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                     T-test functions 
                
                    
T-test functions are used for statistical examination of two population means. A two-sample t-test examines whether two samples are different and is commonly used when two normal distributions have unknown variances and when an experiment uses a small sample size.
                
                In the following sections, the  t-test statistical test functions are grouped according to the sample student test that applies to each type of function. 
                
                    Use the drop-down on each function to see a brief description and the syntax of each function. Click the function name in the syntax description for further details.  
                
                Creating a typical t-test report  
                
                Two independent samples t-tests 
                The following functions apply to two independent samples student's t-tests.
                ttest_conf 
                        TTest_conf  returns the aggregated t-test confidence interval value for two independent samples. 
                        ttest_conf   ( 
 grp, value [, sig[, eq_var]]) 
                      
                ttest_df 
                        TTest_df()  returns the aggregated student's t-test value (degrees of freedom) 
 for two independent series of values.
                        ttest_df   ( grp, value [, eq_var) 
                      
                ttest_dif 
                        TTest_dif()  is a numeric function that returns the aggregated student's t-test mean difference for two independent series of values.
                        ttest_dif   ( grp, value) 
                      
                ttest_lower 
                        TTest_lower()  returns the aggregated value for the lower end of the confidence interval 
 for two independent series of values.
                        ttest_lower   ( grp, value [, sig[, eq_var]]) 
                      
                ttest_sig 
                        TTest_sig()  returns the aggregated student's t-test 2-tailed level of significance for two independent series of values.
                        ttest_sig   ( grp, value [, eq_var]) 
                      
                ttest_sterr 
                        
                            TTest_sterr()  returns the aggregated student's t-test standard error of the mean difference for two independent series of values.
                        ttest_sterr   ( grp, value [, eq_var]) 
                      
                ttest_t 
                        TTest_t()  returns the aggregated t value for two independent series of values.
                        ttest_t   ( grp, value 
[, eq_var]) 
                      
                ttest_upper 
                        
                            TTest_upper()  returns the aggregated value for the upper end of the confidence interval 
 for two independent series of values.
                        ttest_upper   ( grp, value [, sig [, eq_var]]) 
                      
                Two independent weighted samples t-tests 
                The following functions  apply to two independent samples student's t-tests where the input data series is given in weighted two-column format.
                ttestw_conf 
                        
                            TTestw_conf()  returns the aggregated t value for two independent series of values.
                        ttestw_conf   ( weight, grp, value [, sig[, eq_var]]) 
                      
                ttestw_df 
                        
                            TTestw_df()  returns the aggregated student's t-test df value (degrees of freedom) for two independent series of values.
                        ttestw_df   ( weight, grp, 
 value [, eq_var]) 
                      
                ttestw_dif 
                        
                            TTestw_dif()  returns the aggregated student's t-test mean difference for two independent 
 series of values.
                        ttestw_dif   ( 
 weight, grp, value) 
                      
                ttestw_lower 
                        
                            TTestw_lower()  returns the aggregated value for the lower end of the confidence interval for two independent series of values.
                        ttestw_lower   ( weight, grp, 
value [, sig[, eq_var]]) 
                      
                ttestw_sig 
                        
                            TTestw_sig()  returns the aggregated student's t-test 2-tailed level of significance 
 for two independent series of values.
                        ttestw_sig   ( 
 weight, grp, value [, eq_var]) 
                      
                ttestw_sterr 
                        
                            TTestw_sterr()  returns the aggregated student's t-test standard error of the mean difference 
 for two independent series of values.
                        ttestw_sterr   ( weight, grp, 
 value [, eq_var]) 
                      
                ttestw_t 
                        TTestw_t()  returns the aggregated t value for two independent series of values.
                        ttestw_t   ( weight, grp, 
value [, eq_var]) 
                      
                ttestw_upper 
                        
                            TTestw_upper()  returns the aggregated value for the upper end of the confidence interval 
 for two independent series of values.
                        ttestw_upper   ( weight, grp, 
value [, sig [, eq_var]]) 
                      
                One sample t-tests 
                The following functions apply to one-sample student's t-tests.
                ttest1_conf 
                        TTest1_conf()  returns the aggregated confidence interval value for a series of values.
                        ttest1_conf   ( value [, 
 sig]) 
                      
                ttest1_df 
                        
                            TTest1_df()  returns the aggregated student's t-test df value (degrees of freedom) 
 for a series of values.
                        ttest1_df   ( value)  
                      
                ttest1_dif 
                        
                            TTest1_dif()   returns the aggregated student's t-test mean difference for a series of values.
                        ttest1_dif   ( value)  
                      
                ttest1_lower 
                        
                            TTest1_lower()   returns the aggregated value for the lower end of the confidence interval for a series of values.
                        ttest1_lower   ( value [, 
sig]) 
                      
                ttest1_sig 
                        
                            TTest1_sig()   returns the aggregated student's t-test 2-tailed level of significance 
 for a series of values.
                        ttest1_sig   ( value)  
                      
                ttest1_sterr 
                        
                            TTest1_sterr()  returns the aggregated student's t-test standard error of the mean difference for a series of values.
                        ttest1_sterr   ( value)  
                      
                ttest1_t 
                        
                            TTest1_t()  returns the aggregated t value for a series of values.
                        ttest1_t   ( value)  
                      
                ttest1_upper 
                        
                            TTest1_upper()  returns the aggregated value for the upper end of the confidence interval for a series of values.
                        ttest1_upper   ( value [, 
sig]) 
                      
                One weighted sample t-tests 
                The following functions apply to one-sample student's t-tests where the input data series is given in weighted two-column format.
                ttest1w_conf 
                        
                            TTest1w_conf()  is a numeric  function that returns the aggregated confidence interval value for a series of values.
                        ttest1w_conf   ( weight, value [, sig]) 
                      
                ttest1w_df 
                        
                            TTest1w_df()  returns the aggregated student's t-test df value (degrees of freedom) 
 for a series of values.
                        ttest1w_df   ( weight, value)  
                      
                ttest1w_dif 
                        
                            TTest1w_dif()   returns the aggregated student's t-test mean difference for a series of values.
                        ttest1w_dif   ( weight, value)  
                      
                ttest1w_lower 
                        
                            TTest1w_lower()  returns the aggregated value for the lower end of the confidence interval for a series of values.
                        ttest1w_lower   ( weight, value [, sig]) 
                      
                ttest1w_sig 
                        
                            TTest1w_sig()   returns the aggregated student's t-test 2-tailed level of significance 
 for a series of values.
                        ttest1w_sig   ( weight, value)  
                      
                ttest1w_sterr 
                        
                            TTest1w_sterr()  returns the aggregated student's t-test standard error of the mean difference for a series of values.
                        ttest1w_sterr   ( weight, value)  
                      
                ttest1w_t 
                        
                            TTest1w_t()   returns the aggregated t value for a series of values.
                        ttest1w_t   ( 
weight, value)  
                      
                ttest1w_upper 
                        
                            TTest1w_upper()  returns the aggregated value for the upper end of the confidence interval 
 for a series of values.
                        ttest1w_upper   ( weight, value [, sig])