# A Profile of Families Cycling on and off Welfare. Appendix: Calculating Regression-Adjusted Means

The estimates displayed in Tables 8 and 11 were regression-adjusted, using ordinary least squares and controlling for the background characteristics and environmental variables displayed in Table 6. In this model, 0/1 (dummy) variables for cycler (CYCLER) and short-term recipient (STRECIP) represent the independent variables. Sample members have the following values for these measures:

Outcome Group CYCLER STRECIP
Cyclers 1 0
Short-Term Recipient 0 1
Long-Term Recipient 0 0

The background characteristics and environmental variables included in the model represent the control variables, or covariates.

For each outcome measure, the coefficient associated with CYCLER displays the difference between cyclers and long-term recipients. Similarly, the coefficient associated with STRECIP displays the difference between short-term recipients and long-term recipients. The difference between cyclers and short-term recipients can be inferred by calculating the difference between the two coefficients. All of these differences are weighted equally by site.

When calculating the adjusted means shown in Tables 8 and 11, it is assumed that sample members have no other differences except for their being a cycler, short-term recipient, or long-term recipient. This assumption is implemented in the calculations by keeping each sample member's original values of CYCLER and STRECIP, but resetting the value of all of the covariates to their weighted full sample means. For instance, as shown in Table 5, 41.9 percent of sample members were aged 25 to 34 at sample intake. Therefore, each sample member would get the value of 0.419 (instead of a 0 or a 1) for the covariate associated with membership in this age group.

The following formulas are used to calculate adjusted means for each outcome group. For illustration, we include the numbers required for calculating the adjusted means for average total months of welfare receipt during the observation period, that are displayed in Table 8:

 38.6 = Adjusted mean for long-term recipients 25.8Weighted full sample mean - (-11.3 * 0.0847)Weighted coefficient for CYCLER *Weighted proportion of the sample who are cyclers -(-25.4 * 0.4665)Weighted coefficient for STRECIP *Weighted proportion of the sample who are short-term recipients 27.3= Adjusted mean for cyclers 38.6 Adjusted mean for long-term recipients + (-11.3)Weighted coefficient for CYCLER 13.2= Adjusted mean for short-term recipients 38.6 Adjusted mean for long-term recipients + (-25.4)Weighted coefficient for CYCLER 14.1= Difference between cyclers and short-term recipients (-11.3)Weighted coefficient for CYCLER + (-25.4)Weighted coefficient for CYCLER

Appendix Table 1.
Selected Characteristics of Sample Members, by Site
Characteristic Evaluation Sites Vermont WRP Urban Change Sites Full Sample
Connecticut Jobs First Florida FTP Cleveland Philadelphia
Female (%) 97.2 97.8 93.3 96.3 93.6 95.6
Age (%)
18-24 28.5 32.1 27.6 34.9 32.0 31.0
25-34 41.9 46.0 43.7 39.7 38.0 41.9
35-44 24.5 19.2 24.0 20.8 21.7 22.0
45 or older 5.1 2.7 4.7 4.6 8.3 5.1
Average age (years) 30.6 29.0 30.8 29.7 30.8 30.2
Ethnicity (%)
White 38.2 42.0 96.9 26.3 14.6 43.6
Black 38.9 54.8 1.6 67.1 69.3 46.4
Hispanic 22.1 1.4 0.2 5.2 12.8 8.3
Other 0.8 1.8 1.2 1.4 3.3 1.7
Number of children (%)
1 50.4 42.9 43.1 45.1 34.5 43.2
2 25.9 28.7 34.3 28.2 29.2 29.3
3 14.7 16.8 15.8 15.6 18.5 16.3
4 or more 9.0 11.7 6.9 11.2 17.8 11.3
Average number of children 1.9 2.0 1.9 2.0 2.4 2.0
Age of youngest child (%)
2 or under 43.9 44.3 36.9 56.2 60.6 48.4
3 to 5 20.7 27.7 22.6 16.6 14.7 20.4
6 to 12 26.4 21.6 30.2 18.9 17.7 23.0
13 to 18 9.0 6.5 10.3 8.3 7.0 8.2
Average age at birth of oldest child 22.3 20.8 21.7 22.0 22.4 21.9
Had a child as a teenager (%) 39.6 53.6 39.8 42.7 43.4 43.8
Welfare Status (%)
New recipient 39.4 36.5 34.1 42.4 45.1 39.5
Ongoing recipient 60.6 63.5 65.9 57.6 54.9 60.5
Average number of months of welfare receipt during two yearsprior to month of sample intake 14.1 14.2 15.0 12.7 11.9 13.6
Average number of months of food stamp receipt during two years prior to month of sample intake 14.7 16.2 15.8 16.2 13.9 15.4
Any earnings in two years prior to quarter of sample intake (%) 57.1 55.6 57.2 61.9 45.7 55.5
Average number of quarters of employment in two years prior to quarter of sample intake (%) 2.2 2.0 2.3 2.4 1.9 2.2
Sample size 2,184 1,150 4,051 55,764 97,858 161,007
Sources: MDRC calculations from state and county administrative records and Background Information Forms.
Notes: Calculations for the full sample were weighted equally by site.

Appendix Table 2A.
Odds Ratios for Becoming a Welfare Cycler Versus Becoming a Short-Term Recipient
During Years 1 to 4 After Sample Intake,
for Selected Sample Member Chartacteristics And Environmental Conditions, by Site
Characteristic or Environmental Condition Odds Ratios and Statiscal Significance
For Becoming a Cycler Versus Becoming a Short-Term Recipient
Evaluation Sites Vermont WRP Urban Change Sites
Connecticut Jobs First Florida FTP Cleveland Philadelphia
Ongoing recipient at sample intake 0.50 0.82 1.18 0.79 ** 1.11
Total months of welfare receipt during two years prior to sample intake 1.00 1.02 0.99 1.00 1.02 **
Average monthly welfare grant during year prior to sample intake 1.13 1.14 0.98 0.99 0.87 **
Total months of food stamp receipt during two years prior to sample intake 1.00 1.02 1.03 ** 1.03 ** 1.03 **
Number of children 1.16 1.06 1.00 1.17 ** 1.49 **
Youngest child is less than 6 years old 1.38 0.78 1.65 ** 1.33 ** 1.23 **
Had a child as a teenager 0.78 0.95 1.32 ** 1.00 1.05
Female 1.21 1.60 0.95 2.00 ** 1.32 **
Age 18 to 24 2.75 4.19 2.18 4.40 ** 3.01 **
Age 25 to 34 1.61 2.22 1.83 2.39 ** 1.88 **
Age 35 to 44 1.31 1.31 1.32 1.80 ** 1.57 **
Black 1.77 ** 1.21 0.80 2.17 ** 2.10 **
Hispanic 1.19 0.69 n/a 1.36 ** 1.49 **
Other n/a 0.76 0.90 0.99 0.89
No high school diploma or GED 0.86 1.44 1.55 n/a n/a
Missing high school diploma or GED variable 1.23 0.85 0.98 n/a n/a
Total quarters of employment during year prior to sample intake 1.14 1.03 1.05 1.20 ** 1.26 **
Total earnings during year prior to sample intake 1.00 0.98 1.03 0.95 ** 0.97 **
Randomly assigned in quarter 2, 1994 n/a n/a n/a n/a 1.00
Randomly assigned in quarter 3, 1994 n/a 1.24 n/a n/a 1.27 **
Randomly assigned in quarter 4, 1994 n/a 1.05 1.13 0.77 ** 0.92
Randomly assigned in quarter 1, 1995 n/a 0.92 1.12 0.86 0.80
Randomly assigned in quarter 2, 1995 n/a n/a 1.05 0.72 ** 0.93
Randomly assigned in quarter 3, 1995 n/a n/a n/a 0.70 ** 0.98
Randomly assigned in quarter 4, 1995 n/a n/a n/a 0.67 ** 0.97
Randomly assigned in quarter 1, 1996 n/a n/a n/a 0.75 ** 1.04
Randomly assigned in quarter 2, 1996 1.16 n/a n/a 0.56 ** 1.04
Randomly assigned in quarter 3, 1996 1.78 n/a n/a 0.51 ** 0.98
Randomly assigned in quarter 4, 1996 1.10 n/a n/a 0.51 ** 1.22
Randomly assigned in quarter 1, 1997 n/a n/a n/a n/a 1.39 **
Randomly assigned in quarter 2, 1997 n/a n/a n/a n/a 1.18
Randomly assigned in quarter 3, 1997 n/a n/a n/a n/a 1.51 **
Randomly assigned in quarter 4, 1997 n/a n/a n/a n/a 1.57 **
Sources: MDRC calculations from state and county administrative records and Background Information Forms.
Notes: The full sample includes 10,393 cyclers, 62,388 short-term recipients, and 88,226 long-term recipients. Effects were estimated with logistic regression with "Cycler" as the dependent variable. Separate regressions were run for samples of cyclers and short-term recipients and for samples of cyclers and long-term recipients.
"**" indicates statistical significance at the 0.05 level or smaller.
"n/a" indicates "not applicable." There are few or no observations for these categories. For the Urban Change sites, the high school diploma measure was unavailable.

Appendix Table 2B.
Odds Ratios for Becoming a Welfare Cycler Versus Becoming a Long-Term Recipient
During Years 1-4 After Sample Intake,
For Selected Sample Member Characteristics And Environmental Conditions, by Site
Characteristic or Environmental Condition Odds Ratios and Statiscal Significance
For Becoming a Cycler Versus Becoming a Short-Term Recipient
Evaluation Sites Vermont WRP Urban Change Sites
Connecticut Jobs First Florida FTP Cleveland Philadelphia
Ongoing recipient at sample intake 0.45 1.09 0.99 0.77 ** 0.94
Total months of welfare receipt during two years prior to sample intake 1.01 0.98 1.02 1.00 1.00
Average monthly welfare grant during year prior to sample intake 1.00 0.80 0.86 ** 0.93 ** 0.91 **
Total months of food stamp receipt during two years prior to sample intake 0.99 1.01 0.98 1.00 1.00
Number of children 1.03 0.92 0.95 0.87 ** 0.96
Youngest child is less than 6 years old 1.03 1.00 1.09 1.04 0.91
Had a child as a teenager 0.83 1.38 1.78 ** 1.15 ** 1.06
Female 1.11 0.95 0.53 ** 1.21 0.88
Age 18 to 24 0.93 2.12 1.91 2.29 ** 3.62 **
Age 25 to 34 0.84 2.09 2.00 1.92 ** 3.66 **
Age 35 to 44 0.72 1.02 1.43 1.72 ** 3.04 **
Black 1.21 0.53 ** 1.14 1.30 ** 1.62 **
Hispanic 1.29 0.66 n/a 1.42 ** 1.43 **
Other n/a 1.06 1.77 1.06 0.65 **
No high school diploma or GED 0.47 ** 0.75 1.10 n/a n/a
Missing high school diploma or GED variable 1.83 1.00 1.47 n/a n/a
Total quarters of employment during year prior to sample intake 1.10 1.10 1.14 ** 1.34 ** 1.60 **
Total earnings during year prior to sample intake 1.03 1.03 1.04 1.03 ** 0.98 **
Randomly assigned in quarter 2, 1994 n/a n/a n/a n/a 1.02
Randomly assigned in quarter 3, 1994 n/a 1.90 n/a n/a 1.27 **
Randomly assigned in quarter 4, 1994 n/a 1.48 1.26 0.72 ** 0.97
Randomly assigned in quarter 1, 1995 n/a 1.72 1.19 0.79 ** 0.89
Randomly assigned in quarter 2, 1995 n/a n/a 1.03 0.69 ** 0.95
Randomly assigned in quarter 3, 1995 n/a n/a n/a 0.82 ** 1.09
Randomly assigned in quarter 4, 1995 n/a n/a n/a 0.92 1.05
Randomly assigned in quarter 1, 1996 n/a n/a n/a 1.21 1.21
Randomly assigned in quarter 2, 1996 1.03 n/a n/a 1.02 1.45 **
Randomly assigned in quarter 3, 1996 1.86 ** n/a n/a 1.26 1.46 **
Randomly assigned in quarter 4, 1996 1.01 n/a n/a 1.43 ** 1.94 **
Randomly assigned in quarter 1, 1997 n/a n/a n/a n/a 2.32 **
Randomly assigned in quarter 2, 1997 n/a n/a n/a n/a 2.00 **
Randomly assigned in quarter 3, 1997 n/a n/a n/a n/a 2.80 **
Randomly assigned in quarter 4, 1997 n/a n/a n/a n/a 2.83 **
Sources: MDRC calculations from state and county administrative records and Background Information Forms.
Notes: The full sample includes 10,393 cyclers, 62,388 short-term recipients, and 88,226 long-term recipients. Effects were estimated with logistic regression with "Cycler" as the dependent variable. Separate regressions were run for samples of cyclers and short-term recipients and for samples of cyclers and long-term recipients.
"**" indicates statistical significance at the 0.05 level or smaller.
"n/a" indicates "not applicable." There are few or no observations for these categories. For the Urban Change sites, the high school diploma measure was unavailable.

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