Payton McCarthy
Professor Davis
MTH 332
7 February, 2020
Does Smoking Affect a Child’s Birth Weight?
Abstract: This study looks to compare data of the birth weights of babies from mothers who smoke and from mothers who do not. The data is from the Child Health and Development Studies (CHDS), which includes all pregnancies from 1960-1967 among women in the Kaiser Foundation Health Plan in Oakland, California. There is a claim that smoking is responsible for a 5.3 to 8.8 ounce reduction in birth weight. In addition, smoking mothers are about twice as likely as non smoking mothers to have a low birth-weight baby (under 88.2 ounces).
Intro and Background: There are many health care practitioners and health organizations that have given strong warnings to pregnant mothers who smoke. However, not everyone has taken these warnings seriously, for example, it was found in 1996 that 15% of pregnant women smoked through their pregnancy (National Center for Health Statistics). This study intends to look at the question if there is a difference between the birth weight of babies born to smoking mothers and non smoking mothers, and if so, is the difference significantly important?
Methods: When this data was recorded, the measurements of each of the 1236 babies were taken at birth. The weights were collected and measured in ounces. The smoking status of the mother was either tallied as a 1 or a 0 to denote if they were smoking or nonsmoking respectively. This study uses the computer program RStudio to make statistical calculations about the dataset. After downloading the data ‘babiesI.data’ from the course website, use this code
data <- read.table(“babiesI.data”,header=TRUE,sep=””)
to label the dataset as ‘data’. Then you want to be able to separate the data into two different datasets of smokers and non smokers so that you can make statistical calculations about each of these two separate groups. Do this by using
smokers <- filter(data, smoke == 1)
smokers <- pull(smokers, var = -2)
to create a list of birth weights of babies born to smoking mothers referred to as ‘smokers’. Do the same for the birth weights of babies born to non smoking mothers and refer to this as ‘nonsmokers’.
nonsmokers <- filter(data, smoke == 0)
nonsmokers <- pull(nonsmokers, var = -2)
Now all the descriptive statistics can be found fairly simply by simply computing them:
mean(smokers)
median(smokers)
sd(smokers)
IQR(smokers)
min(smokers)
max(smokers)
then,
mean(nonsmokers)
median(nonsmokers)
sd(nonsmokers)
IQR(nonsmokers)
min(nonsmokers)
max(nonsmokers)
Next is to find the z-scores, skewness, and kurtosis for both groups. This is done by calculating the z-score for each value in both lists of smokers and non smokers:
z_smokers <- (smokers – mean(smokers))/sd(smokers)
z_nonsmokers <- (nonsmokers – mean(nonsmokers))/sd(nonsmokers)
These new lists are comprised of all the z-scores for all the corresponding birth weights of smokers and non smokers. Now the skewness and kurtosis can be calculated by:
skewness_smokers <-sum(z_smokers ^ 3) / (length(z_smokers) * (sd(smokers)) ^ 3)
kurtosis_smokers <- sum(z_smokers ^ 4) / (length(z_smokers) * (sd(smokers)) ^ 4)
skewness_nonsmokers <- sum(z_nonsmokers ^ 3) / (length(z_nonsmokers) * (sd(nonsmokers)) ^ 3)
kurtosis_nonsmokers <- sum(z_nonsmokers ^ 4) / (length(z_nonsmokers) * (sd(nonsmokers)) ^ 4)
We now want to calculate the probability that a baby could be born underweight (88.2 ounces or below) as mentioned in the abstract. We want to do so for babies born to mothers who smoked and mothers who did not.
underweight_smokers <- (88.2 – mean(smokers))/sd(smokers)
underweight_nonsmokers <- (88.2 – mean(nonsmokers))/sd(nonsmokers)
The next thing performed was to display all the important statistical information in a visual way that would further aid in understanding the results. The first way this is done is by and Box and Whisker plot that compares both ‘smokers’ and ‘nonsmokers’ datasets using this code:
boxPlot_SvN <- boxplot(nonsmokers, smokers, main = “Child Birthweights for
Nonsmoking Mothers and Smoking Mothers”, at = c(1, 2), names = c(“Non-S”,
“Smokers”), xlab = “Birthweight in Ounces”, horizontal = TRUE, notch = TRUE)
This plot will show the locations, dispersions, and outliers of the birth weights of babies to smoking mothers and non smoking mothers fairly well. It may also give a sense for the skewness and the tail size. The second figure that is to be shared is a Normal Distribution graph that also compares the same two datasets:
ggplot(data = data.frame(smokers = c(30, 200)),
mapping = aes(x = smokers)) +
stat_function(mapping = aes(colour = “Smoking Mothers”),
fun = dnorm,
args = list(mean = mean(smokers),
sd = sd(smokers))) +
stat_function(mapping = aes(colour = “Nonsmoking Mothers”),
fun = dnorm,
args = list(mean = mean(nonsmokers),
sd = sd(nonsmokers))) +
scale_colour_manual(values = c(“blue”, “red”)) +
labs(x = “in Ounces”,
y = “Probabilities”,
title = “Normal Curves for Child Birthweights”)
This graph will be beneficial for displaying the mean and standard deviation of both datasets. The skewness and kurtosis of both datasets will be clearly seen and comparable.
Results: Here is a table sharing all of the values of the relevant and descriptive statistics described above.
Table:
| Descriptive Statistic | Smoking Mother | Non Smoking Mother |
| Mean | 114.1095 | 123.0472 |
| Median | 115 | 123 |
| Standard Deviation | 18.09895 | 17.39869 |
| IQR | 24 | 21 |
| Minimum | 58 | 55 |
| Maximum | 163 | 176 |
| Z-3 | 59.81265 | 70.85113 |
| Z-2 | 77.9116 | 88.24982 |
| Z-1 | 96.01055 | 105.64851 |
| Z0 | 114.1095 | 123.0472 |
| Z1 | 132.20845 | 140.44589 |
| Z2 | 150.3074 | 157.84458 |
| Z3 | 168.40635 | 175.24327 |
| Skewness | -5.6489e-6 | -3.543044e-5 |
| Kurtosis | 2.7732e-5 | 4.393673e-5 |
| Probability of Underweight (88.2 ounces) | 7.6136% | 2.2596% |
Box and Whisker Plot:
Normal Distribution:
Discussion and Conclusion: The question that this study looked at is if there is a difference between the birth weight of babies born to smoking mothers and non smoking mothers, and if so, is the difference significantly important? There are a couple claims that are being tested, that is, is smoking responsible for a 5.3 to 8.8 ounce reduction in birth weight, and are mothers who smoke about twice as likely as non smoking mothers to have a low birth-weight baby (under 88.2 ounces)?
If we look at the data, there is a mean difference of 8.9377 ounces between babies whose mothers did not smoke through their pregnancy and those who did not. For the given data, this first claim would appear to be true. Very true. As the mean difference is at the higher end of the plausible range given from the claim.
As to if mothers who smoke are about twice as likely as non smoking mothers to have a low birth-weight baby (under 88.2 ounces), we look at the calculated statistics. We see that in the table, babies born to smoking mothers are 7.6136% likely to be born underweight. Compared to babies born to non smoking mothers who are 2.2596% likely to be born underweight. According to the given data, babies of non smoking mothers are 3.37x less likely to be born underweight than babies born to mothers who smoked. This difference is about 70% larger than the original claim made in the abstract that they would be at least 2x less likely.
One factor that seemingly would be important, yet unavailable, to this study would be to include the ages of all the pregnant women. Certainly the age of a woman has some effect on the child’s health and birth weight. It would be curious to see how this extra variable, conditional with if the mother smokes or not, would affect the data and the results. However, we have affirmed with the given data that mothers who smoke seem to be responsible for at least a 5.3 to 8.8 ounce reduction in birth weight, and such mothers are about twice as likely as non smoking mothers to have a baby born underweight (88.2 ounces or less).