BMR 617: Statistical Techniques for the Biomedical Sciences

Principles for presenting statistical ananlyses

Statistical analyses are an important part of any experiment or study. The same principles that apply to other parts of the scientific process also apply to the statistical analyses. In particular:

• Statistical analyses should be valid, and in a publication must be verifiable. This means the appropriate analyses should be used, and sufficient detail should be provided so that a reader or reviewer can verify that the appropriate analyses have been performed.
• Analyses should be reproducible. In the context of the statistical analyses, this means that another scientist should be able to start from the same data and produce the same results of the analysis.

Structure of a journal article

Journal articles are typically presented in three main sections:

• Methods
• Results
• Discussion
When presenting the statistics, the methods section should contain sufficient detail on the statistical methods used that another scientist, given the raw data, would be able to reproduce the results:
• What statistical tests were performed for each analysis?
• What software and version of the software were used to perform the analyses?
The results section should include the results of the statistical analyses performed. This can be in the form of graphs, text, or both. In either case, the results of each statistical test should include:
• The effect size. This is the difference in means between two groups (for a t-test, or post-hoc tests for an ANOVA), or the relative risk or odds ratio (for comparing proportions), or a correlation coefficient, \(R^2\) value, or parameter estimate for a linear regression.
• Confidence intervals for the effect sizes. State the level of confidence chosen (this will usually be 95%).
• The p-value. Avoid simply characterizing the p-value as "significant" or "not significant"; always give an actual value. Include all p-values, even those not considered significant.
Always give sufficient information to make it clear what the results mean. For example, in an ANOVA, make sure it is clear which is the "reference" level.

Do not try to interpret the results in the results section. Biological implications of the results obtained should be in the discussion section.

Example

Let's work through our Cholesterol example from the mouse data. Here is the R code for performing a two-way ANOVA and plotting a graph:

	
library(tidyverse)
met <- read_csv("https://denvirlab.marshall.edu/BMR617-2022/data/TH-B6-metabolic.csv") %>%
  separate(MouseID, into=c("Strain", "Diet", "ID"), sep='-')

aov.full <- aov(Cholesterol ~ Strain * Diet, data = met)
aov.full$coefficients
confint(aov.full)
summary(aov.full)

png(filename = "figure1.png", width=4*960, height = 4*480, res=4*72)
ggplot(met, aes(x=Strain, y=Cholesterol, fill=Diet)) +
  geom_boxplot(outlier.shape = NA) + 
  geom_point(position=position_jitterdodge(jitter.width = 0.1, dodge.width = 0.75)) +
  xlab("Cholesterol Level (mg/dl)") +
  ggtitle("Cholesterol Level by Mouse Strain and Diet")
dev.off()

sessionInfo()
	
	

Here is the console output:

> library(tidyverse)
> met <- read_csv("https://denvirlab.marshall.edu/BMR617-2022/data/TH-B6-metabolic.csv") %>%
+   separate(MouseID, into=c("Strain", "Diet", "ID"), sep='-')
Rows: 29 Columns: 7                                                                                                         
── Column specification ──────────────────────────────────────────────────────────────────────────────────────────────────────
Delimiter: ","
chr (1): MouseID
dbl (6): BodyWeight, Insulin, TG, Cholesterol, Glucose, FatMass

ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
> 
> aov.full <- aov(Cholesterol ~ Strain * Diet, data = met)
> aov.full$coefficients
    (Intercept)        StrainTH          DietHF          DietLF StrainTH:DietHF StrainTH:DietLF 
      42.945000       58.290000       72.140998       38.783333        8.934004        7.221669 
> confint(aov.full)
                      2.5 %    97.5 %
(Intercept)      13.1490209  72.74098
StrainTH         19.8235566  96.75644
DietHF           32.1654973 112.11650
DietLF            0.3168892  77.24978
StrainTH:DietHF -49.1490529  67.01706
StrainTH:DietLF -45.5208619  59.96420
> summary(aov.full)
            Df Sum Sq Mean Sq F value   Pr(>F)    
Strain       1  19984   19984  24.082 5.87e-05 ***
Diet         2  25773   12887  15.529 5.40e-05 ***
Strain:Diet  2    102      51   0.062     0.94    
Residuals   23  19086     830                     
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> 
> png(filename = "figure1.png", width=4*960, height = 4*480, res=4*72)
> ggplot(met, aes(x=Strain, y=Cholesterol, fill=Diet)) +
+   geom_boxplot(outlier.shape = NA) + 
+   geom_point(position=position_jitterdodge(jitter.width = 0.1, dodge.width = 0.75)) +
+   xlab("Cholesterol Level (mg/dl)") +
+   ggtitle("Cholesterol Level by Mouse Strain and Diet")
> dev.off()
RStudioGD 
        2 
> 
> sessionInfo()
R version 4.0.3 (2020-10-10)
Platform: x86_64-apple-darwin17.0 (64-bit)
Running under: macOS Big Sur 10.16

Matrix products: default
LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] forcats_0.5.1   stringr_1.4.0   dplyr_1.0.7     purrr_0.3.4     readr_2.0.2     tidyr_1.1.4     tibble_3.1.5   
[8] ggplot2_3.3.5   tidyverse_1.3.1

loaded via a namespace (and not attached):
 [1] tidyselect_1.1.1 haven_2.4.3      colorspace_2.0-2 vctrs_0.3.8      generics_0.1.0   yaml_2.2.1       utf8_1.2.2      
 [8] rlang_0.4.11     pillar_1.6.3     glue_1.4.2       withr_2.4.2      DBI_1.1.1        bit64_4.0.5      dbplyr_2.1.1    
[15] modelr_0.1.8     readxl_1.3.1     lifecycle_1.0.1  munsell_0.5.0    gtable_0.3.0     cellranger_1.1.0 rvest_1.0.2     
[22] labeling_0.4.2   tzdb_0.1.2       parallel_4.0.3   curl_4.3.2       fansi_0.5.0      broom_0.7.9      Rcpp_1.0.7      
[29] scales_1.1.1     backports_1.2.1  vroom_1.5.5      jsonlite_1.7.2   farver_2.1.0     fs_1.5.0         bit_4.0.4       
[36] digest_0.6.28    hms_1.1.1        stringi_1.7.5    grid_4.0.3       cli_3.0.1        tools_4.0.3      magrittr_2.0.1  
[43] crayon_1.4.1     pkgconfig_2.0.3  ellipsis_0.3.2   xml2_1.3.2       reprex_2.0.1     lubridate_1.8.0  assertthat_0.2.1
[50] httr_1.4.2       rstudioapi_0.13  R6_2.5.1         compiler_4.0.3  
	

Methods

For the methods, we need to state the analysis that was performed. What we actually performed was a two-way ANOVA with interaction. That should be the first thing we state. The sessionInfo() command gives us details of the version of R and any packages we are using.

Statistical methods

The effect of mouse strain and diet on cholesterol level was assessed using a two-way ANOVA with interaction.

All statistical analyses were performed using the statistical computing environment R [1], version 4.0.3, with the "tidyverse" package [2], version 1.3.1.

To get the correct references, we can use the citation() function:

citation()
citation("tidyverse")
	

So here our references would be
1. R Core Team (2020). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/.
2. Wickham et al., (2019). Welcome to the tidyverse. Journal of Open Source Software, 4(43), 1686, https://doi.org/10.21105/joss.01686

Results

The R code above generates a PNG graphics file: The figure should have a legend that states simply what is represented.

Cholesterol levels for C57BL/6 ("B6") and TALLYHO ("TH") mice fed Chow, high-fat ("HF"), or Low-fat ("LF") diets from weaning until 16 weeks of age. Box plots indicate median (solid line), interquartile range (box) and range. Points indicate individual values for replicates (n=3-6)

If you choose to use bar charts, then the figure legend should state what the error bars represent.