% Rapport package team % t-test Template % 2011-04-26 20:25 CET ## Description A t-test report with table of descriptives, diagnostic tests and t-test specific statistics. ### Introduction In a nutshell, _t-test_ is a statistical test that assesses hypothesis of equality of two means. But in theory, any hypothesis test that yields statistic which follows [_t-distribution_](https://en.wikipedia.org/wiki/Student%27s_t-distribution) can be considered a _t-test_. The most common usage of _t-test_ is to: - compare the mean of a variable with given test mean value - **one-sample _t-test_** - compare means of two variables from independent samples - **independent samples _t-test_** - compare means of two variables from dependent samples - **paired-samples _t-test_** ### Overview Independent samples _t-test_ is carried out with _Internet usage in leisure time (hours per day)_ as dependent variable, and _Gender_ as independent variable. Confidence interval is set to 95%. Equality of variances wasn't assumed. ### Descriptives In order to get more insight on the underlying data, a table of basic descriptive statistics is displayed below. ------------------------------------------------------ Gender min max mean sd var median IQR -------- ----- ----- ------ ----- ----- -------- ----- male 0 12 3.27 1.953 3.816 3 3 female 0 12 3.064 2.355 5.544 2 3 ------------------------------------------------------ Table: Table continues below --------------------- skewness kurtosis ---------- ---------- 0.9443 0.9858 1.398 1.87 --------------------- ### Diagnostics Since _t-test_ is a parametric technique, it sets some basic assumptions on distribution shape: it has to be _normal_ (or approximately normal). A few normality test are to be applied, in order to screen possible departures from normality. #### Normality Tests We will use _Shapiro-Wilk_, _Lilliefors_ and _Anderson-Darling_ tests to screen departures from normality in the response variable (_Internet usage in leisure time (hours per day)_). -------------------------------------------- N p --------------------------- ------ --------- Shapiro-Wilk normality test 0.9001 1.618e-20 Lilliefors 0.168 3e-52 (Kolmogorov-Smirnov) normality test Anderson-Darling normality 18.75 7.261e-44 test -------------------------------------------- As you can see, applied tests yield different results on hypotheses of normality, so you may want to stick with one you find most appropriate or you trust the most.. ### Results Welch Two Sample t-test was applied, and significant differences were found. --------------------------------------------------------   statistic df p CI(lower) CI(upper) ------- ----------- ----- ------ ----------- ----------- **t** 1.148 457.9 0.2514 -0.1463 0.5576 -------------------------------------------------------- ## Description A t-test report with table of descriptives, diagnostic tests and t-test specific statistics. ### Introduction In a nutshell, _t-test_ is a statistical test that assesses hypothesis of equality of two means. But in theory, any hypothesis test that yields statistic which follows [_t-distribution_](https://en.wikipedia.org/wiki/Student%27s_t-distribution) can be considered a _t-test_. The most common usage of _t-test_ is to: - compare the mean of a variable with given test mean value - **one-sample _t-test_** - compare means of two variables from independent samples - **independent samples _t-test_** - compare means of two variables from dependent samples - **paired-samples _t-test_** ### Overview One-sample _t-test_ is carried out with _Internet usage in leisure time (hours per day)_ as dependent variable. Confidence interval is set to 95%. Equality of variances wasn't assumed. ### Descriptives In order to get more insight on the underlying data, a table of basic descriptive statistics is displayed below. ------------------------------------------------------------- Variable min max mean sd var ------------------------------ ----- ----- ------ ----- ----- Internet usage in leisure time 0 12 3.199 2.144 4.595 (hours per day) ------------------------------------------------------------- Table: Table continues below ------------------------------------ median IQR skewness kurtosis -------- ----- ---------- ---------- 3 2 1.185 1.533 ------------------------------------ ### Diagnostics Since _t-test_ is a parametric technique, it sets some basic assumptions on distribution shape: it has to be _normal_ (or approximately normal). A few normality test are to be applied, in order to screen possible departures from normality. #### Normality Tests We will use _Shapiro-Wilk_, _Lilliefors_ and _Anderson-Darling_ tests to screen departures from normality in the response variable (_Internet usage in leisure time (hours per day)_). -------------------------------------------- N p --------------------------- ------ --------- Shapiro-Wilk normality test 0.9001 1.618e-20 Lilliefors 0.168 3e-52 (Kolmogorov-Smirnov) normality test Anderson-Darling normality 18.75 7.261e-44 test -------------------------------------------- As you can see, applied tests yield different results on hypotheses of normality, so you may want to stick with one you find most appropriate or you trust the most.. ### Results One Sample t-test was applied, and significant differences were found. -------------------------------------------------------   statistic df p CI(lower) CI(upper) ------- ----------- ---- ------ ----------- ----------- **t** -0.007198 671 0.9943 3.037 3.362 ------------------------------------------------------- ------- This report was generated with [R](http://www.r-project.org/) (3.0.1) and [rapport](https://rapporter.github.io/rapport/) (0.51) in _0.88_ sec on x86_64-unknown-linux-gnu platform. ![](images/logo.png)