Brilliant Answer

In these two examples, Veterans Health Administration (VHA) hospitals in the Midwest and contiguous states were the units of analysis (N=32).  Data were taken from here:  https://www.va.gov/health/access-audit.asp .

 

Example of a one-sample T test

 

The first analysis is intended to be a benchmarking test.  Our VHA hospital of interest has a mean wait for primary care of 4.09 days.  The research question is this: Is the average wait for primary care among the hospitals in the sample significantly different from the wait in Madison?

H0: There is no significant difference between Madison and other VHA hospitals in mean wait times for primary care visits.

H1: There is a significant difference between Madison and other VHA hospitals in mean wait times for primary care visits.

The dependent variable is the mean wait in days for a primary care visit.  The independent variable is the VHA hospital.

The overall mean was 5.78 (Table 1).  The one-sample test (Table 2) produces a p value of .004 (CI .59-2.79).  The mean difference was 1.68 days.  We can reject the null of no difference between the test value and the mean.  The mean wait in Madison VA hospital is 1.68 days less than in the other VHA hospitals in nearby regions. The effect size (Table 3) is strong (Cohen’s D=.55).

 

 

 

 

 

Table 1.

One-Sample Statistics
	N	Mean	Std. Deviation	Std. Error Mean
PCAvgWaitTimeinDays13	32	5.78	3.06	.54

 

Table 2.

 

One-Sample Test
	Test Value = 4.09
	t	df	Sig. (2-tailed)	Mean Difference	95% Confidence Interval of the Difference
					Lower
PCAvgWaitTimeinDays13	3.122	31	.004	1.68	.59

 

One-Sample Test
	Test Value = 4.09
	95% Confidence Interval of the Difference
	Upper
PCAvgWaitTimeinDays13	2.79

 

Table 3.

 

One-Sample Effect Sizes
	Standardizera	Point Estimate	95% Confidence Interval
			Lower
PCAvgWaitTimeinDays13	Cohen's d	3.06	.552	.176
	Hedges' correction	3.13	.538	.171

 

One-Sample Effect Sizes
	95% Confidence Intervala
	Upper
PCAvgWaitTimeinDays13	Cohen's d	.921
	Hedges' correction	.898

 

a. The denominator used in estimating the effect sizes. Cohen's d uses the sample standard deviation. Hedges' correction uses the sample standard deviation, plus a correction factor.

 

T-TEST GROUPS=ResearchPeers(1 0)

  /MISSING=ANALYSIS

  /VARIABLES=PCAvgWaitTimeinDays13

  /ES DISPLAY(TRUE)

  /CRITERIA=CI(.95).

 

Example of an Independent Sample T test

In this two-sample t test, the units of analysis were the 32 VHA hospitals.  The hospitals were scored as 1 if they were research institutions and 0 if not.  The research question was this: Is the average wait time in days for primary care visits significantly different between research and non-research hospitals?

H0: There is no significant difference in mean wait times for primary care visits between research and non-research hospitals.

H1: There is a significant difference in mean wait times for primary care visits between research and non-research hospitals.

The dependent variable is mean wait time in days for primary care visits.  The independent variable was research status (yes vs no).

Eleven hospitals were classified as research institutions and 21 were not. The mean number of days wait for primary care visits was 6.06 in research hospitals and 5.63 in other hospitals (Table 4).  The Levene’s test was not significant, so we can assume the variances are equal.  The p value for the t test was .710, indicating no significant difference between the groups (Table 5).  We can accept the null hypothesis.  The mean wait time in days is not different in research hospitals and non-research hospitals in this sample. Effect size (Table 6) is not relevant since there is no significant difference between the means. 

 

 

Table 4

 

Group Statistics
	ResearchPeers	N	Mean	Std. Deviation
PCAvgWaitTimeinDays13	1	11	6.06	2.98
	0	21	5.63	3.16

 

Group Statistics
	ResearchPeers	Std. Error Mean
PCAvgWaitTimeinDays13	1	.90
	0	.69

 

Table 5

 

Independent Samples Test
	Levene's Test for Equality of Variances	t-test for Equality of Means
	F	Sig.	t
PCAvgWaitTimeinDays13	Equal variances assumed	.027	.871	.376
	Equal variances not assumed			.383

 

Independent Samples Test
	t-test for Equality of Means
	df	Sig. (2-tailed)	Mean Difference
PCAvgWaitTimeinDays13	Equal variances assumed	30	.710	.434
	Equal variances not assumed	21.487	.706	.434

 

Independent Samples Test
	t-test for Equality of Means
	Std. Error Difference	95% Confidence Interval of the Difference
		Lower	Upper
PCAvgWaitTimeinDays13	Equal variances assumed	1.153839015224656	-1.922730696075869	2.790176583521755
	Equal variances not assumed	1.132796661318518	-1.918810326453821	2.786256213899707

 

 

 

 

 

Table 6.

 

Independent Samples Effect Sizes
	Standardizera	Point Estimate	95% Confidence Interval
			Lower
PCAvgWaitTimeinDays13	Cohen's d	3.10	.140	-.592
	Hedges' correction	3.18	.136	-.577
	Glass's delta	3.16	.137	-.595

 

Independent Samples Effect Sizes
	95% Confidence Intervala
	Upper
PCAvgWaitTimeinDays13	Cohen's d	.869
	Hedges' correction	.847
	Glass's delta	.866

 

a. The denominator used in estimating the effect sizes. Cohen's d uses the pooled standard deviation. Hedges' correction uses the pooled standard deviation, plus a correction factor. Glass's delta uses the sample standard deviation of the control group.