# Interacting with Users with R Functions

Here’s a selection of statistical functions that come with the standard R installation. You’ll find many others in R packages. R provides the `shiny `

package and the `shinydashboard `

package for developing interactive applications. Here are selected functions from these packages:

Function |
What it Calculates |

`mean(x)` |
Mean of the numbers in vector x. |

`median(x)` |
Median of the numbers in vector x |

`var(x)` |
Estimated variance of the population from which the numbers in vector x are sampled |

`sd(x)` |
Estimated standard deviation of the population from which the numbers in vector x are sampled |

`scale(x)` |
Standard scores (z-scores) for the numbers in vector x |

**Relative Standing**

Function |
What it Calculates |

`sort(x)` |
The numbers in vector x in increasing order |

`sort(x)[n]` |
The nth smallest number in vector x |

`rank(x)` |
Ranks of the numbers (in increasing order) in vector x |

`rank(-x)` |
Ranks of the numbers (in decreasing order) in vector x |

`rank(x, ties.method= "average")` |
Ranks of the numbers (in increasing order) in vector x, with tied numbers given the average of the ranks that the ties would have attained |

`rank(x, ties.method= "min")` |
Ranks of the numbers (in increasing order) in vector x, with tied numbers given the minimum of the ranks that the ties would have attained |

`rank(x, ties.method = "max")` |
Ranks of the numbers (in increasing order) in vector x, with tied numbers given the maximum of the ranks that the ties would have attained |

`quantile(x)` |
The 0th, 25th, 50th, 75th, and 100th percentiles (i.e, the quartiles) of the numbers in vector x. (Thatâ€™s not a misprint: quantile(x) returns the quartiles of x.) |

**T-tests**

Function |
What it Calculates |

`t.test(x,mu=n, alternative = "two.sided")` |
Two-tailed t-test that the mean of the numbers in vector x is different from n. |

`t.test(x,mu=n, alternative = "greater")` |
One-tailed t-test that the mean of the numbers in vector x is greater than n. |

`t.test(x,mu=n, alternative = "less")` |
One-tailed t-test that the mean of the numbers in vector x is less than n. |

`t.test(x,y,mu=0, var.equal = TRUE, alternative = "two.sided")` |
Two-tailed t-test that the mean of the numbers in vector x is different from the mean of the numbers in vector y. The variances in the two vectors are assumed to be equal. |

`t.test(x,y,mu=0, alternative = "two.sided", paired = TRUE)` |
Two-tailed t-test that the mean of the numbers in vector x is different from the mean of the numbers in vector y. The vectors represent matched samples. |

**Analysis of Variance (ANOVA)**

Function |
What it Calculates |

`aov(y~x, data = d)` |
Single-factor ANOVA, with the numbers in vector y as the dependent variable and the elements of vector x as the levels of the independent variable. The data are in data frame d. |

`aov(y~x + Error(w/x), data = d)` |
Repeated Measures ANOVA, with the numbers in vector y as the dependent variable and the elements in vector x as the levels of an independent variable. Error(w/x) indicates that each element in vector w experiences all the levels of x (i.e., x is a repeated measure). The data are in data frame d. |

`aov(y~x*z, data = d)` |
Two-factor ANOVA, with the numbers in vector y as the dependent variable and the elements of vectors x and z as the levels of the two independent variables. The data are in data frame d. |

`aov(y~x*z + Error(w/z), data = d)` |
Mixed ANOVA, with the numbers in vector z as the dependent variable and the elements of vectors x and y as the levels of the two independent variables. Error(w/z) indicates that each element in vector w experiences all the levels of z (i.e., z is a repeated measure). The data are in data frame d. |

**Correlation and Regression**

Function |
What it Calculates |

`cor(x,y)` |
Correlation coefficient between the numbers in vector x and the numbers in vector y |

`cor.test(x,y)` |
Correlation coefficient between the numbers in vector x and the numbers in vector y, along with a t-test of the significance of the correlation coefficient. |

`lm(y~x, data = d)` |
Linear regression analysis with the numbers in vector y as the dependent variable and the numbers in vector x as the independent variable. Data are in data frame d. |

`coefficients(a)` |
Slope and intercept of linear regression model a. |

`confint(a)` |
Confidence intervals of the slope and intercept of linear regression model a |

`lm(y~x+z, data = d)` |
Multiple regression analysis with the numbers in vector y as the dependent variable and the numbers in vectors x and z as the independent variables. Data are in data frame d. |

When you carry out an ANOVA or a regression analysis, store the analysis in a list.

For example, `a <- lm(y~x, data = d)`

.

Then, to see the tabled results, use the `summary()`

function:

`summary(a)`