# C: Technical Notes and Formulas

Significance Tests for Proportions

State Versus Subgroup Comparisons

The following test is used to determine whether or not a subgroup (county, city, or race) percent (p1) is different from the state percent (P). The Null and Alternate hypotheses tested are:

Ho : p1 equal P vs. H1 : p1 not equal P

The formula for the Z-score is:   Z = (p1 - P)/SQRT[(P * Q)/n1]

where:   p1 is the subgroup percent,
P is the state percent,
Q is 1-P,
n1 is the number of births in the subgroup (denominator of p1), and
SQRT denotes the square root of the expression in brackets.

In a single comparison, if the absolute value of the resulting Z-score is greater than or equal to 1.96, the null hypothesis is rejected, and it can be concluded that the subgroup percent is not equal to the state percent, but rather is larger (or smaller) than the state percent. This critical value (1.96) represents a two-tailed test at alpha equal to .05 (.025 in each tail of the normal distribution).

When a large number of comparisons are made, as is the case when comparing percents for all of the counties or all of the cities against the state percent, the probability that a difference is significant increases substantially due to chance alone. Bonferroni's theory of inequalities is used to account for the increased chance of a significant result when making multiple comparisons.1 The significance level for each individual comparison is adjusted by the number of comparisons made. For the county comparisons, the alpha level was set to .05/92, or ~.0005. This corresponds to a critical Z-score of ~3.458 for a two-tailed test. For the city comparisons, the alpha level was set to .05/31, or ~.0016. This corresponds to a critical Z-score of ~3.15 for a two-tailed test.

Subgroup Versus Subgroup Comparisons

The following test is used to compare two subgroup percents. It is used to compare one county versus another county or one city versus another city. It is also used, for example, to determine if the percents in two racial subgroups of the state are significantly different from each other. The Null and Alternate hypotheses are:

Ho : p1 = p2 vs. H1 : p1 not equal p
2

The formula for the Z-score is:   Z = (p1 - p2) / SQRT[(p*q/n1) + (p*q/n2)]

where:    p1 is the percent for one group,
p2 is the percent for the second group,
p is the pooled percent,
q is 1-p,
n1 is the number of births in group 1,
n2 is the number of births in group 2,
SQRT denotes the square root of the expression in brackets,

and the pooled percent is:   p = (f1 + f2 )/( n1 + n2)

where:   f1 = the number with the characteristic in group 1,
f2 = the number with the characteristic in group 2.

For single comparisons, if the resulting Z-score is greater than or equal to 1.96, the null hypothesis is rejected, and it can be concluded that the two subgroup percents are not equal. This critical value (1.96) represents a two-tailed test at alpha equal to .05 (.025 in each tail of the normal distribution).

When making multiple comparisons, the critical Z values must be adjusted according to the number of comparisons being made. Multiple subgroup comparisons were not made within the context of this report.

Significance Tests for Rates

State Versus Subgroup Comparisons

A comparison between rates is considered statistically significant if the difference between the rates would have occurred by chance less than 5 times out of 100 (i.e., p < 0.05). All statistical tests were conducted using the Z-score method, described in basic statistics texts. While the form of the Z test is similar, the calculation of the standard error for a rate is not straightforward. The following formula can be used to approximate the standard error of a rate:2

SE(rate) = rate / [events]1/2

where, in this case, "events" is the number of births used to calculate the rate.

Subsequently, the Z test for the difference between the state and county rates takes the form:

Z = (state rate - county rate) / SE(diff)

where the SE(diff) is defined as:

SE(diff) = [(SE(s))2 + (SE(c))2 ]1/2

where SE(s) is the standard error of the state rate and SE(c) is the standard error of the county rate.

When testing the differences between the Indiana rate and the rate for each of the 92 counties, the large number of possible comparisons increases the chance that a rate would be statistically significant due to chance alone. To account for multiple comparisons, based on Bonferroni's theory of inequalities, the significance level for each individual comparison was set equal to 0.05/92, where 92 is the number of comparisons made.1 Thus, any individual comparison with an associated "p" value less than ~0.0005 (Z ~ 3.458) was considered to be statistically significant.

When testing the difference between the Indiana rate and the rate for each of the 31 cities, the significance level was set to 0.05/31. The associated "p" value of less than ~.0016 was considered to be statistically significant. This corresponds to a critical Z score of ~3.15 for a two-tailed test.

Subgroup Versus Subgroup Comparisons

The above test can be used to compare two subgroup rates. It is used to compare one county to another county or one city to another city. It is also used, for example, to determine if the rates in two racial subgroups of the state are significantly different from each other.

Method of Computing Cesarean Delivery Rates

Overall Cesarean Rate

To calculate this rate, divide the total number of births by cesarean delivery by the total number of births minus the not-stated method of delivery, and multiply by 100 to express the rate as a percent.

Overall cesarean rate =                          Number of births by cesarean                        x 100
Total number of births - not-stated method of delivery

Primary Cesarean Rate

To calculate this rate, divide the number of first cesarean births by the total number of births to women who have not had a previous cesarean delivery, and multiply by 100 to express as a percent.

Primary cesarean rate =                                Number of primary cesarean births                            x 100
Total # births - VBACs - repeated cesareans - not-stated method

VBAC (Vaginal Birth After Cesarean) Rate

To calculate this rate, divide the number of vaginal births to women who had a previous birth by cesarean delivery by the total number of births (vaginal and cesarean) to women who had a previous birth by cesarean delivery, and multiply by 100 to express as a percent.

VBAC rate =                       VBACS                       x 100
VBACS + repeated cesareans

Information for Former Table 22 - Number and Percent of Mothers Who Used Alcohol During Pregnancy by Age and Race of Mother and Former Table 23 - Number and Percent of Mothers Who Used Alcohol During Pregnancy by Birthweight of Infant and Race of Mother

Information concerning alcohol use during pregnancy is no longer asked on the birth certificate. The National Center for Health Statistics has found that alcohol use is substantially underreported on the birth certificate compared with data collected in nationally representative surveys of pregnant women. The birth certificate question on alcohol use from the 1989 revision was not sensitive enough to measure this behavior accurately. The question’s wording as well as the lack of specific time reference for the birth certificate questions are probable factors contributing to the underreporting. In addition, the stigma of maternal alcohol use likely contributes to underreporting.

Information for Former Tables 27 and 27a - Live Births with Selected Congenital Anomalies

The Indiana Natality Report has contained information on live births with selected congenital anomalies since 1994.  For the majority of anomalies, this information is obtained from a count of the number of check boxes selected on the medical portion of the Indiana Certificate of Live Birth.  In the cases of Heart or Circulatory, Respiratory, Other Genital or Urinary, and some other anomalies, the data are recorded as text entries, not check boxes.  Occasionally, the text entries are not appropriate and, consequently, the number of anomalies is over-counted.  Beginning in 2001, each entry was examined using the standards of the Indiana Birth Problems Registry where possible.  This resulted in far fewer, but more accurate, reports of anomalies in these categories.

In 2004, the Indiana Birth Defects and Problems Registry (IBDPR) was established.  This registry requires the reporting of a diagnosed birth problem for infants and children who are Indiana residents.  Reporting is provided by hospitals, birthing centers, health facilities, physicians and other facilities and health professionals.  The information obtained for each infant and child is verified for accuracy by medical chart review.

Since the information obtained by the IBDPR is verified and accurate, the Indiana Natality Report will no longer provide the tables based on check boxes, but will provide a link to the IBDPR Web site for this information:  http://www.in.gov/isdh/20218.htm