# Statistical Analysis of Glucose and Protein Measurements: A Comprehensive Assignment Overview

Embark on an analytical journey as we detect Westgard rule breaks, construct precise 95% confidence intervals, and dissect the equality of variances and means between old and new instruments. Unveil nuanced insights that redefine our understanding of instrument performance in the realm of biomedical analytics.

## Problem Description:

The statistical analysis assignment addresses statistical analyses related to Glucose and Protein measurements using old and new instruments. Key tasks include detecting Westgard rule breaks, calculating 95% confidence intervals, testing for equality of variances, and examining equality of means.

### Q1: Detection of Westgard Rule Breaks

Problem Description:

Identify instances of Westgard rule breaks based on consecutive observations with more than a 4-standard deviation difference.

Chart 1: Glucose old level control variations

Chart 2: Glucose new level control variations

Chart 3: Protein old level control variations

Chart 4: Protein new level control variations

Solution Summary: Two Westgard rule breaks detected - one in Glucose Level 1 from the old instrument and another in Protein Level 1 from old equipment. Three more observations showed exactly a 4-standard deviation difference.

### Q2: 95% Confidence Intervals for Each Treatment

Problem Description:

Calculate and present the 95% confidence intervals for different treatments involving glucose and protein levels measured with both old and new instruments.

Treatment Lower Level Upper Level
Glucose Old Instrument Level 1 5.57 5.63
Glucose Old Instrument Level 2 14.12 14.28
Protein Old Instrument Level 1 38.93 41.07
Protein Old Instrument Level 2 66.90 69.10
Glucose New Instrument Level 1 5.57 5.63
Glucose Old Instrument Level 2 14.12 14.28
Protein New Instrument Level 1 42.93 45.07
Protein New Instrument Level 2 73.90 76.10

Table 1: Glucose and protein treatments on all levels

Solution Summary: Confidence intervals presented for glucose and protein levels with both old and new instruments, providing a range for each treatment.

### Q3: Equality of Variances Test

Problem Description:

Test for equality of variances between old and new instruments for Glucose Level 1 and Level 2, and Protein Level 1 and Level 2.

Statistics Glucose Protein
Level 1 Level 2 Level 1 Level 2
Old New Old New Old New Old New
Standard Deviation 0.095 0.103 0.284 0.235 3.976 3.367 3.03 4.106
F-value 0.05 6.68 0.08 2.27
p-value 0.819 0.011 0.774 0.135

Table 2: Test for variance equality on glucose and protein levels

Solution Summary: F-tests conducted for equality of variances. Conclusions drawn based on p-values, indicating significant differences in Glucose Level 2 variances between old and new instruments.

### Q4: Equality of Means Test

Problem Description: Test for equality of means between old and new instruments for Glucose Level 1 and Level 2, and Protein Level 1 and Level 2.

Statistics Glucose Protein
Level 1 Level 2 Level 1 Level 2
Old New Old New Old New Old New
Mean 5.571 5.571 14.12 14.21 40.53 44.64 68.3 75.00
SD 0.095 0.103 0.284 0.235 3.976 3.367 3.03 4.106
t-value 0.000 -1.73 -6.07 -10.08
p-value 1.000 0.086 <.001 <.001

Table 3: Test for means equality on glucose and protein levels

Solution Summary: T-tests conducted for equality of means. Conclusions drawn based on p-values, indicating significant differences in protein measurements for both Level 1 and Level 2, but no significant differences in glucose measurements.