Glaucoma is a leading cause of blindness in the United States, N. Ehlers measured the difference in corneal thickness (in microns) between the two eyes of eight patients. Each patient had one eye that had glaucoma and one eye that was normal. The difference was measured as the corneal thickness of normal eye – corneal thickness of eye with Glaucoma. Corneal thickness is important because it can mask an accurate reading of eye pressure. Use ? = .05. Hypothesis: H0: μd=0Ha: μd≠0 Using output
Glaucoma is a leading cause of blindness in the United States, N. Ehlers measured the difference in corneal thickness (in microns) between the two eyes of eight patients. Each patient had one eye that had glaucoma and one eye that was normal. The difference was measured as the corneal thickness of normal eye – corneal thickness of eye with Glaucoma. Corneal thickness is important because it can mask an accurate reading of eye pressure. Use ? = .05.
Hypothesis:
H0: μd=0Ha: μd≠0
Using output
Test statistics :
t=0.134P value=0.897
Degrees of freedom (df):
df=7
Level of significance:
α=0.05
Decision:
P value > 0.05 thus we fails to reject null hypothesis.
Question
a)Write a report summarizing your findings. When writing the
report consider that medical staff estimate that a difference of 4.5 microns or more could impact on their ability to interpret eye pressure correctly.
b) Define for the hypothesis stated in part b) what a type 1 error and type 2 error would mean. Is it possible that we could have committed a type 2 error in conducting the test in part b)?
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Visible: 2 of 2 Variables
Patient
Corneal_Diff
var
var
var
var
1
1
-4.00
2
.00
12.00
4
4
18.00
-4.00
6
6
-12.00
7
7
6.00
8.
8
16.00
9.
10
11
12
13
14
15
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Paired Samples Statistics
Mean
Std. Deviation Std. Error Mean
Pair 1
Patient
4.50
2.449
.866
Corneal thickness
4.0000
8
10.74377
3.79850
difference (normal-
glaucoma) microns
Paired Samples Correlations
Significance
Correlation One-Sided p Two-Sided p
N
Pair 1
Patient & Corneal
.206
.312
.624
thickness difference
(normal-glaucoma)
microns
Paired Samples Test
Paired Differences
Significance
95% Confidence Interval of the
Difference
Mean
Std. Deviation Std. Error Mean
Lower
Upper
df
One-Sided p
Two-Sided p
Pair 1
Patient - Corneal thickness
.50000
10.51529
3.71772
-8.29101
9.29101
134
7
448
.897
difference (normal-
glaucoma) microns
Paired Samples Effect Sizes
95% Confidence Interval
Standardizera Point Estimate
Lower
Upper
Pair 1
Patient - Corneal thickness
Cohen's d
7.792
064
-.632
756
difference (normal-
glaucoma) microns
Hedges' correction
8.773
.057
-.561
.671
a. The denominator used in estimating the effect sizes.
Cohen's d uses the square root of the average variane
Hedges' correction uses the square root of the average variance of measures, plus a correction factor.
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