Introduction
Tattoos have been talked and debated about for years in our society. Dating back as far as 12,000 BC; they have always had an important role in ritual and tradition. Most often, women and men would mark their bodies with a symbol signifying a certain skill or trait. As time went on, the practice practically vanished from western culture from the 12th to the 16th century. Although many religions ban tattoos, today, tattooing has become a more common practice, mainly among the younger generations as a form of masculinity, symbolism and self-expression. Although this practice is greatly frowned upon by the older generations, many are coming to accept it.
For this research project, I am interested in the relationship between gender (independent variable) and number of tattoos (dependent variable) as there seems to be a societal belief that men are more likely to have a tattoo (and more of them) than women, Therefore, gender might significantly impact the number of tattoos an individual has. Because I am surrounded by a large number of the young generation, I decided that this would be a place to test my hypothesis: Because many men in college are trying to appear more masculine and portray manly characteristics, I expect to find that males have significantly more tattoos than females. An independent samples t-test will be used to test this hypothesis.
To test this hypothesis, I collected data from 14 females and 21 males in Baker Center in the afternoon on a Monday. My process of collecting data was to wait on the first floor near the escalators and aske every sixth person of each gender to participate in my study, as well as assuring that their answers would be kept confidential. Each participant was asked to mark the respective boxes for gender and then to write the number of tattoos he or she had.
During my data collection, there were several things that I controlled for. First, I tried to keep personal bias towards certain participants down. In order to do so I asked every sixth person to participate in my study. This is an example of trying to obtain a random and unbiased sample using a random selection process. Second, I made sure that there were exactly 14 females and 21 males in my study, as per the guidelines.
However, there were a few things I did not control for that could have affected my study. For example, I did not control for age. This is important because research shows that individuals under the age of 45 are twice as likely to have a tattoo compared to someone over the age of 45 (http://www.foxnews.com/us/2014/03/14/fox-news-poll-tattoos-arent-just-for-rebels-anymore.html ). Furthermore, I did not control for religion. This is important because some religions prohibit the marking of your body. Another variable I did not control for was types and frequency of risk-taking behaviors (smoking, number of sexual partners, drug use, etc.). This is important because research shows that individuals who participate on more risk-taking behaviors, are also more likely to have tattoos (https://www.ncbi.nlm.nih.gov/pubmed/22153289 ). Therefore, we would expect those with more risk-taking behaviors to skew the mean negatively for one or both groups.
Below is my raw data, where 1=Female and 2=Male:
Gender Number of tattoos
1 2.00
1 2.00
1 1.00
1 3.00
1 3.00
1 3.00
1 .00
1 .00
1 5.00
1 2.00
1 1.00
1 1.00
1 1.00
1 2.00
2 2.00
2 2.00
2 2.00
2 1.00
2 .00
2 1.00
2 .00
2 3.00
2 5.00
2 4.00
2 3.00
2 2.00
2 1.00
2 3.00
2 2.00
2 2.00
2 2.00
2 1.00
2 1.00
2 .00
2 .00
Assumptions of an Independent samples t-test
There are three assumptions associated with an independent samples t-test. These are: normality of the dependent variable, homogeneity of variances, and independence of observations. The assumption of normality of the dependent variable refers the random error in the relationship between the independent variables and the dependent variable.
with regards to this assumption, you can see in the above histogram for females that it looks most normally distributed and the histogram for males looks positively skewed. This is seen not only visually, but also by comparing the mean listed next to the histograms to the median. When the mean is greater than the median, you can conclude that the distribution may be positively skewed. However, in males, the mean is less than the median. Given that the distribution for males is skewed and not normally distributed, the assumption of normality may have been violated in this case. According to the central limit theorem, the test is still valid with sample sizes greater than 30 with skewed distributions. This particular sample size is less than 30. Therefore, this means that the test may not be valid.
The second assumption of the independent samples t-test is homogeneity of variances. The assumption of homogeneity of variance is that the variance within each of the populations is equal.
From the table below, you can see that the standard deviation for females is 1.35062. The standard deviation for males is 1.33809. Squaring these values will give us our variances. The variance for females is 1.82417. The variance for males is 1.7904. Because these values are within 4 times of each other I have not violated the assumption of homogeneity.
Group Statistics
Gender of subjects
N
Mean
Std. Deviation
Std. Error Mean
number of tattoos
Female
14
1.8571
1.35062
.36097
Male
21
1.7619
1.33809
.29199
The last assumption of an independent samples t-test is independence of observations. Independence of observations means that sampling of one observation does not affect the choice of the second observation. What I did to keep from violating this assumption is to make sure that the participants for the sample are selected randomly and one participant’s response does not influence another participant’s response. If this assumption were to be violated, then an independent samples t-test would be inappropriate.
Hypothesis Testing
In order to see if gender is significantly related to number of tattoos, I will be performing an independent t-test. For this two-tailed test, I will be using an alpha of .05. The null hypothesis for this test is: There is no significant difference between gender and number of tattoos. In symbols, the null hypothesis is: Ugender=Utattoos
The alternative hypothesis for this test is: There is a significant difference between gender and number of tattoos. In symbols, the alternative hypothesis is: Ugender=Utattoos. In order to make a decision on whether to reject or fail to reject the null, we need a critical value. Because the degrees of freedom for this test is 33, the alpha is .05, and it is 2-tailed, the critical value is 2.042. Therefore, the test statistic, or obtained value, must be more extreme than +/– 2.042.
Based on the SPSS output below, the appropriate test statistic is .206. This is because the homogeneity of variance assumption was not violated. Because this value does not exceed our critical value in either direction, we can fail to reject our null.
According to the table below, the mean difference was .09524, the standard error was .46339, and lower and upper limits for the 95% confidence interval were: -.84754 and 1.03802, respectively. In other words, I am 95% confident that the difference between population means of males and females in number of tattoos falls between -.84754 and 1.03802.
If I changed my alpha to .01, the new critical value would be +/- 2.733. This would not change my decision regarding my null hypothesis because my obtained t-value is .206 in relation to my critical t-value.
Levene’s Test for Equality of Variances
t-test for Equality of Means
F
Sig.
t
df
Sig. (2-tailed)
Mean Difference
Std. Error Difference
95% Confidence Interval of the Difference
Lower
Upper
number of tattoos
Equal variances assumed
.002
.962
.206
33
.838
.09524
.46339
-.84754
1.03802
Equal variances not assumed
.205
27.833
.839
.09524
.46428
-.85606
1.04654
POWER
Power at the alpha level of .01 has been computed and the output is shown below.
According to this output, the power value for my test is .010. In order to get this value, I unlinked my sample sizes and standard deviations. I inputted my sample means and standard deviations into the program to estimate my population means and population standard deviations. My power of .010 means that there is a low probability of rejecting the null as power is defined as the likelihood of correctly rejecting a false null hypothesis. The closer it is to 1, the higher the power is. Based on this definition, my power is low.
Conclusion
In this study, I investigated whether or not there was a statistically significant difference in gender and the number of tattoos. Because I wanted my data to be as unbiased as possible, I asked every sixth person to be in my study. I also made sure that all answers were kept confidential. This is necessary to keep bias and error to a low. With that said, there were several factors that were out of my control, including age, religion and number of other risk- taking behaviors. I expected that males would have a higher number of tattoos than females, and my results partially support this. My data showed that males are slightly more likely to have a greater number of tattoos, however, this could be because of unequal sample sizes of my groups, as I had 21 males and only 14 females. Because of the fact that I violated my assumption of normality with my males, I am not sure whether the results would remain the same in the larger population. This is because my sample sizes were very small, and therefore is more likely to be skewed or biased in a larger sample size. Because my male data was skewed, I cannot be sure if this is representative of the male population as a whole, and therefore, I am not sure that my results would remain the same in a larger population.
Along the same lines, although the data for the females was not skewed, we cannot be sure that this data is representative in a larger population because of such a small sample size. However, given our assumption that the data is normally distributed and that the female data did not violate this, I think it is closer to being more representative of the population than the male data. Although I did not find a statistically significant difference in this study, I think that the logic underlying my expectations was sound and that if this study was conducted with a larger sample size, the results might have supported my expectations.