Introduction to Experimental Design

A hypothesis must be something that can be tested.
It should be conceptually possible and capable of being performed in real-life conditions.

The independent variable is the factor being changed or manipulated by the scientist.
The scientist purposefully alters this variable to determine if the change produces a different result.
It is called "independent" because its setup does not depend on another change within the experiment; rather, other results depend on it.
In a bean growth experiment, the independent variables are the different solutions chosen to replace standard water. These include:
- Salt solution
- Acidic solution (e.g., vinegar)
- Basic solution (e.g., ammonia)
- Fertilizer/Nitrogen solution
In some cases, an independent variable may not cause a change in the results. For example, if the only change made was the color of the water (e.g., blue, red, green, or purple food coloring), it likely would not affect the outcome of the beans. This indicates that the specific change made does not matter for the result being measured.

The dependent variable is the factor that changes as a result of the independent variable.
It is the variable that is measured during the experiment or the data that is collected.
Any information or data gathered is essentially a measurement of the dependent variable.
There is an expected relationship between the two: a change in the dependent variable is expected based on the specific changes made to the independent variable. If the independent variable is not changed (e.g., using plain water for all groups), no change is expected in the dependent variable.

A control variable, also known as a constant in mathematics, is a factor that stays exactly the same throughout the entire experiment.
Maintaining constants is crucial for isolating causality. This allows a scientist to pinpoint and state that only one specific change is responsible for the overall end result.
The experimental design is only valid if only one thing is changed at a time. Changing multiple factors at once makes it impossible to know which factor had the biggest impact.
The Basketball Analogy for Constants:
- Consider a basketball game where Team A is leading Team B by $20$ points. There are five players on the floor for each team.
- In the first scenario, Team B subs in their best player. Over the next $10$ minutes, the team ties the game. Because only one player was changed, that specific player can be credited with the outcome.
- In the second scenario, the coach subs out all five players at once. If the team ties the game, it is impossible to know which of the five players was responsible for the comeback. The credit cannot be singled out.
Applying this to the bean experiment, constants include:
- The state of the liquid (all are liquids).
- The size of the bags used.
- The use of paper towels to wrap the beans.
- The quantity of beans (exactly $5$ per bag).
- The volume of liquid (all bags receive approximately the same amount).
- The temperature of the environment (all bags are kept in an incubator at approximately $77\,^{\circ}F$ ).

While the terms sound similar, control variables and control groups are distinct concepts.
Control Group: This is the baseline group that does not receive the special treatment or the "special liquid." It represents the standard, normal condition.
- In the bean experiment, the group receiving water is the control group because water is what plants normally receive to grow. Using vinegar or fertilizer as a control would be illogical because they are not the basic standard for plant growth.
Experimental Group: These are the groups that receive the treatment or the manipulated independent variables (e.g., the salt, vinegar, ammonia, or nitrogen groups).
Importance of a Control Group: It provides a basis for comparison. Without a standard to compare results against, the data collected from the experimental groups would be pointless and impossible to interpret properly.