Bridges Lab Protocols

General Statistics: Difference between revisions

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[[ Category: General ]]
[[ Category: Data ]]
[[ Category: Statistics ]]
= General Statistical Methods =
= General Statistical Methods =


There are several important concepts that we will adhere to in our group. These involve design considerations, execution considerations and analysis concerns.
There are several important concepts that we will adhere to in our group. These involve design considerations, execution considerations and analysis concerns. The standard for our field is null hypothesis significance testing, which means that we are generally comparing our data to a null hypothesis, generating an '''effect size''' and a '''p-value'''. As a general rule, we report both of these both within our Rmd scripts, and in our publications.
 
We generally use an <math>\alpha</math> of <math>p<0.05</math> to determine significance, which means that (if true) we are rejecting the null hypothesis.


== Experimental Design ==
== Experimental Design ==
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* The desired power (normally 0.8). This indicates that 80% of the time you will detect the effect if there is one. This is also known as 1 minus the false negative rate or 1 minus the Type II error rate.
* The desired power (normally 0.8). This indicates that 80% of the time you will detect the effect if there is one. This is also known as 1 minus the false negative rate or 1 minus the Type II error rate.


We use the R package '''pwr''' to do a power analysis (Champely, 2017). Here is an example:
We use the R package '''pwr''' to do a power analysis (Champely, 2020). Here is an example:


=== Pairwise Comparasons ===
=== Pairwise Comparasons ===
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leveneTest(Result ~ Treatment, data=test.data) %&gt;% tidy %&gt;% kable</pre>
leveneTest(Result ~ Treatment, data=test.data) %&gt;% tidy %&gt;% kable</pre>
{|
{|
! term
!align="right"| df
!align="right"| statistic
!align="right"| statistic
!align="right"| p.value
!align="right"| p.value
!align="right"| df
!align="right"| df.residual
|-
|-
| group
|align="right"| 1
|align="right"| 0.368
|align="right"| 0.368
|align="right"| 0.558
|align="right"| 0.558
|-
|align="right"| 1
|
 
|align="right"| 10
|align="right"| 10
|align="right"| NA
|align="right"| NA
|}
|}


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t.test(Result~Treatment,data=test.data, var.equal=T) %&gt;% tidy %&gt;% kable</pre>
t.test(Result~Treatment,data=test.data, var.equal=T) %&gt;% tidy %&gt;% kable</pre>
{|
{|
!align="right"| estimate1
!align="right" width="8%"| estimate
!align="right"| estimate2
!align="right" width="9%"| estimate1
!align="right"| statistic
!align="right" width="9%"| estimate2
!align="right"| p.value
!align="right" width="9%"| statistic
!align="right"| parameter
!align="right" width="7%"| p.value
!align="right"| conf.low
!align="right" width="9%"| parameter
!align="right"| conf.high
!align="right" width="8%"| conf.low
! method
!align="right" width="9%"| conf.high
! alternative
!width="16%"| method
!width="11%"| alternative
|-
|-
|align="right"| -1.1
|align="right"| 8.79
|align="right"| 8.79
|align="right"| 9.89
|align="right"| 9.89
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t.test(Result~Treatment,data=test.data, var.equal=F) %&gt;% tidy %&gt;% kable</pre>
t.test(Result~Treatment,data=test.data, var.equal=F) %&gt;% tidy %&gt;% kable</pre>
{|
{|
!align="right"| estimate
!align="right" width="8%"| estimate
!align="right"| estimate1
!align="right" width="9%"| estimate1
!align="right"| estimate2
!align="right" width="9%"| estimate2
!align="right"| statistic
!align="right" width="9%"| statistic
!align="right"| p.value
!align="right" width="7%"| p.value
!align="right"| parameter
!align="right" width="9%"| parameter
!align="right"| conf.low
!align="right" width="8%"| conf.low
!align="right"| conf.high
!align="right" width="9%"| conf.high
! method
!width="20%"| method
! alternative
!width="10%"| alternative
|-
|-
|align="right"| -1.1
|align="right"| -1.1
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|align="right"| 12
|align="right"| 12
|align="right"| 0.394
|align="right"| 0.394
| Wilcoxon rank sum test
| Wilcoxon rank sum exact test
| two.sided
| two.sided
|}
|}
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<pre class="r">sessionInfo()</pre>
<pre class="r">sessionInfo()</pre>
<pre>## R version 3.4.2 (2017-09-28)
<pre>## R version 4.4.1 (2024-06-14)
## Platform: x86_64-apple-darwin15.6.0 (64-bit)
## Platform: x86_64-apple-darwin20
## Running under: macOS High Sierra 10.13.1
## Running under: macOS Monterey 12.7.6
##  
##  
## Matrix products: default
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRblas.0.dylib
## BLAS:   /Library/Frameworks/R.framework/Versions/4.4-x86_64/Resources/lib/libRblas.0.dylib  
## LAPACK: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRlapack.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.4-x86_64/Resources/lib/libRlapack.dylib;  LAPACK version 3.12.0
##  
##  
## locale:
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
##
## time zone: America/Detroit
## tzcode source: internal
##  
##  
## attached base packages:
## attached base packages:
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##  
##  
## other attached packages:
## other attached packages:
## [1] car_2.1-6          broom_0.4.3         bindrcpp_0.2     
## [1] car_3.1-2            carData_3.0-5        broom_1.0.6          
## [4] pwr_1.2-1          knitcitations_1.0.9 dplyr_0.7.4      
## [4] pwr_1.3-0            knitcitations_1.0.12 dplyr_1.1.4        
## [7] tidyr_0.7.2        knitr_1.17       
## [7] tidyr_1.3.1          knitr_1.48         
##  
##  
## loaded via a namespace (and not attached):
## loaded via a namespace (and not attached):
##  [1] Rcpp_0.12.14      nloptr_1.0.4       compiler_3.4.2  
##  [1] jsonlite_1.8.8    compiler_4.4.1    tidyselect_1.2.1 Rcpp_1.0.13     
## [4] plyr_1.8.4        highr_0.6          bindr_0.1       
##  [5] xml2_1.3.6       stringr_1.5.1    jquerylib_0.1.4  yaml_2.3.10     
##  [7] tools_3.4.2       lme4_1.1-14        digest_0.6.12   
## [9] fastmap_1.2.0    R6_2.5.1         plyr_1.8.9        generics_0.1.3    
## [10] jsonlite_1.5      lubridate_1.7.1    evaluate_0.10.1  
## [13] backports_1.5.0   tibble_3.2.1     RefManageR_1.4.0  lubridate_1.9.3 
## [13] tibble_1.3.4      nlme_3.1-131      lattice_0.20-35    
## [17] bslib_0.8.0      pillar_1.9.0     rlang_1.1.4       utf8_1.2.4     
## [16] mgcv_1.8-22        pkgconfig_2.0.1    rlang_0.1.4      
## [21] stringi_1.8.4    cachem_1.1.0      xfun_0.46        sass_0.4.9     
## [19] Matrix_1.2-12      psych_1.7.8        bibtex_0.4.2      
## [25] bibtex_0.5.1     timechange_0.3.0  cli_3.6.3         withr_3.0.0    
## [22] yaml_2.1.15        parallel_3.4.2     SparseM_1.77     
## [29] magrittr_2.0.3    digest_0.6.36     lifecycle_1.0.4  vctrs_0.6.5     
## [25] RefManageR_0.14.20 stringr_1.2.0      httr_1.3.1       
## [33] evaluate_0.24.0  glue_1.7.0        abind_1.4-5      fansi_1.0.6      
## [28] xml2_1.1.1         MatrixModels_0.4-1 nnet_7.3-12     
## [37] rmarkdown_2.27   purrr_1.0.2      httr_1.4.7       tools_4.4.1     
## [31] rprojroot_1.2      grid_3.4.2         glue_1.2.0      
## [41] pkgconfig_2.0.3   htmltools_0.5.8.1</pre>
## [34] R6_2.2.2          foreign_0.8-69     rmarkdown_1.8   
## [37] minqa_1.2.4        reshape2_1.4.2    purrr_0.2.4      
## [40] magrittr_1.5      splines_3.4.2     MASS_7.3-47     
## [43] backports_1.1.1   htmltools_0.3.6    pbkrtest_0.4-7  
## [46] assertthat_0.2.0   mnormt_1.5-5      quantreg_5.34   
## [49] stringi_1.1.6</pre>
= References =
= References =


<a name=bib-pwr></a>[[#cite-pwr|[1]]] S. Champely. ''pwr: Basic Functions for Power Analysis''. R package version 1.2-1. 2017. URL: https://CRAN.R-project.org/package=pwr.
<a name=bib-pwr></a>[[#cite-pwr|[1]]] S. Champely. ''pwr: Basic Functions for Power Analysis''. R package version 1.3-0. 2020. URL: https://CRAN.R-project.org/package=pwr.
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