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Created: Oct 24, 2017
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Week 10- Bone Strength
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StatCrunch week 10

Introduction

Concerns for maintaining bone strength are nothing new. We all grew up being told to drink milk so our bones grow strong. Not to mention, if anyone has experienced a broken bone, it can be excruciatingly painful. In this study, we examined bone strength from three different age groups to assess how much force is required to fracture a bone.

Methods

We collected ten cadaveric femurs from young individuals (19-49 years), nine cadaveric femurs from middle-aged individuals (50-69 years), and ten cadaveric femurs were collected from elderly individuals (70 years old or greater). The force required to break each bone was measured in Newtons. Ideally, we wished to use ANOVA to assess differences in average force required across the three age groups. Checking our validity assumptions: Data is interval/ratio, Levene’s test for homogeneity of variance indicates lack of evidence to dispute constant variability and we have no reason to suspect these groups are not independent. However, we were not convinced the assumption of normality had been met due to shape of the QQ plot. For this reason, we will be using the Kruskal-Wallis test.

 

Result 1: One Way ANOVA QQ plot Wk 10   [Info]
Right click to copy

Result 2: Homogeneity of Variance Test wk 10   [Info]
Homogeneity of Variance results:
Samples in Residuals for Force.
Group by Age Group.

Levene's Test for Homogeneity of Variance
Test StatisticDF 1DF 2P-value
1.2195199 2 26 0.3117

Analysis

 

Result 3: Kruskal-Wallis Wk 10   [Info]
Kruskal-Wallis results:
Responses stored in Force.
Factors stored in Age Group.
Results adjusted for ties
DFChi-SquareP-value
2 14.220453 0.0008

Summary statistics
Age GroupnMedianAve. Rank
Elderly1068.557.25
Middle-Aged998.816.5
Young10114.921.4

Based on our p-value of 0.0008, we can conclude that evidence exists that the median force needed to break each bone does differ among at least one pair of age groups. To isolate these differences, we will perform Mann Whitney pairwise comparisons. Before interpreting these results, we must reconsider our significance level and incorporate a Bonferroni Adjustment. This makes the new significance level 0.017.

 

Result 4: Mann-Whitney Wk 10 part 1   [Info]
Hypothesis test results:
m1 = median of Force where "Age Group" = "Young"
m2 = median of Force where "Age Group" = "Middle-Aged"
m1-m2 : m1 - m2
H0 : m1-m2 = 0
HA : m1-m2 ≠ 0
Differencen1n2Diff. Est.Test Stat.P-valueMethod
m1 - m2210916.85119.50.1207Norm. Approx.

Result 5: Mann-Whitney Wk 10 part 2   [Info]
Hypothesis test results:
m1 = median of Force where "Age Group" = "Middle-Aged"
m2 = median of Force where "Age Group" = "Elderly"
m1-m2 : m1 - m2
H0 : m1-m2 = 0
HA : m1-m2 ≠ 0
Differencen1n2Diff. Est.Test Stat.P-valueMethod
m1 - m2291029.71230.0057Exact

Result 6: Mann-Whitney wk 10 part 3   [Info]
Hypothesis test results:
m1 = median of Force where "Age Group" = "Young"
m2 = median of Force where "Age Group" = "Elderly"
m1-m2 : m1 - m2
H0 : m1-m2 = 0
HA : m1-m2 ≠ 0
Differencen1n2Diff. Est.Test Stat.P-valueMethod
m1 - m22101046.3149.50.0009Norm. Approx.

Based on the results of the first Mann Whitney comparison, we can conclude there is no evidence of a difference in median force required to break bones between the young age group and the middle-aged  (group (p-value 0.12).

Based on the results of the second Mann Whitney comparison, we can conclude that there is evidence of a difference in median force required to break bones between the middle-aged group and the elderly group (p-value 0.0057). By reviewing the sample medians we can see that the direction of this difference is that the force required is greater in the middle-aged group.

Based on the results of the third Mann Whitney comparison, we can conclude that there is evidence of a difference in median force required to break bones between the young age group and the elderly age group (p-value 0.0009). By reviewing the sample medians we can see that the direction of this difference is that the force required is greater in the young age group.

Discussion

Based on our results it appears that elderly individuals have weaker bones than young and middle-aged individuals. When comparing these results to those of the ANOVA, they appear quite similar.

 

Result 7: One Way ANOVA wk 10   [Info]
Analysis of Variance results:
Responses: Force
Factors: Age Group

Response statistics by factor
Age GroupnMeanStd. Dev.Std. Error
Elderly1070.0716.4435775.1999156
Middle-Aged9100.0444419.1217236.3739076
Young10120.232.68254710.335129

ANOVA table
SourceDFSSMSF-StatP-value
Age Group212714.6876357.343611.0400160.0003
Error2614971.983575.84551
Total2827686.67

Tukey HSD results (95% level)
Elderly subtracted from
DifferenceLowerUpperP-value
Middle-Aged29.9744442.576601457.3722870.03
Young50.1323.46289876.7971020.0002
Middle-Aged subtracted from
DifferenceLowerUpperP-value
Young20.155556-7.242287447.5533990.1804

With the ANOVA and Tukey comparisons, there is again evidence of a difference in average force required to break each bone between the age groups except for young and middle-aged.

Conclusions/Further Study

As we now know that the median force required to break bones is less in the elderly, this age population should focus on bone health. Clinicians should screen for risk factors for osteoporosis, falls and vitamin depletion so that bone fractures can be avoided. Further studies should focus on possible treatments for bone weakness that will increase the required force to fracture.

HTML link:
<A href="https://www.statcrunch.com/5.0/viewreport.php?reportid=73074">Week 10- Bone Strength</A>

Comments
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By ekilburn81
Oct 27, 2017

Great job on your report. I agree that further studies need to be done to better treat and catch symptoms earlier. I did the same report as you and to be honest I was not at all surprised by the results.
By danielle.hubbard85
Oct 27, 2017

Great job on your study. I wonder if it would be important to screen people earlier with dexa scans to look at bone density and then tell people what they can do to prevent further issues.
By sadouskasm
Oct 26, 2017

Good job on your study. I agree that further study should be completed on possible treatments for bone weakness. This is a huge problem in the elderly population.

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