Example of an Independent Sample T test

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
 ResearchPeersNMeanStd. Deviation
PCAvgWaitTimeinDays131116.062.98
0215.633.16
Group Statistics
 ResearchPeersStd. Error Mean
PCAvgWaitTimeinDays131.90
0.69

Table 5

Independent Samples Test 
 Levene’s Test for Equality of Variancest-test for Equality of Means 
FSig.t 
 
PCAvgWaitTimeinDays13Equal variances assumed.027.871.376 
Equal variances not assumed  .383 
Independent Samples Test 
 t-test for Equality of Means 
dfSig. (2-tailed)Mean Difference 
 
PCAvgWaitTimeinDays13Equal variances assumed30.710.434 
Equal variances not assumed21.487.706.434 
Independent Samples Test
 t-test for Equality of Means
Std. Error Difference95% Confidence Interval of the Difference
LowerUpper
PCAvgWaitTimeinDays13Equal variances assumed1.153839015224656-1.9227306960758692.790176583521755
Equal variances not assumed1.132796661318518-1.9188103264538212.786256213899707

Table 6.

Independent Samples Effect Sizes
 StandardizeraPoint Estimate95% Confidence Interval
Lower
PCAvgWaitTimeinDays13Cohen’s d3.10.140-.592
Hedges’ correction3.18.136-.577
Glass’s delta3.16.137-.595
Independent Samples Effect Sizes
 95% Confidence Intervala
Upper
PCAvgWaitTimeinDays13Cohen’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.
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