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Data Analytics and Research 2

Data Analytics and Research:

4.2 Assignment

Data Analytics & Research

Research Question Selection

1) Is there a relationship between whether a mother smokes or not and the birth weight of her child?

2) Is the birth weight of babies from white moms different than those from non-white moms?

3) Is there a relationship between the mother’s weight gain during pregnancy and the birth weight of her child?

Question 1

Is there a relationship between whether a mother smokes or not and the birth weight of her child?

For the first part we find two articles dealing with the above research question and provide a summary of each article:

Article 1

The behaviour of infants whose mothers smoke in pregnancy

The behavior of infants whose mothers smoke in pregnancy by David Saxton

In this study, the author compares the infants of mothers who had smoked more than 15 cigarettes/day throughout their pregnancy and the infants whose mothers did not smoke. The author observes that all the infants were spontaneously delivered at the end of the pregnancy term and they were of normal birth weight. The author also matches the two groups for maternal age, social class and parity. The author observes that the duration of labour and analgesia during labour were similar for mothers who smoked and the mothers who were not smokers. Although the author does not observe any significance effect in the birth weight of infants due to smoking, he finds evidence to suggest the child’s auditory senses could be affected by the mother smoking during pregnancy (Saxton, 1978).

Article 2

Maternal smoking and birthweight

The study was aimed to find if mother’s smoking during pregnancy affected the birthweight of the child. The data collected and analysed was of 1016 pairs of births that occurred in 1946- 1963 in Washington County, Maryland. The author examines the mean birth weight of first and second members of pairs of consecutive births of the same mother with respect to her smoking habits. He concludes no significant difference in the birth weight of the infants in which the mother was a smoker in both or either of the two pregnancies (Silverman, 1977). But the author observes that the birth weights of the infants of women who were non-smokers throughout both pregnancies was higher than that of infants of women who smoked during both pregnancies. He also observes that the infants of first members of pairs in which the mothers smoked only during the second pregnancy tended to have birth weights which were lower than that of infants of non-smokers and higher than that of infants of smokers (Silverman, 1977). Hence, he concludes that these findings neither confirm nor deny the hypothesis that smoking during pregnancy causes a reduction in birth weight of the infant.

Analysis

Now for analysing our data we find the mean, median, mode, variance and the standard deviation of our data in the table below:

	Birth weight of the child Mother Smoking	Birth weight of the child Mother Non-Smoking
Mean Median Mode Variance Standard Deviation	7.144273 7.31 7.44 2.303749 1.517811	6.82873 7.06 7.31 1.906244 1.380668

Now we do the statistical tests to see if there is any correlation between the two populations. Let the populations non-smoking mother and Smoking Mother be A and B respectively. Let and be the total number in both the populations.

Now,

Null Hypothesis: The difference in the population means, .

Alternate Hypothesis: .

We are going to conduct the test in the 0.05 level of significance. The degrees of freedom for our population, df = n-1 where n is the minimum of and . Here we are going to conduct the two tailed student’s t test. Firstly, for our populations A and B we calculate the t- value using where is the mean of the population A and is the mean of the population B, is the variance of population A and is the variance of the population B and is the total number of values in population A and is the total number of values in population B.

After calculation, we get t = 1.809311. We use a t- distribution calculator to find the p- value for the null hypothesis to be true, p = 0.072807 which is greater than our significance value 0.05. Hence, we conclude that our alternate hypothesis is not significant at the 0.05 significance level. We do not claim that our null hypothesis to be true. We do not have sufficient data to conclude that.

Question 2

Is the birth weight of babies from white moms different than those from non-white moms?

For the first part we find two articles dealing with the above research question and provide a summary of each article:

Article 1

Birth weight of US biracial (black-white) infants: regional differences

The author examines the prevalence of low birth weight among biracial infants (black mother-white father vs. white mother-black father) in different regions of United States using the data base in 1991. He observes that the rate of low birth weight was 31% higher in the black mother and white father group than in the white mother and black father group (Polednak & King, 1998). He also observes that the difference was smaller in the Northeast United States, is larger in the Western United States. He concludes that there is prevalence of low birth weight among biracial infants and that more studies are needed to identify the maternal factors involved in the regional difference.

Article 2

Diverging associations of maternal age with low birthweight for black and white mothers

In United States, studies suggest a risk of low birth weight increases more quickly with maternal age for black women than it does for white women. The aim was to study the above statement. They take the birth data in Chicago from 1994 to 1996. They study the link between maternal age with risk of low birth weight with respect to maternal race/ethnicity, marital status, education, and neighbourhood poverty of the mothers (Rich-Edwards et al., 2003). In their findings, they see the risk of low birthweight rose steeply with maternal age for black, but not white, mothers. After making the data bit adjusted by considering various other factors, they conclude that the risk of low birth weight rises more quickly with maternal age for women who are disadvantaged, regardless of their race and ethnicity. They conclude that the particularly steep increase in risk of low birth weight with increasing maternal age for black women is due to the high prevalence of disadvantaged women in this population (Rich-Edwards et al., 2003).

Analysis

Now for analysing our data we find the mean, median, mode, variance and the standard deviation of our data in the table below:

	A Birth weight of child White mother	B Birth weight of child Non-white mother
Mean Median Mode Variance Standard Deviation	7.172539683 7.47 7.56 2.575158629 1.60473008	6.75404762 6.845 6.75 2.94240346 1.71534354

We will use the student’s t test to see if there is any correlation between the two populations.

Our Null Hypothesis will be: The difference in the population means is 0, that is

And the Alternate Hypothesis will be:

We are going to conduct the test in the 0.05 level of significance. Hence The degrees of freedom for our population, df = n-2 where n is the minimum of and . Here we are going to conduct the two tailed student’s t test. Firstly, for our populations A and B we calculate the t- value using the following formula where is the mean of the population A and is the mean of the population B, is the variance of population A and is the variance of the population B and is the total number of values in population A and is the total number of values in population B. After putting in the values in the formula, we get t =. Now, the next step is to calculate the probability value or p value for the null hypothesis to be true. We use the t- distribution calculator to find the p- value which turns out to be less than significance value.

Now we do the statistical tests to see if there is any correlation between the two populations. Let the birth weights of the white mother and non-white mother be A and B respectively. Let and be the total number in both the populations.

Now,

Null Hypothesis: The difference in the population means, .

Alternate Hypothesis: .

We are going to conduct the test in the 0.05 level of significance. The degrees of freedom for our population, df = n-1 where n is the minimum of and . Here we are going to conduct the two tailed student’s t test. Firstly, for our populations A and B we calculate the t- value using where is the mean of the population A and is the mean of the population B, is the variance of population A and is the variance of the population B and is the total number of values in population A and is the total number of values in population B.

After calculation, we get t = 2.58579949. We use a t- distribution calculator to find the p- value for the null hypothesis to be true, p = 0.010218 which is which is less than our significance value 0.05. Hence, we reject our null hypothesis. And we conclude that our alternate hypothesis is significant at the 0.05 significance level. We see that our results match with the results of the articles we reviewed. It could be because we got our p-value around 0.01 which is very much lesser than our significance value 0.05.

Question 3

Is there a relationship between the mother’s weight gain during pregnancy and the birth weight of her child?

For the first part we find two articles dealing with the above research question and provide a summary of each article.

Article 1

The association between pregnancy weight gain and birthweight: A within-family comparison

The authors aim to examine the association between maternal weight gain and birthweight using state-based birth registry data. They use the data of births in Michigan and New Jersey, USA, between Jan 1, 1989, and Dec 31, 2003. From their data they excluded the following data points, 1) gestation less than 37 weeks or 41 weeks or more 2) maternal diabetes 3) birthweight less than 500 g or more than 7000 g and 4) those women whose data for pregnancy weight gain was missing. On their analysis, they find a consistent link between pregnancy weight gain and birthweight. They observe that the infants of women who gained more than 24 kg during pregnancy were 148·9 g heavier at birth than were infants of women who gained 8-10 kg (Ludwig & Currie, 2010). They conclude that the maternal weight gain during pregnancy increases birthweight independent of the genetic factors.

Article 2

Gestational weight gain and its relationship with the birthweight of offspring

The authors aim to study the relationship between the weight gain during pregnancy ang the birthweight of the offspring. Data of child births from Beijing Obstetrics and Gynecology Hospital and Haidian Maternity and Child Health Care Hospital in 2010 were used for the study. And they observed only singleton pregnancies. All the pregnant women were divided into underweight, normal weight and overweight group (Wang et al., 2013). They defined the Birthweight between 2500 g and 4000 g as normal birthweight, and 2900 g to 3499 g as appropriate birthweight. They divided the population into different groups and explored were used it to analyse the gestational weight gain (GWG). After researching the data for all the diferent groups using appropriate statistical analysis, they conclude the mother’s weight gain during pregnancy is positively related to the child’s birth weight (Wang et al., 2013).

Analysis

Now for analysing our data we find the mean, median, mode, variance and the standard deviation of our data in the table below:

	Mother’s weight gain during pregnancy (x)	Birth weight of the child (y)
Mean Median Mode Variance Standard Deviation	30.3258 30 30 202.6061 14.23398	7.119507 7.31 7.44 2.220635 1.49018

Here we are going to conduct the two tailed student’s t test. We will use the student’s t test to see if there is any correlation between the two populations.

Null Hypothesis: The population correlation coefficient

Alternate Hypothesis: The population correlation coefficient

The degrees of freedom for our population, df = n-2 = 998 -2 = 996. Firstly, for our variables x and y, we calculate the population correlation coefficient,

.

By calculating, we get r = 0.154171555.

Now for the t-value, we use the formula

where r is the sample correlation coefficient we computed in the previous step and n is the total number in the sample. Now the next step is to calculate the probability value or. By using t- distribution calculator we find that the p value for the null hypothesis to be true is, p < .00001. We can see that it is less than our significance value 0.05. Hence we reject our null hypothesis. And we conclude that our alternate hypothesis is significant in our given significance level. We see that our results match with the results of the articles we reviewed. It could be because we got our p-value around 0.01 which is very much lesser than our significance value 0.05.

References

Ludwig, D. S., & Currie, J. (2010). The association between pregnancy weight gain and birthweight: a within-family comparison. The Lancet, 376(9745), 984-990.

Polednak, A. P., & King, G. (1998). Birth weight of US biracial (black-white) infants: regional differences. Ethnicity & disease, 8(3), 340-349.

Rich-Edwards, J. W., Buka, S. L., Brennan, R. T., & Earls, F. (2003). Diverging associations of maternal age with low birthweight for black and white mothers. International journal of epidemiology, 32(1), 83-90.

Saxton, D. W. (1978). The behaviour of infants whose mothers smoke in pregnancy. Early human development, 2(4), 363-369.

Silverman D.T. (1977). Maternal smoking and birth weight. Am J Epidemiol, 105, 513-21.

Wang, W. P., Chen, F. F., Mi, J., Teng, Y., Zhao, J., Wu, M. H. & Teng, H. H. (2013). Gestational weight gain and its relationship with the birthweight of offspring. Zhonghua fu chan ke za zhi, 48(5), 321-325.