30.8 Example: Health Promotion services
A study (Becker et al. 1991) compared the access to health promotion (HP) services for people with and without a disability. (This study was seen in Sect. 24.10.) Access was measured using the Barriers to Health Promoting Activities for Disabled Persons BHADP scale, where higher scores mean greater barriers. The RQ is:
Is the mean BHADP score the same for people with and without a disability?
The parameter is \(\mu_D - \mu_N\), the difference between the population mean BHADP score (people with disabilities, minus people without disabilities).
In this case, only numerical summary data is available (Table 30.3), not the original data. (An appropriate graphical summary, an error bar chart, can be constructed from the summary information (Fig. 24.11, though a boxplot cannot be constructed from the information.) Denoting those with and without a disability with subscripts \(D\) and \(N\) respectively, the hypotheses are:
- \(H_0\): \(\mu_D - \mu_N = 0\): There is no difference in the population mean BHADP scores
- \(H_1\): \(\mu_D - \mu_N \ne 0\): There is a difference in the population mean BHADP scores
| Sample mean | Std deviation | Sampe size | Std error | |
|---|---|---|---|---|
| Disability | 31.83 | 7.73 | 132 | 0.6728 |
| No disability | 25.07 | 4.8 | 137 | 0.4101 |
| Difference | 6.76 | 0.80285 |
The best estimate of the difference in population means is the difference between the sample means: \((\bar{x}_D - \bar{x}_{ND}) = 6.76\). The table also gives the standard error for estimating this difference as \(\text{s.e.}(\bar{x}_D - \bar{x}_{ND}) = 0.80285\) (as given in the article).
Using the summary information in Table 30.3, the \(t\)-score is computed using Equation (27.1):
\[ t = \frac{6.76 - 0}{0.80285} = 8.42. \] (Recall that \(\mu_D - \mu_N = 0\) from the null hypothesis.) Using the 68–95–99.7 rule, this very large \(t\)-score implies the \(P\)-value will be very small. We conclude:
Strong evidence exists in the sample (\(t = 8.42\); two-tailed \(P < 0.001\)) that people with a disability (mean: 31.83; \(n = 132\); standard deviation: \(7.73\)) and people without a disability (mean: 25.07; \(n = 137\); standard deviation: \(4.80\)) have different population mean access to health promotion services (95% CI for the difference: 5.17 to 8.35).