Question

Evaluate and provide example of how hypothesis testing and confidence interval are used together in healthcare research. Also provide a workplace example that illustrates your ideas.

Answer 1

Solution-

Hypothesis testing and estimation are used to reach conclusions about a population by examining a sample of that population. Hypothesis testing is widely used in medicine, dentistry, health care, biology and other fields as a means to draw conclusions about the nature of populations.

Hypothesis testing is to provide information in helping to make decisions. The administrative decision usually depends a test between two hypotheses. Decisions are based on the outcome.

There is an extremely close relationship between confidence intervals and hypothesis testing. When a 95% confidence interval is constructed, all values in the interval are considered plausible values for the parameter being estimated. Values outside the interval are rejected as relatively implausible. If the value of the parameter specified by the null hypothesis is contained in the 95% interval then the null hypothesis cannot be rejected at the 0.05 level. If the value specified by the null hypothesis is not in the interval then the null hypothesis can be rejected at the 0.05 level. If a 99% confidence interval is constructed, then values outside the interval are rejected at the 0.01 level.

Imagine a researcher wishing to test the null hypothesis that the mean time to respond to an auditory signal is the same as the mean time to respond to a visual signal. The null hypothesis therefore is:

μ_visual - μ_auditory = 0.

For Example-

Ten subjects were tested in the visual condition and their scores (in milliseconds) were: 355, 421, 299, 460, 600, 580, 474, 511, 550, and 586 , auditory condition and their scores were: 275, 320, 278, 360, 430, 520, 464, 311, 529, and 326.

To solve this with the help of SPSS output we get the following output. firstly put the data in spss then go through

Analyze> compare means > paired t-test

Auditory condition	Visual condition
275	355
320	421
278	299
360	460
430	600
520	580
464	474
311	511
529	550
326	586

Output-

Paired Samples Test
		Paired Differences					t	df	Sig. (2-tailed)
		Mean	Std. Deviation	Std. Error Mean	95% Confidence Interval of the Difference
					Lower	Upper
Pair 1	VisualC - AuditoryC	102.30000	83.68599	26.46383	42.43465	162.16535	3.866	9	.004

The 95% confidence interval on the difference between means is:

42.43 ≤ μ_visual - μ_auditory ≤ 162.165

interpretation-  Therefore only values in the interval between 42.43 and 162.165 are retained as plausible values for the difference between population means. Since zero, the value specified by the null hypothesis, is not in the interval, the null hypothesis of no difference between auditory and visual presentation can be rejected at the 0.05 level. The probability value for this example is 0.004 which is less than 0.05. Any time the parameter specified by a null hypothesis is not contained in the 95% confidence interval estimating that parameter, the null hypothesis can be rejected at the 0.05 level or less. Similarly, if the 99% interval does not contain the parameter then the null hypothesis can be rejected at the 0.01 level. The null hypothesis is not rejected if the parameter value specified by the null hypothesis is in the interval since the null hypothesis would still be plausible.