Let's start with data from a hypothetical study (i.e., these are not real data)*. *The investigator wished to know the typical growth rate for seedlings of a species of maple, *Acer palmatum*. She planted several hundred seeds in a plot area large enough so that individual plants did not complete for light, space, or nutrients.

Despite all efforts to use seeds of equal quality and to maintain the same conditions for all plants, individual seedlings varied in height at any given time. We refer to this kind of variation as *random error. *Most experimental studies are subject to random error, due to factors that cannot be controlled by the investigator. To measure growth, the investigator determined the height of 12 maple seedlings on the same day every other week starting one week after germination. Each *sample* of 12 measurements then provided an estimate of the *central tendency* of plant height at the time the measurements were taken. A central tendency is a measurement of the middle, or center, of a distribution.

Below is the complete set of data as it would appear in a Microsoft Excel spreadsheet. The week of the first measurement was arbitrarily assigned the value "week zero," and height was recorded in inches.

week | 0 | 2 | 4 | 6 | 8 | 10 | 12 |

measured | 1.2 | 1.4 | 1.4 | 1.9 | 5.8 | 5.7 | 5.3 |

heights | 0.3 | 0.5 | 2.0 | 3.0 | 2.9 | 4.8 | 5.1 |

in inches | 1.1 | 1.0 | 2.3 | 3.8 | 4.9 | 4.8 | 8.5 |

1.1 | 1.7 | 2.2 | 2.6 | 3.7 | 8.2 | 8.2 | |

1.0 | 1.8 | 2.4 | 3.5 | 5.6 | 6.1 | 7.0 | |

1.5 | 2.2 | 2.0 | 2.3 | 4.8 | 4.8 | 5.5 | |

1.3 | 1.5 | 2.0 | 3.1 | 1.1 | 8.3 | 5.6 | |

0.8 | 1.5 | 2.1 | 3.1 | 4.6 | 6.1 | 2.2 | |

1.7 | 1.7 | 2.5 | 4.3 | 4.2 | 7.4 | 4.8 | |

1.5 | 1.6 | 1.6 | 5.0 | 5.1 | 3.7 | 8.4 | |

1.6 | 1.2 | 2.7 | 1.8 | 3.8 | 4.3 | 4.3 | |

1.1 | 1.2 | 1.5 | 2.8 | 7.4 | 4.3 | 5.9 |

In addition to plant height the investigator needed to measure root mass and length, and dry weight of the seedlings, therefore she had to uproot and destroy each plant that was sampled. Because she measured 12 different seedlings each time instead of following the growth patterns of the same plants, each set of data is considered to be an *independent sample**.* This is important to know if a statistical analysis is to be applied to the data.

In a different context, we use the terms *dependent* and *independent* to describe types of variables. When an investigator determines the values, such as time intervals for sampling, you have an independent variable. Data that we observe and record constitute one or more dependent variables. The value of each independent variable determines the value of the corresponding dependent variable.

Now for the first questions. We are presently working with two variables, namely time and height.

Which is the independent variable?

Time

Height

Which is the dependent variable?

Time

Height

Select your responses and go to the next page.