Question

(i) identify the variable(s) in the study, (ii) for each variable tell the type of variable (e.g., categorical and ordinal, discrete, etc.), (iii) identify the observational unit (the thing sampled), and (iv) determine the sample size. (a) A biologist measured the body mass \((\mathrm{g})\) and sex of each of 123 blue jays. (b) A biologist measured the lifespan (in days), the thorax length (in \(\mathrm{mm}\) ), and the percent of time spent sleeping for each of 125 fruit flies.

Short answer

For the blue jays, the variables are body mass (continuous quantitative) and sex (categorical nominal); the observational unit is each blue jay; the sample size is 123. For the fruit flies, the variables are lifespan, thorax length (both continuous quantitative), and percent of time spent sleeping (continuous quantitative); the observational unit is each fruit fly; the sample size is 125.

Step-by-step solution

Identifying the Variables for the Blue Jay Study

First, identify the variables measured in the blue jay study which are body mass and sex of blue jays.

Classifying the Variables for the Blue Jay Study

The body mass is a continuous quantitative variable because it can take on any value within a range and is measured in grams. The sex of the blue jays is a categorical and nominal variable because it divides the subjects into categories without a natural order.

Identifying the Observational Unit for the Blue Jay Study

In the blue jay study, the observational unit is each individual blue jay that was measured.

Determining the Sample Size for the Blue Jay Study

The sample size for the blue jay study is given as 123 blue jays.

Identifying the Variables for the Fruit Fly Study

For the fruit fly study, the variables are the lifespan, thorax length, and percent of time spent sleeping for each fruit fly.

Classifying the Variables for the Fruit Fly Study

The lifespan and thorax length are both continuous quantitative variables as they can take on a range of values and are measured in days and millimeters, respectively. The percent of time spent sleeping is also a continuous quantitative variable as it represents a proportion of time within a range from 0 to 100.

Identifying the Observational Unit for the Fruit Fly Study

The observational unit in the fruit fly study is each individual fruit fly that was measured.

Determining the Sample Size for the Fruit Fly Study

The sample size for the fruit fly study is given as 125 fruit flies.

Key concepts

Observational Unit

When conducting a biostatistics study, it's crucial to determine what the observational unit is, as it lays the foundation of how the data will be collected and analysed. The observational unit is essentially what or who is being studied and measured in any given experiment. In simpler terms, it's the individual unit of analysis.

For instance, in the presented blue jay study, the observational unit is each individual blue jay. Similarly, each individual fruit fly serves as the observational unit in the fruit fly study. By identifying the unit of observation, researchers ensure that the results are specific to what is being studied, which increases the accuracy of their conclusions. It's important to note that observational units can be people, animals, plants, organizations, or even geographical areas, depending on the research goal.

Types of Variables

Understanding the types of variables in any study is key to proper data analysis. Variables come in different forms and can be classified based on their attributes and the types of data they include. There are main categories such as quantitative and qualitative variables. Within these, further distinctions can be made such as continuous or discrete for quantitative variables, and nominal or ordinal for qualitative variables.

Using the exercise examples, body mass of blue jays is a continuous quantitative variable because its measurement can vary along a continuum and include any value within a range. On the other hand, the sex of the blue jays is a categorical and nominal variable because it categorizes the subjects into distinct groups - male and female - without a particular order. In the fruit fly study, lifespan, thorax length, and percent of time spent sleeping are also continuous quantitative variables. This is because they can each assume any value within a range. Lifespan and thorax length are measured using a scale (days and millimeters, respectively), whereas percent of time spent sleeping is expressed as a proportion.

Sample Size

The sample size of a study matters a great deal as it not only affects the precision of study results but also the statistical power of the analysis. The sample size refers to the number of observational units included in a study. Deciding on the appropriate sample size is complicated and should be guided by the study’s objective, the variability of data, desired precision, and available resources.

In the case of the blue jay and fruit fly studies, the sample sizes are 123 and 125, respectively. These numbers represent the total count of each species that were measured in the studies. It is critical that the sample size is determined before the data collection begins, as an inadequate size could lead to incorrect conclusions, or require additional collection efforts, impacting the overall viability of the research.