Mentioned here: Biased results, recorded variable types and linear models (the effect of a set of variables onto a response variable). This blogpost makes part of Stat Chats (Stat Chats).
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Here we chat about an anthropological study that looks at the effects of physical group activity onto social bonding. Part of the study conducted an experiment was conducted with groups of rowers (different levels of expertise), for which social bonding measurements were taken after 30 minute rowing trials in four conditions that varied intensity and synchrony of the exercise performed.
Individuals of study
A total of 68 university students of ages 18-49 volunteered for the study which as a reward offered a small amount of money, lets say 10 gold (fake unit).
The experiment
The aim of the experiment is to explore the effects of exercise intensity and synchrony on the level of group cooperation (as a way to assess social bonding). This level of group cooperation is measured through an economic game.
Participants were assigned into groups of three people and rowed for 30 minutes in parallel ergometers (commonly known as “rowing machines”). After the exercise participants played a game. Each individual was given 5 gold which they could keep to themselves or, if they wanted, they could give part, or the whole 5 gold to a group fund. This decision was confidential. The money given to the fund would then be multiplied by 1.5 and redistributed equally among all three group members regardless of how much, each gave to the group fund.
Stat chat
Now we discuss some key elements of the aforementioned study. In particular, components that need to be taken into account at the moment of setting the experiment and at the moment of the analysis of the measurements taken in the economic game.
A fairly common query relates to possible bias linked to the experimental setup, e.g. consider the following:
What is the criterium by which people are assigned to groups?
What happens if the groups are conformed by males or females only?
How well did the participants know one another?
A simple way to deal with possible bias is to randomise individuals into groups and gather additional information, such as measures of how well individuals within groups knew each other.
What type of working variables are at hand?
Regarding the main objective of the study, the effect of physical group activity on social bonding, is measured by the amount of money each individual gives from the 5 gold to the group fund (called variable X). Other variables linked to the study, among some others, are the treatments: intensity and synchrony of the exercise. Here we focus on X.
So, what type of variable is X? Is it continuous, or, could it be discrete?
Theoretically the amount of money a person could give is would lead to a continuous variable, however, in reality and for this kind of experiment, people won’t give 
In such cases, the variable at hand (here X), should perhaps be considered as a discrete variable, and possibly one with a finite number of possible outcomes. (People could give exactly zero and 5 gold more easily, leading to large frequencies of such values).
What type of analysis can be performed? and, how can confounding variables be taken into account in the study?
Usual analyses, when interested in the effect of some covariables on a response variable (amount of money given), are linear models or generalised linear models, as they directly model the effect of each covariable on the response variable. In addition, these models allow easy incorporation of the confounding variables (simply added as additional covariables).
Selection of a generalised linear model is usually given by the distribution of the response variable. In this study an ordinal model was used, as the response variable X was categorised into different levels in order to obtain a clearer wide overview of the subject of interest (social bonding). An example of such categorisation is, people giving [0,2] gold, (2,3.5] gold, (3.5,5) gold and 5 gold.
Curiosity
Why would 5 be a category on its own? Could have zero been a category on its own as well?
Project details
Permission for the discussion of this project was given by Arran Davis. For more details about this project contact arran.davis@anthro.ox.ac.uk .
(Webpage currently out of date) - Luis Ospina-Forero 