Abstract

Title: Recreational Analysis of Height Growth Effects of Dietary Supplement “TrueHieght” from SF Institute’s Primary Study

Background: The SF Institute published a comprehensive study funded by a company claiming height growth benefits from their proprietary dietary powder. This recreation focused exclusively on the height growth metric, the central claim of the supplement company.

Objective: To reanalyze and validate the primary data from the SF Institute’s publication regarding the impact of the dietary powder on height growth.

Methods: The recreated study employed an experimental setup comparing two groups: a control group and a treatment group using the powder supplement. Height measurements were taken at three separate time points (SV1, SV2, and SV3) to trace growth over 6 months.

Findings: The between-group analysis revealed a significant mean growth difference from SV1 to SV3, with the powder group showing a growth of 2.94 cm compared to the control group’s 1.25 cm (t-value: -2.1881, p-value: 0.04377, 95% CI: [-3.32665363, -0.05334637]). While the control group’s mean height difference from SV1 to SV3 was not statistically significant, the powder group exhibited notable growth, corroborated by a p-value less than 0.0001.

Conclusion: The reanalysis of the SF Institute’s primary data supports the dietary powder’s claim to boost height growth over a 6-month period. However, potential biases, including the funding source, and factors like randomization and generalizability, warrant further investigation for a comprehensive understanding of the powder’s efficacy.

Data Loading

Data is read from the study source: https://www.sfinstitute.com/

# Inputting Data
data <- data.frame(
  Subject = c(1,4,5,20,21,22,23,25,26,27,28,29,31,2,3,6,7,30,9,10,11,12,13,14,15,16,17,19,24,8,32),
  Treatment = c('control','control','control','control','control','control','control','control','control',
                'control','control','control','control','powder','powder','powder','powder','powder','powder',
                'powder','powder','powder','powder','powder','powder','powder','powder','powder','powder','powder','powder'),
  Height_cm_SV1 = c(104,152,160,119,144,152,148,167,156,142,126,164,161,115,107,159,118,133,141,170,117,131,100,159,128,166,154,144,161,156,139),
  Height_cm_SV2 = c(126.5,155,155,122.5,144,152,150,168.5,156.5,144.5,126.5,164,161.5,117,108.5,160,118.5,135,142.5,170.5,119.5,132.5,101.5,159,130,166.5,158,144,163.5,153,141),
  Height_cm_SV3 = c(NA,155,155,119,145.5,152,151,168.5,157,147,128,165,163,118,111,160,120.5,137,145,172,120,133,103.5,160,132,167,159.1,148,NA,NA,NA)
)

# Previewing the Data
print(data)
##    Subject Treatment Height_cm_SV1 Height_cm_SV2 Height_cm_SV3
## 1        1   control           104         126.5            NA
## 2        4   control           152         155.0         155.0
## 3        5   control           160         155.0         155.0
## 4       20   control           119         122.5         119.0
## 5       21   control           144         144.0         145.5
## 6       22   control           152         152.0         152.0
## 7       23   control           148         150.0         151.0
## 8       25   control           167         168.5         168.5
## 9       26   control           156         156.5         157.0
## 10      27   control           142         144.5         147.0
## 11      28   control           126         126.5         128.0
## 12      29   control           164         164.0         165.0
## 13      31   control           161         161.5         163.0
## 14       2    powder           115         117.0         118.0
## 15       3    powder           107         108.5         111.0
## 16       6    powder           159         160.0         160.0
## 17       7    powder           118         118.5         120.5
## 18      30    powder           133         135.0         137.0
## 19       9    powder           141         142.5         145.0
## 20      10    powder           170         170.5         172.0
## 21      11    powder           117         119.5         120.0
## 22      12    powder           131         132.5         133.0
## 23      13    powder           100         101.5         103.5
## 24      14    powder           159         159.0         160.0
## 25      15    powder           128         130.0         132.0
## 26      16    powder           166         166.5         167.0
## 27      17    powder           154         158.0         159.1
## 28      19    powder           144         144.0         148.0
## 29      24    powder           161         163.5            NA
## 30       8    powder           156         153.0            NA
## 31      32    powder           139         141.0            NA

Growth Calculation

This section calculates the growth for each subject by subtracting the initial height measurement (SV1) from the last one (SV3).

# Calculate growth by subtracting SV1 from SV3
data$Growth_SV3_SV1 <- data$Height_cm_SV3 - data$Height_cm_SV1

Statistical Analysis

Statistical tests are conducted to understand the effect of the treatment on growth.

# Conduct the t-test for difference between the treatments
result <- t.test(Growth_SV3_SV1 ~ Treatment, data = data, var.equal = FALSE) 
print(result)
## 
##  Welch Two Sample t-test
## 
## data:  Growth_SV3_SV1 by Treatment
## t = -2.1881, df = 16.084, p-value = 0.04377
## alternative hypothesis: true difference in means between group control and group powder is not equal to 0
## 95 percent confidence interval:
##  -3.32665363 -0.05334637
## sample estimates:
## mean in group control  mean in group powder 
##                  1.25                  2.94
# Paired t-test for Control group
control_test <- t.test(data$Height_cm_SV1[data$Treatment == "control"], 
                       data$Height_cm_SV3[data$Treatment == "control"], 
                       paired = TRUE)
print(control_test)
## 
##  Paired t-test
## 
## data:  data$Height_cm_SV1[data$Treatment == "control"] and data$Height_cm_SV3[data$Treatment == "control"]
## t = -1.7987, df = 11, p-value = 0.09953
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
##  -2.7795731  0.2795731
## sample estimates:
## mean difference 
##           -1.25
# Paired t-test for Powder group
powder_test <- t.test(data$Height_cm_SV1[data$Treatment == "powder"], 
                      data$Height_cm_SV3[data$Treatment == "powder"], 
                      paired = TRUE)
print(powder_test)
## 
##  Paired t-test
## 
## data:  data$Height_cm_SV1[data$Treatment == "powder"] and data$Height_cm_SV3[data$Treatment == "powder"]
## t = -8.7228, df = 14, p-value = 4.933e-07
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
##  -3.662892 -2.217108
## sample estimates:
## mean difference 
##           -2.94

Visualization of Growth Data

Histograms help visualize the distribution of growth for both groups.

# Setting Plot Layout
par(mfrow=c(1,2))

# Plotting Control Group Growth
hist(data$Growth_SV3_SV1[data$Treatment == "control"], main="Control Group Growth", xlab="Growth", ylab="Frequency", col=rgb(0.2,0.5,0.2,0.7))

# Plotting Powder Group Growth
hist(data$Growth_SV3_SV1[data$Treatment == "powder"], main="Powder Group Growth", xlab="Growth", ylab="Frequency", col=rgb(0.5,0.2,0.2,0.7))

Approach:

This study aimed to investigate the effects of a powder dietary supplement taken daily for 6 months on height growth. The study was designed as an experimental setup with two groups: the control group and the treatment (powder) group. Height measurements were taken at three different time points (SV1, SV2, and SV3) to track growth over the study duration.

Findings:

Statistical Results:

Between-group Analysis (Welch Two Sample t-test): The mean growth difference between the control group and the powder group from SV1 to SV3 was significant with a t-value of -2.1881, a p-value of 0.04377, and a 95% confidence interval of [-3.32665363, -0.05334637]. The powder group had a mean growth of 2.94 cm while the control group had a mean growth of 1.25 cm. Within-group Analysis for the Control group (Paired t-test): The mean height difference from SV1 to SV3 was not statistically significant (p-value = 0.09953). Within-group Analysis for the Powder group (Paired t-test): The mean height difference from SV1 to SV3 was statistically significant with a t-value of -8.7228 and a p-value less than 0.0001, indicating notable growth in the powder group.

Histogram Analysis:

Control Group: The growth distribution shows most subjects having growth around 0 to 2 cm with a few experiencing a decrease or a slight increase in height. Powder Group: The distribution is notably shifted to the right, indicating more growth. Most subjects in the powder group experienced growth ranging from 2 to 4 cm. Generalizability and Comparison to the Ideal Randomized Controlled Trial (RCT): The study shares some features with an ideal RCT: having a control group, multiple measurements, and a treatment group. However, for complete generalizability:

1.

Random assignment of subjects to treatment or control group ensures that the groups are equivalent at the outset.

2.

Blind assessment where neither the participants nor the researchers know which group they are in, avoiding biases.

3.

Large sample sizes to increase the statistical power of the results.

Given the data, while the powder seems to have a positive effect on growth, caution should be exercised when generalizing these results. It would be essential to consider potential confounding variables, ensure randomization, and account for any biases.