxes to return the favor. In a study, the subjects were presented with smiling picture of someone and were ask to frown but instead they found the facial expressions went directly to imitation of what they saw. It took conscious effort to make frowning face. Though smiling is perceived as a positive emotion most of the time but there are many cultures that perceive smiling as a negative expression and consider a sign of stupidity and dishonesty. Studies show in certain countries like Germany, Switzerland, China and Malaysia smiling faces were rated as significantly more intelligence than non-smiling people while in other countries like Japan, India, Iran, South Korea and Russia, vice versa is consider to be true. American culture is a Pro-smiling that believes in a general values of emotional openness and broadcasting feelings, while non-pro-smiling cultures like Japanese culture shun overt display of emotion. Russian only smile to genuinely express a good mood or personal regards for an acquaintance. Smiling when carrying out serious work would be seen as an expression of inappropriate levity. As we see different culture perceive smiling very differently in different situations.

There are some evidences that smiling can lessen judgment of possible wrongdoing. This phenomenon is termed as " the smile-leniency effect“, it was center of a study by Marianne Lafrance and Marvin Hechtc in 1995. Given the fact that different cultures perceive smiling very differently, my objective is to substantiate or reject this claim by using statistical software based on the sample data. In this article I will try to understand”Will smiling person accused of a crime be treated more leniently than one who is not smiling or other way round"

Data and Method

To examine the claim the smiling face are treated leniently by jury, an experiment was conducted on a 68 random people (sample size of n = 68). The data for this experiment has been organized into the Smiles dataset in CRAN repository.

For the experiment random participants took the role of members of a college disciplinary panel judging the students accused of cheating. Each participant received a file that contain a description of the offense they commited, a picture was provided with either a smile or neutral facial expression.

A leniency score was calculated based on the disciplimary decisions made by the participants. For this case observation are from simple random sample and consist of fewer than 10% of the population, so they are independent.

The dataset has 68 observations, with two variable of interest the leniency.

Leniency :Score assigned by a judgement panel(higher is more lenient)
Group : Treatment group: neutral or smile.

The side-by-side boxplots of both the groups will give a good starting point for analysis (Figure 1.0). The red dashed line is the average overall leniency score for both groups and the black dot representing the avg for the group.

Figure 1.0: Side-by-side Boxplots

The plot shows that the smile led to greater leniency than the neutral expression.The median leniency for the smile is very close to the 75th percentile leniency score for the neutral expression. The distributions do not appear to have much skew,as the median and mean of the groups are not very far away from each other.

To better understand the effects of smiling on decision making, in other words whether or nor people are more lenient toward people with smiling faces than with neutral faces, I will use statistical inference.

Lets analyze the difference in mean leniency score between two group and if it can be generalized to all people in the world. The larger population for this study would be all people in the world.

Key Parameters for Analysis

$\mu$.Neutral = Mean of Leniency score for neutral group
$\mu$.Smile = Mean of Leniency score for smile group.

Null Hypothesis $H_0$

$H_0$ = $\mu$.Smile - $\mu$.Neutral = 0

There is no difference in the mean leniency score between picture with Neutral or Smiling faces.

Alternative Hypothesis is $H_a$

$H_a$ = $\mu$.Smile - $\mu$.Neutral != 0

There is a difference in the leniency score between smiling pictures and neutral pictures.

Preliminaries

The area of interest here is the difference between the $\mu$.Smile and $\mu$.Neutral mean leniency score between picture with Neutral or Smiling faces. My target population is the entire world population who does not suffer from any form of blindness.Since both the neutral group and smile group have more than 5 observations each, I will assume a normal distribution in the population and use the welch’s two sample t-test to anlayse the difference in mean score.

The descriptive statistics (side-by-side boxplot) shows that smiling pictures score more leniency than thr neutral picture , but its a good idea to test for the possibility of difference in both direction. For this I will conduct a welch’s Two sided t-test with a significance level $\alpha$=0.05. Given that the population mean is unknown,the sample mean ${x} is used for estimation.

Point estimate for a difference of means leniency score is 0.8 , which is simply difference between the mean leniency score between smile group and neutral group (i.e. $\bar{x}.Smile$ - $\bar{x}.Neutral$).

So our best guess is a difference of 0.8 in leniency score between pictures with smiling faces and picture with neutral face.

Next goal is to construct a confidence interval for the difference of two sample means.I have assigned “neutral group” as 0 and “smile group” as 1 for my ease.

R-Studio Statistical Software Results

The output below is a Welch’s two sample T-test with a significance level of 0.05 and an alternative hypothesis that the difference in the mean is not equal to 0.

Figure 1.2: Welch Two Sample t-test

## 
##  Welch Two Sample t-test
## 
## data:  Smiles$Leniency by Smiles$Group
## t = 2.0415, df = 65.367, p-value = 0.04524
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  0.01735362 1.57088168
## sample estimates:
## mean in group 1 mean in group 0 
##        4.911765        4.117647

From the above test, the mean leniency score for smile group $\bar{x}.Smile$ is 4.91 and the mean leniency score for neutral group $\bar{x}.Neutral$ is 4.11.

The t-test statistic is about 2.04 with about 65.37 degrees of freedom(df). This value of degree of freedom is used to calculate the critical value to help to interpret the t-test statistic. With a degree of freedom of 65.37,the critical values for the t- distribution

Figure 1.3 The t-distribution with df = 65.37

From the above figure, the critical t-value is $t_(\frac{\alpha}{2})$ = -/+ 1.99.

For a two-sided test if |t| > $t_(\frac{\alpha}{2})$ the null hypothesis is rejected.

Analysis

Our t-test statistic value is 2.04, this value is not very far away from the mean of 0 and it also very close to the critical value to 1.99.The critical value |t-test statistic| of |2.04| is greater than 1.99 at $/alpha$=0.05. Thus the sample data does not confirmed with null hypothesis, i.e. there is no difference in leniency score with smile group and neutral group. Based on the critical value approach, null hypothesis is rejected against the alternate hypothesis, that the difference in the two means does not equal 0. The sample mean leniency score for smile group is 4.91 and the sample mean leniency score for neutral group is 4.11. As discussed earlier the delta between the two means is 0.80. The 95% confidence interval from our Welch’s test is 0.017 to 1.57, note that the O is not in the range.

p -value Approach: A p-value is the propability of getting the observed or more extreme results, than the one we have in our sample data, given the null hypothesis is true.

With a two -sided test, the p -value = 2 * P(T >= |t|). Above test shows the probability (p-value)of observing a difference in mean of leniency score od smile group and neutral group is about 0.04. This value is less than 0.05 though not substantially. Before rejecting the null hypothesis,lets conduct a quick ANOVA test to determine whether the difference in mean is statistically significant as suggested by the above analysis.

Anova Test Results

## Analysis of Variance Table
## 
## Response: Leniency
##           Df  Sum Sq Mean Sq F value Pr(>F)  
## Group      1  10.721 10.7206  4.1679 0.0452 *
## Residuals 66 169.765  2.5722                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Anova test suggests F-statistic is 4.16 with a p-value equal to 0.045 with a significance level of 0.05, suggesting that the null hypothesis of equal means leniency score for Smile and Neutral group can be rejected.

Both the analysis suggests that the null hypothesis of no difference beween the leniency score between smile group snd neutrsl group can be rejected against the alternate hypothesis that the leniency score is not equal for both the groups at a significance level $\alpha$=0.05.

Conclusion

The current study examine whether smiling face of convict can lessen the judgement of her possible wrongdoing or vice versa.Based on the above study, it can be concluded that at significance level $\alpha$ =0.05, there is difference between the mean Leniency score for smile group and the neutral group. People are more lenient toward smile group. This study suggests that with 95% confidence we can say that the leniency score of smile group is 0.017 to 1.57 more than the leniency score for neutral group. This study appears to be US people are a little more lenient toward convicted person with smiling face than neutral face. However it is important to note that these are not very strong claims due to two reasons. One is the fact that the convicts and wrongdoings for the study are students convicted of cheating in college,not hard-core criminals with serious offense. People will have different perceptions for hard-core criminals with more serious offenses. Secondly, only a picture of the convict was shown, the respondent might have reacted differently to actual person with smiling or neutral face.

Also, as we discussed in the beginning of the article, that different cultures and societies perceive smiling very differently in serious situations like an cheating-offense or wrongdoing,so these results might not hold true for people outside US.

From this study , we see smiling surely increase leniency.Further works should examine jury’s reaction to actual people with similing or neutral faces rather than a picture with similar offenses (i.e. student cheating in college),pictures of convicts with more serious offenses. Does different type of smile have different impact on leniency score. Also it will be interesting to record the ethnicity of the respondent, so that the smile-leniency score can be compared based on different ethnicity and cultural believes.

Reference

https://cran.r-project.org/web/packages/Lock5Data/index.html
LaFrance, M., & Hecht, M. A., “Why smiles generate leniency”, Personality and Social Psychology Bulletin, 21, 1995, 207-214.