# A Primer For Statistical Tests

# Theory

These are the solutions to the exercises contained within the handout to A Primer For Statistical Tests which walks you through the basics of variables, their scales and distributions. Keep in mind that there is probably a myriad of other ways to reach the same conclusions as presented in these solutions.

I have prepared some Lecture Slides for this session.

# Data

Find the data for this exercise here.

# Loading the `R`

Environment Object

`load("Data/Primer.RData") # load data file from Data folder`

# Variables

## Finding Variables

`ls() # list all elements in working environment`

```
## [1] "Colour" "Depth" "IndividualsPassingBy"
## [4] "Length" "Reproducing" "Sex"
## [7] "Size" "Temperature"
```

`Colour`

`class(Colour) # mode`

`## [1] "character"`

`barplot(table(Colour)) # fitting?`

Question | Answer |
---|---|

Mode? | character |

Which scale? | Nominal |

What’s implied? | Categorical data that can’t be ordered |

Does data fit scale? | Yes |

`Depth`

`class(Depth) # mode`

`## [1] "numeric"`

`barplot(Depth) # fitting?`

Question | Answer |
---|---|

Mode? | numeric |

Which scale? | Interval/Discrete |

What’s implied? | Continuous data with a non-absence point of origin |

Does data fit scale? | Debatable (is 0 depth absence of depth?) |

`IndividualsPassingBy`

`class(IndividualsPassingBy) # mode`

`## [1] "integer"`

`barplot(IndividualsPassingBy) # fitting?`

Question | Answer |
---|---|

Mode? | integer |

Which scale? | Integer |

What’s implied? | Only integer numbers with an absence point of origin |

Does data fit scale? | Yes |

`Length`

`class(Length) # mode`

`## [1] "numeric"`

`barplot(Length) # fitting?`

Question | Answer |
---|---|

Mode? | numeric |

Which scale? | Relation/Ratio |

What’s implied? | Continuous data with an absence point of origin |

Does data fit scale? | Yes |

`Reproducing`

`class(Reproducing) # mode`

`## [1] "integer"`

`barplot(Reproducing) # fitting?`

Question | Answer |
---|---|

Mode? | integer |

Which scale? | Integer |

What’s implied? | Only integer numbers with an absence point of origin |

Does data fit scale? | Yes |

`Sex`

`class(Sex) # mode`

`## [1] "factor"`

`barplot(table(Sex)) # fitting?`

Question | Answer |
---|---|

Mode? | factor |

Which scale? | Binary |

What’s implied? | Only two possible outcomes |

Does data fit scale? | Yes |

`Size`

`class(Size) # mode`

`## [1] "character"`

`barplot(table(Size)) # fitting?`

Question | Answer |
---|---|

Mode? | character |

Which scale? | Ordinal |

What’s implied? | Categorical data that can be ordered |

Does data fit scale? | Yes |

`Temperature`

`class(Temperature) # mode`

`## [1] "numeric"`

`barplot(Temperature) # fitting?`

Question | Answer |
---|---|

Mode? | numeric |

Which scale? | Interval/Discrete |

What’s implied? | Continuous data with a non-absence point of origin |

Does data fit scale? | Yes (the data is clearly recorded in degree Celsius) |

# Distributions

`Length`

`plot(density(Length)) # distribution plot`

`shapiro.test(Length) # normality check`

```
##
## Shapiro-Wilk normality test
##
## data: Length
## W = 0.99496, p-value = 0.4331
```

The data is **normal distributed**.

`Reproducing`

`plot(density(Reproducing)) # distribution`

`shapiro.test(Reproducing) # normality check`

```
##
## Shapiro-Wilk normality test
##
## data: Reproducing
## W = 0.98444, p-value = 0.2889
```

The data is **binomial distributed** (i.e. “How many individuals manage to reproduce”) but looks **normal distributed**. The normal distribution doesn’t make sense here because it implies continuity whilst the data only comes in integers.

`IndividualsPassingBy`

`plot(density(IndividualsPassingBy)) # distribution`

`shapiro.test(IndividualsPassingBy) # normality check`

```
##
## Shapiro-Wilk normality test
##
## data: IndividualsPassingBy
## W = 0.96905, p-value = 0.0187
```

The data is **poisson distributed** (i.e. “How many individuals pass by an observer in a given time frame?”).

`Depth`

`plot(density(Depth)) # distribution`

The data is **uniform distributed**. You don’t know this distribution class from the lectures and I only wanted to confuse you with this to show you that there’s much more out there than I can show in our lectures.