day2

Việc 2 so sánh MĐX giữa nam và nữ

2.1 Histogram đánh giá phân bố

library(lessR)

## 
## lessR 4.5                            feedback: gerbing@pdx.edu 
## --------------------------------------------------------------
## > d <- Read("")  Read data file, many formats available, e.g., Excel
##   d is the default data frame, data= in analysis routines optional
## 
## Many examples of reading, writing, and manipulating data, graphics,
## testing means and proportions, regression, factor analysis,
## customization, forecasting, and aggregation to pivot tables.
##   Enter: browseVignettes("lessR")
## 
## View lessR updates, now including modern time series forecasting
##   and many, new Plotly interactive visualizations output. Most
##   visualization functions are now reorganized to three functions:
##      Chart(): type="bar", "pie", "radar", "bubble", "treemap", "icicle"
##      X(): type="histogram", "density", "vbs" and more
##      XY(): type="scatter" for a scatterplot, or "contour", "smooth"
##    Most previous function calls still work, such as:
##      BarChart(), Histogram, and Plot().
##   Enter: news(package="lessR"), or ?Chart, ?X, or ?XY
## There is also Flows() for Sankey flow diagrams, see ?Flows
## 
## Interactive data analysis for constructing visualizations.
##   Enter: interact()

Histogram(
  data=df,
  fnbmd,
  fill="blue",
  main = "Phân bố mật độ xương cổ xương đùi",
  xlab = "Mật độ xương cổ xương đùi (g/cm2)",
  ylab = "Số người"
)

## lessR visualizations are now unified over just three core functions:
##   - Chart() for pivot tables, such as bar charts. More info: ?Chart
##   - X() for a single variable x, such as histograms. More info: ?X
##   - XY() for scatterplots of two variables, x and y. More info: ?XY
## 
## Histogram() is deprecated, though still working for now.
## Please use X(..., type = "histogram") going forward.

## [Interactive plot from the Plotly R package (Sievert, 2020)]

## >>> Suggestions 
## bin_width: set the width of each bin 
## bin_start: set the start of the first bin 
## bin_end: set the end of the last bin 
## X(fnbmd, type="density")  # smoothed curve + histogram 
## X(fnbmd, type="vbs")  # Violin/Box/Scatterplot (VBS) plot 
## 
## --- fnbmd --- 
##  
##        n    miss      mean        sd       min       mdn       max 
##      2122      40     0.829     0.155     0.280     0.820     1.510 
##  
## 
##   
## --- Outliers ---     from the box plot: 33 
##  
## Small      Large 
## -----      ----- 
##  0.3      1.5 
##  0.3      1.5 
##  0.4      1.4 
##  0.4      1.4 
##  0.4      1.4 
##  0.4      1.4 
##  0.4      1.4 
##  0.4      1.4 
##  0.4      1.3 
##  0.4      1.3 
##  0.4      1.3 
##           1.3 
##           1.3 
##           1.3 
##           1.3 
##           1.2 
##           1.2 
##           1.2 
## 
## + 15 more outliers 
## 
## 
## Bin Width: 0.1 
## Number of Bins: 14 
##  
##        Bin  Midpnt  Count    Prop  Cumul.c  Cumul.p 
## --------------------------------------------------- 
##  0.2 > 0.3    0.25      1    0.00        1     0.00 
##  0.3 > 0.4    0.35      9    0.00       10     0.00 
##  0.4 > 0.5    0.45     15    0.01       25     0.01 
##  0.5 > 0.6    0.55    103    0.05      128     0.06 
##  0.6 > 0.7    0.65    306    0.14      434     0.20 
##  0.7 > 0.8    0.75    522    0.25      956     0.45 
##  0.8 > 0.9    0.85    534    0.25     1490     0.70 
##  0.9 > 1.0    0.95    371    0.17     1861     0.88 
##  1.0 > 1.1    1.05    183    0.09     2044     0.96 
##  1.1 > 1.2    1.15     48    0.02     2092     0.99 
##  1.2 > 1.3    1.25     21    0.01     2113     1.00 
##  1.3 > 1.4    1.35      6    0.00     2119     1.00 
##  1.4 > 1.5    1.45      2    0.00     2121     1.00 
##  1.5 > 1.6    1.55      1    0.00     2122     1.00 
##

2.2 TTest

ttest(fnbmd ~ sex ,data = df)

## 
## Compare fnbmd across sex with levels Male and Female 
## Grouping Variable:  sex
## Response Variable:  fnbmd
## 
## 
## ------ Describe ------
## 
## fnbmd for sex Male:  n.miss = 23,  n = 822,  mean = 0.910,  sd = 0.153
## fnbmd for sex Female:  n.miss = 17,  n = 1300,  mean = 0.778,  sd = 0.132
## 
## Mean Difference of fnbmd:  0.132
## 
## Weighted Average Standard Deviation:   0.141 
## 
## 
## ------ Assumptions ------
## 
## Note: These hypothesis tests can perform poorly, and the 
##       t-test is typically robust to violations of assumptions. 
##       Use as heuristic guides instead of interpreting literally. 
## 
## Null hypothesis, for each group, is a normal distribution of fnbmd.
## Group Male: Sample mean assumed normal because n > 30, so no test needed.
## Group Female: Sample mean assumed normal because n > 30, so no test needed.
## 
## Null hypothesis is equal variances of fnbmd, homogeneous.
## Variance Ratio test:  F = 0.023/0.018 = 1.336,  df = 821;1299,  p-value = 0.000
## Levene's test, Brown-Forsythe:  t = 3.449,  df = 2120,  p-value = 0.001
## 
## 
## ------ Infer ------
## 
## --- Assume equal population variances of fnbmd for each sex 
## 
## t-cutoff for 95% range of variation: tcut =  1.961 
## Standard Error of Mean Difference: SE =  0.006 
## 
## Hypothesis Test of 0 Mean Diff:  t-value = 21.080,  df = 2120,  p-value = 0.000
## 
## Margin of Error for 95% Confidence Level:  0.012
## 95% Confidence Interval for Mean Difference:  0.120 to 0.144
## 
## 
## --- Do not assume equal population variances of fnbmd for each sex 
## 
## t-cutoff: tcut =  1.961 
## Standard Error of Mean Difference: SE =  0.006 
## 
## Hypothesis Test of 0 Mean Diff:  t = 20.407,  df = 1560.981, p-value = 0.000
## 
## Margin of Error for 95% Confidence Level:  0.013
## 95% Confidence Interval for Mean Difference:  0.119 to 0.145
## 
## 
## ------ Effect Size ------
## 
## --- Assume equal population variances of fnbmd for each sex 
## 
## Standardized Mean Difference of fnbmd, Cohen's d:  0.939
## 
## 
## ------ Practical Importance ------
## 
## Minimum Mean Difference of practical importance: mmd
## Minimum Standardized Mean Difference of practical importance: msmd
## Neither value specified, so no analysis
## 
## 
## ------ Graphics Smoothing Parameter ------
## 
## Density bandwidth for sex Male: 0.044
## Density bandwidth for sex Female: 0.034

### bootrap

placebo <- c(105, 119, 100, 97, 96, 101, 94, 95, 98)
cafe    <- c(96, 99, 94, 89, 96, 93, 88, 105, 88)

ttest(placebo, cafe)

## 
## Compare Y across X with levels Group1 and Group2 
## Grouping Variable:  X
## Response Variable:  Y
## 
## 
## ------ Describe ------
## 
## Y for X Group1:  n.miss = 0,  n = 9,  mean = 100.556,  sd = 7.699
## Y for X Group2:  n.miss = 0,  n = 9,  mean = 94.222,  sd = 5.608
## 
## Mean Difference of Y:  6.333
## 
## Weighted Average Standard Deviation:   6.735 
## 
## 
## ------ Assumptions ------
## 
## Note: These hypothesis tests can perform poorly, and the 
##       t-test is typically robust to violations of assumptions. 
##       Use as heuristic guides instead of interpreting literally. 
## 
## Null hypothesis, for each group, is a normal distribution of Y.
## Group Group1  Shapiro-Wilk normality test:  W = 0.780,  p-value = 0.012
## Group Group2  Shapiro-Wilk normality test:  W = 0.924,  p-value = 0.427
## 
## Null hypothesis is equal variances of Y, homogeneous.
## Variance Ratio test:  F = 59.278/31.444 = 1.885,  df = 8;8,  p-value = 0.389
## Levene's test, Brown-Forsythe:  t = 0.230,  df = 16,  p-value = 0.821
## 
## 
## ------ Infer ------
## 
## --- Assume equal population variances of Y for each X 
## 
## t-cutoff for 95% range of variation: tcut =  2.120 
## Standard Error of Mean Difference: SE =  3.175 
## 
## Hypothesis Test of 0 Mean Diff:  t-value = 1.995,  df = 16,  p-value = 0.063
## 
## Margin of Error for 95% Confidence Level:  6.731
## 95% Confidence Interval for Mean Difference:  -0.397 to 13.064
## 
## 
## --- Do not assume equal population variances of Y for each X 
## 
## t-cutoff: tcut =  2.136 
## Standard Error of Mean Difference: SE =  3.175 
## 
## Hypothesis Test of 0 Mean Diff:  t = 1.995,  df = 14.624, p-value = 0.065
## 
## Margin of Error for 95% Confidence Level:  6.782
## 95% Confidence Interval for Mean Difference:  -0.449 to 13.116
## 
## 
## ------ Effect Size ------
## 
## --- Assume equal population variances of Y for each X 
## 
## Standardized Mean Difference of Y, Cohen's d:  0.940
## 
## 
## ------ Practical Importance ------
## 
## Minimum Mean Difference of practical importance: mmd
## Minimum Standardized Mean Difference of practical importance: msmd
## Neither value specified, so no analysis
## 
## 
## ------ Graphics Smoothing Parameter ------
## 
## Density bandwidth for X Group1: 5.642
## Density bandwidth for X Group2: 4.112

library(boot)

dat <- data.frame(
  value = c(placebo, cafe),
  group = rep(c("placebo","cafe"), each = 9)
)

boot_fun <- function(data, index) {
  d <- data[index, ]
  mean(d$value[d$group=="placebo"]) -
    mean(d$value[d$group=="cafe"])
}

set.seed(123)
b <- boot(dat, boot_fun, R = 10000)

boot.ci(b, type = c("perc","bca","norm","basic"))

## BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS
## Based on 10000 bootstrap replicates
## 
## CALL : 
## boot.ci(boot.out = b, type = c("perc", "bca", "norm", "basic"))
## 
## Intervals : 
## Level      Normal              Basic         
## 95%   ( 0.209, 12.396 )   (-0.138, 12.000 )  
## 
## Level     Percentile            BCa          
## 95%   ( 0.667, 12.805 )   ( 1.325, 13.783 )  
## Calculations and Intervals on Original Scale

so sánh tỷ lệ gãy xương

library(table1)

## 
## Attaching package: 'table1'

## The following object is masked from 'package:lessR':
## 
##     label

## The following objects are masked from 'package:base':
## 
##     units, units<-

table1(~as.factor(fx)|sex,data=df)

	Female (N=1317)	Male (N=845)	Overall (N=2162)
as.factor(fx)
0	916 (69.6%)	701 (83.0%)	1617 (74.8%)
1	401 (30.4%)	144 (17.0%)	545 (25.2%)

chisq.test(df$fx,df$sex)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  df$fx and df$sex
## X-squared = 48.363, df = 1, p-value = 3.542e-12

day2

tt

2026-01-07

Việc 2 so sánh MĐX giữa nam và nữ

2.1 Histogram đánh giá phân bố

2.2 TTest

so sánh tỷ lệ gãy xương