Attachment E--Power Analysis and Simulation Study

IMPAQ_Part A&B_AJC_Accessibility_Study_Attachment_E_020414.docx

Evaluating the Accessibility of American Job Centers for People with Disabilities

Attachment E--Power Analysis and Simulation Study

OMB: 1290-0010

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ATTACHMENT E.

POWER ANALYSIS AND SIMULATION STUDY


1. Power Analysis


A base sample size is computed based on the following conditions.

  • Binary measure of accessibility or variance in population (10%, 20% and 25%), which is an expected proportion of accessible AJC;

  • +/- 3 and +/- 5 percent margin of error or precision;

  • Confidence level of 95%;

  • Expected response rate (50%, 60%, 70%, 80% and 90%); and

  • Population size of 2,700.


A required sample size, n, is computed by an equation:

where N is a population size, V is a binary measure of accessibility, P is a precision (margin of error), and Z is a confidence level, and R is an estimated response rate. Table 1 shows the required sample size based on different conditions.


Table 1.








Sample Size


Binary Measure of Accessibility

Precision

Response rate

90%

80%

75%

70%

60%

50%

+/- 5

0.9

146

250

289

320

361

374


0.8

164

282

325

360

406

420


0.7

188

322

372

412

464

480


0.6

219

376

434

480

541

561


0.5

263

451

521

576

649

673

+/- 3

0.9

374

606

686

748

825

850


0.8

420

681

772

841

928

956


0.7

480

779

882

961

1061

1093


0.6

561

908

1029

1122

1238

1275


0.5

673

1090

1235

1346

1485

1530





2. Simulation Study


The IMPAQ team has conducted simulation studies to evaluate the impact of the number of site visits based on the proposed analytical framework, Facet model, in terms of the bias and precision of the latent construct measure and the respondent effects (as facet) of AJC survey.


Survey responses are generated over 2,000 respondents, which is approximately 75% of total AJCs (including both comprehensive and satellite centers) in addition to varied number (i.e. 10-100) of site visits. The parameters of interests, accessibility level was generated from the standard normal distribution and the SDR effect (or respondent effect) had -0.5 for 2,000 respondent simulating the expected SDR bias by center directors and +0.5 by site visitors.


For both simulation studies, data was generated based on a Facet Model with a total of 32 questions (16 binary questions and 16 rating scale items) based on the specifications of communication domain of current AJC surveys. A simulation condition of three step parameters, , for survey item with rating scale is:


and for a dichotomous survey item is:

The latent construct score, , (e.g AJC accessibility level) used a following condition:


A bias of the latent construct estimates is defined as:


where is the estimated latent construct score.


Table 2 shows the mean, standard deviation, 2.5th percentile, and 97.5th percentile bias values for the latent construct and respondent effect estimates.

Table 2: Bias and Standard error of the latent construct estimates


Accessibility Estimates Bias

Respondent Effect Estimates Bias

# of site visits

Mean

SD

P2.5

P97.5

Mean

SD

P2.5

P97.5

10

0.055

0.022

0.017

0.097

0.000

0.104

-0.148

0.148

20

0.064

0.024

0.023

0.112

0.000

0.114

-0.157

0.157

30

0.047

0.027

0.000

0.100

0.000

0.116

-0.165

0.165

40

0.042

0.023

-0.005

0.093

0.000

0.102

-0.158

0.158

50

0.040

0.024

-0.004

0.084

0.000

0.086

-0.121

0.121

60

0.038

0.025

-0.001

0.085

0.000

0.086

-0.121

0.121

70

0.039

0.024

-0.001

0.087

0.000

0.080

-0.114

0.114

80

0.043

0.022

-0.001

0.088

0.000

0.077

-0.108

0.108

90

0.045

0.022

0.004

0.089

0.000

0.074

-0.102

0.102

100

0.043

0.023

-0.004

0.085

0.000

0.074

-0.097

0.097



OMB Part B Attachment D – Page 4 February 4, 2014

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