Fellow The Carolina Population Center University of North Carolina Chapel Hill, NC
Regarding Karlin et al. v. Foust et al. August 9, 1995

Change in the Number of Abortions Related to the Mississippi 24Hour Delay Law
In Exhibits B and C of the Declaration of Stanley K. Henshaw, Dr. Henshaw presented the analyses that led him to conclude that the 24hour delay law caused a decrease in the number of abortions obtained by women in Mississippi and that this decrease occurred because the law placed an increased burden on women seeking an abortion. The procedure he used to detect a change in abortion levels during 1992 was simple. The number of abortions performed in the first 7 months of the year (before the law changed) is used to obtain an "expected" number of abortions for the last 5 months of 1992 (after the law had changed). A ratio of expected abortions in the last 5 months to the number in the first 7 months is calculated by comparing abortions in the last 5 months to the number in the first 7 months of 1990, 1991 and 1993. Multiplying the ratio by the number observed in the first 7 months of 1992 gives the "expected" number in the last 5 months of 1992. The number of observed abortions in the last 5 months of 1992 is then compared to the "expected" number.
I have replicated the analysis reported in the first 4 rows of Table 1 in the Exhibit B article and obtained essentially the same results. There are, however, three basic problems with the procedure used to determine the expected number in this analysis:
First, it is not appropriate to use data from 1993 (after the law was in effect) to derive a base line seasonal adjustment ratio that is then applied to data obtained in 1992 before the law changed. This is simply not an acceptable practice. In the alternative procedure that I describe below, I use data from 1988 through 1991 to obtain a seasonal adjustment ratio that provides a more reliable estimate.
Second, a significant error is made by including data from the months of July and August in the analysis. The new law went into effect on August 8, 1992. It is inexplicable why August would be included in the analysis because part of the month preceded the change in law and part of it followed the change. In anticipation of the law, it is very possible that a significant number of women desiring an abortion around this time period advanced the timing of their abortions thereby increasing the number in late July. Therefore a reasonable test of change associated with the law would exclude data from July. In the alternative analysis shown below, I exclude the months of July and August for the reasons indicated above.
Third, and most important, by choosing to include data on abortions performed in the first quarter of 1992 (JanuaryMarch) as part of the base for obtaining expected abortions later in the year, the authors greatly inflate the number of expected abortions.
Table 1 Replication of Regression Analysis Performed by Dr. Henshaw Analysis of Variance Sum of Mean Source DF Squares Square F Value Prov>F Model 13 185369.13889 14259.16453 4.259 0.0014 Error 22 73657.61111 3348.07323 C Total 35 259026.75000 Root MSE 57.86254 Rsquare 0.7156 Dep Mean 593.08333 Adj Rsq 0.5476 C.V. 9.75622 Parameter Estimates Parameter Standard T for HO: Prob Variable DF Estimate Error Parameter = 0 > T INTERCEP 1 628.944444 43.12818898 14.583 0.0001 INTAUG92 1 100.916667 40.91499256 2.466 0.0219 JAN 1 75.736111 48.73835202 1.554 0.1345 FEB 1 97.611111 48.37924343 2.018 0.0560 MAR 1 29.819444 48.09808314 0.620 0.5416 APR 1 17.361111 47.89624388 0.362 0.7205 MAY 1 1.569444 47.77473101 0.033 0.9741 JUN 1 64.555556 47.73415799 1.352 0.1900 JUL 1 35.986111 47.77473101 0.753 0.4593 AUG 1 1.500000 47.89624388 0.031 0.9753 SEP 1 6.625000 47.61223146 0.139 0.8906 OCT 1 17.750000 47.40832375 0.374 0.7117 NOV 1 56.875000 47.28555706 1.203 0.2418 TREND 1 0.125000 1.96852350 0.063 0.9499 II. The Most Critical Factor: Estimating the Expected Number of Abortions
In this type of analysis everything hinges on how one derives the expected number of abortions. It is the responsibility of the demographic analyst to clearly defend the method that is used. In this case, using the number of abortions performed in the first quarter of 1992 as part of the base for predicting the number in the last months of that year is not acceptable for reasons that will be developed.
It is of critical importance to consider the change in the number of abortions obtained by Mississippi residents between the first and second quarter of 1992in advance of any changes as a result of the law that took effect in August. If the number of abortions in the second quarter is close to what would be expected in the absence of a downward trend, then the number of abortions in the first quarter could be used to predict the number of abortions later in the year. However, if there is evidence of a significant decrease in abortions between the first and second quarter, clearly it would not be appropriate to include first quarter abortions in the base used to predict abortions later in the same year.
In the first quarter (JanuaryMarch) there were 2227 abortions performed on Mississippi residents; in the second quarter there were 1839 abortions. Was this a significant decrease? Using the method proposed by Dr. Henshaw, I calculated the ratio of abortions performed in AprilJune of 1988, 1989, 1990 and 1991 to the number in JanuaryMarch of those same years. This ratio is .959 (ranges from .905 in 1990 to 1.03 in 1991). Applying this ratio to first quarter abortions in 1992 (2227), the expected number for the second quarter is 2136. The differences between the actual (1839) and expected (2136) is 338, or an average decrease of 129 per month. A chisquare test of significance shows this to be significant at the .001 level (there is less than one chance in 1000 that this difference could be the result of random fluctuations.)
This finding of a highly significant decrease in the number of abortions obtained by Mississippi women in advance of the new law has two important implications:
First, it demonstrates why great care must be exercised in attributing causality for changes that occur over time. Had the law gone into effect on April 1, one might conclude that the law caused this large and significant decrease. In reality, we know that the law going into effect could not be responsible, because no change in law occurred at this time.
Second, and very relevant for this analysis, the large decrease observed between the first and second quarter suggests that it is not appropriate to use data from the first quarter to predict what will happen in the last part of that year. If the first quarter data cannot accurately predict what happened in the second quarter, why would one use these data to predict what will happen in the last 5 months of the year?
Given the three methodological problems in the procedures used in the analysis reported by Dr. Henshaw, I propose a similar analysis that avoids these three errors. Namely, I will: [a] use data from 19881991 to derive a seasonal adjustment ratio that provides a more reliable estimate; [b] exclude data for the months of July and August from the analysis; and [c] use the number of abortions in the second quarter of 1992 as the base for determining an expected number of abortions for the last 4 months of 1992. (If a decline in abortion levels were occurring in Mississippi before the new law went into effect, as the data suggests is likely, then this procedure will also inflate the expected numbers. But at least this is closest to the latter part of the year and so is more defensible. Also, the number of abortions in the second quarter of 1992 was not abnormally lowit is larger than the average number in the second quarter during the years 19881991.)
Using Mississippi data for 19881991, the ratio of abortions in SeptemberDecember to those in AprilJune is 1.206. Applying this ratio to abortions in AprilJune of 1992 (1839 abortions) the expected number for SeptemberDecember of 1992 is 2219. The actual number of abortions in SeptemberDecember of 1992 was 2166. Thus the difference between actual and expected was 53, or an average of 13 fewer per month than expected. A chisquare test of the difference between actual and expected for the period SeptemberDecember, 1992 indicates that no statistically significant decline in abortions occurred. This finding is, of course, very different from the one reported by Dr. Henshaw in Family Planning Perspectives, (1994, 26:228) which showed an average monthly decrease of 78 abortions for the months following the change in the law. (Note that the average monthly decrease between the first and second quarters of 1992 was 129 per month.)

Educational Differences
In Exhibit B (Althaus & Henshaw, 1994) of Dr. Henshaw's declaration, in Table 1, rows 5 and 6, the actual and expected number of abortions for Mississippi residents in AugustDecember 1992 were broken down by educational level. The same procedural problems discussed above apply to these data. In addition and more importantly, the validity of these figures is questionable for two reasons.
First, data available on the number of abortions by the number of years of school completed pertains to all procedures performed in Mississippi, not to all abortions performed on Mississippi residents. Some Mississippi residents obtained abortions in other states, and some procedures in Mississippi were performed on nonresident women from other states. Therefore the data on education in this table are misleading and mislabeled.
Second, and of greater concern, Mississippi data on abortions by completed education is very incomplete. For example, the proportion of abortions in Mississippi in which educational level of the women is "unknown" was 50% in 1990, 36% in 1991, 27% in 1992, and 42% in 1993. Presumably what Dr. Henshaw did...