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Paired t test

Source: R/ifr-ts-paired-ttest.R
ifr_ts_paired_ttest.Rd

ifr_ts_paired_ttest tests that two samples have the same mean, assuming paired data.

Usage

ifr_ts_paired_ttest(
  data,
  x,
  y,
  confint = 0.95,
  alternative = c("both", "less", "greater", "all")
)

Arguments

data

a data.frame or tibble

x

numeric; column in data

y

numeric; column in data

confint

confidence level

alternative

a character string specifying the alternative hypothesis, must be one of "both" (default), "greater", "less" or "all". You can specify just the initial letter.

Value

ifr_ts_paired_ttest returns an object of class "ifr_ts_paired_ttest". An object of class "ifr_ts_paired_ttest" is a list containing the following components:

Obs

number of observations

b

mean, standard deviation and standard error of x, y and their difference

tstat

t statistic

p_lower

lower one-sided p-value

p_upper

upper one-sided p-value

p_two_tail

two sided p-value

corr

Correlation of x and y

corsig

p-value of correlation test

conf_int1

confidence interval for mean of x

conf_int2

confidence interval for mean of y

conf_int_diff

confidence interval for mean of difference of x and y

df

degrees of freedom

confint

confidence level

alternative

alternative hypothesis

var_names

names of x and y

xy

string used in printing results of the test

Deprecated Function

infer_ts_paired_ttest() has been deprecated. Instead use ifr_ts_paired_ttest().

References

Sheskin, D. J. 2007. Handbook of Parametric and Nonparametric Statistical Procedures, 4th edition. : Chapman & Hall/CRC.

See also

t.test

Examples

# lower tail
ifr_ts_paired_ttest(hsb, read, write, alternative = 'less')
#>                          Paired Samples Statistics                           
#> ----------------------------------------------------------------------------
#> Variables    Obs     Mean     Std. Err.    Std. Dev.    [95% Conf. Interval] 
#> ----------------------------------------------------------------------------
#>    read       200    52.23     0.7249921    10.25294        50.8      53.66   
#>    write      200    52.775    0.6702372    9.478586       51.45       54.1    
#> ----------------------------------------------------------------------------
#>    diff       200    -0.545    0.6283822    8.886666       -1.78       0.69    
#> ----------------------------------------------------------------------------
#> 
#>          Paired Samples Correlations         
#> -------------------------------------------
#>   Variables      Obs    Correlation    Sig.
#>  read & write    200       0.60        0 
#> -------------------------------------------
#> 
#>           Paired Samples Test            
#>           -------------------            
#>        Ho: mean(read - write) = 0        
#>        Ha: mean(read - write) < 0        
#> 
#> ----------------------------------------
#>   Variables         t       df     Sig.  
#> ----------------------------------------
#>  read - write    -0.8673    199    0.193 
#> ----------------------------------------

# upper tail
ifr_ts_paired_ttest(hsb, read, write, alternative = 'greater')
#>                          Paired Samples Statistics                           
#> ----------------------------------------------------------------------------
#> Variables    Obs     Mean     Std. Err.    Std. Dev.    [95% Conf. Interval] 
#> ----------------------------------------------------------------------------
#>    read       200    52.23     0.7249921    10.25294        50.8      53.66   
#>    write      200    52.775    0.6702372    9.478586       51.45       54.1    
#> ----------------------------------------------------------------------------
#>    diff       200    -0.545    0.6283822    8.886666       -1.78       0.69    
#> ----------------------------------------------------------------------------
#> 
#>          Paired Samples Correlations         
#> -------------------------------------------
#>   Variables      Obs    Correlation    Sig.
#>  read & write    200       0.60        0 
#> -------------------------------------------
#> 
#>           Paired Samples Test            
#>           -------------------            
#>        Ho: mean(read - write) = 0        
#>        Ha: mean(read - write) > 0        
#> 
#> ----------------------------------------
#>   Variables         t       df     Sig.  
#> ----------------------------------------
#>  read - write    -0.8673    199    0.807 
#> ----------------------------------------

# both tails
ifr_ts_paired_ttest(hsb, read, write, alternative = 'both')
#>                          Paired Samples Statistics                           
#> ----------------------------------------------------------------------------
#> Variables    Obs     Mean     Std. Err.    Std. Dev.    [95% Conf. Interval] 
#> ----------------------------------------------------------------------------
#>    read       200    52.23     0.7249921    10.25294        50.8      53.66   
#>    write      200    52.775    0.6702372    9.478586       51.45       54.1    
#> ----------------------------------------------------------------------------
#>    diff       200    -0.545    0.6283822    8.886666       -1.78       0.69    
#> ----------------------------------------------------------------------------
#> 
#>          Paired Samples Correlations         
#> -------------------------------------------
#>   Variables      Obs    Correlation    Sig.
#>  read & write    200       0.60        0 
#> -------------------------------------------
#> 
#>           Paired Samples Test            
#>           -------------------            
#>        Ho: mean(read - write) = 0        
#>       Ha: mean(read - write) ~= 0        
#> 
#> ----------------------------------------
#>   Variables         t       df     Sig.  
#> ----------------------------------------
#>  read - write    -0.8673    199    0.387 
#> ----------------------------------------

# all tails
ifr_ts_paired_ttest(hsb, read, write, alternative = 'all')
#>                          Paired Samples Statistics                           
#> ----------------------------------------------------------------------------
#> Variables    Obs     Mean     Std. Err.    Std. Dev.    [95% Conf. Interval] 
#> ----------------------------------------------------------------------------
#>    read       200    52.23     0.7249921    10.25294        50.8      53.66   
#>    write      200    52.775    0.6702372    9.478586       51.45       54.1    
#> ----------------------------------------------------------------------------
#>    diff       200    -0.545    0.6283822    8.886666       -1.78       0.69    
#> ----------------------------------------------------------------------------
#> 
#>          Paired Samples Correlations         
#> -------------------------------------------
#>   Variables      Obs    Correlation    Sig.
#>  read & write    200       0.60        0 
#> -------------------------------------------
#> 
#>                 Ho: mean(read - write) = mean(diff) = 0                  
#> 
#>    Ha: mean(diff) < 0      Ha: mean(diff) ~= 0       Ha: mean(diff) > 0    
#>        t = -0.8673              t = -0.8673              t = -0.8673       
#>      P < t = 0.193           P > |t| = 0.387           P > t = 0.807