## 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 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.

Table continues 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
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 (Kolmogorov-Smirnov) normality test 0.168 3e-52
Anderson-Darling normality test 18.75 7.261e-44

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 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.

Table continues below
Variable min max mean sd var
Internet usage in leisure time (hours per day) 0 12 3.199 2.144 4.595
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 (Kolmogorov-Smirnov) normality test 0.168 3e-52
Anderson-Darling normality test 18.75 7.261e-44

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 (3.0.1) and rapport (0.51) in 0.88 sec on x86_64-unknown-linux-gnu platform. 