A 0.3-m3 rigid tank initially contains refrigerant- 134a at 14°C. At this state, 55 percent of the mass is in the vapor phase, and the rest is in the liquid phase. The tank is connected by a valve to a supply line where refrigerant at 1.4 MPa and 100°C flows steadily. Now the valve is opened slightly, and the refrigerant is allowed to enter the tank. When the pressure in the tank reaches 1 MPa, the entire refrigerant in the tank exists in the vapor phase only. At this point the valve is closed. Determine (a) the final temperature in the tank, (b) the mass of refrigerant that has entered the tank, and (c) the heat transfer between the system and the surroundings.
COMPLEX DESIGNS So far, we’ve discussed studies with just one IV. But many studies have more than 1. Sometimes, this can hide important findings! Example: » Hypothesis: Caucasian faces are easier to remember than Japanese faces. » IV: Race of face (2 levels: Caucasian and Japanese) » DV: Percentage of faces remembered So let's amend that hypothesis... » Hypothesis: Caucasian participants will remember Caucasian faces better than Japanese faces, but Japanese participants will remember Japanese faces more. » IVs: 1. Race of Face (Caucasian or Japanese) 2. Race of Participant (Caucasian or Japanese) » DV: Percentage of faces remembered This is an example of an interaction between two IV’s. o The effect of one IV (race of face) is different at each level of another IV (participant race). o So if someone asks you, “Are Caucasian faces easier to remember than Japanese faces” o Your answer wouldn’t be “Yes” or “No” Interaction Complex (or “Factorial” Designs: 2 or more IVs (still just 1 DV) IVs cn be independent groups and/or repeated measures o If one of each, a “mixed design” Our previous example of face memory was a mixed design Three Possible Effects in a Complex Design Main Effect o The effect of an individual IV alone In our example, there was possibility of 2 main effects. 1. Participant race and 2. Type of face Interaction o The effect of an IV differs at different levels of another IV In our example, there was an interaction: the effect of race of the face differed depending on the participant’s race o The main advantage of complex designs o Interactions (also called Moderation) Are certain effects true in some cases but not in others Is the effect between an IV and a DV the same for all groups o Another way to think about interactions: “Did the IV have an effect” “Well, it depends…” “If it depends” = an interaction Yes/No = effect Trick to figure out Effect/Interaction: High Anxiety Low Anxiety 200 Caffeine 50 100 150 No Caffeine 100 50 150 150 150 100 **NO Main Effect on any independent variable, but IS an interaction between caffeine consumption and anxiety level (200 > 100) Find interaction(s) by adding across diagonals Example: » Hypothesis: Individuals will receive little sympathy if they are remorseless for a bad act, regardless of whether or not it was intentional. However, if they express remorse, they will receive more sympathy for an unintentional than an intentional bad act. » IV1: Remorse (Low vs. High) » IV2: Intentionality (Intentionality vs. Unintentional) Identifying Main Effects Main Effects o Same as in a simple design – do values on the DV differ between levels of a single IV Confirm with statistics Identify Interactions Interaction: the effect of an IV is different at different levels of another IV No interaction: the effect of an IV is the same at different levels of another IV Confirm with statistics Why should we care about interactions - They provide a much more nuanced understanding of effects! When present, they tell us the limits, or under what conditions, an IV has an effect - Interactions with natural group IVs (e.g., gene, age, psychopathology) are very informative: o No interaction – results may be generalizable to all o Interaction – results are limited to a specific group and main effects are less meaningful (subsumes the main effect; more important than the main effect tells us more) - Interactions can also reveal a “hidden” effect Types of Complex Designs: » Described by the number of IVs and the number of levels in each IV » Simplest: 2 IVs with 2 levels each o 2 x 2 » More complex… o 2 x 2 x 2 o 3 x 3 o 3 x 4 x 2 Rule of thumb: keep it as simple a complex design as you can Conditions (i.e., data points) o Number of conditions = Product of the number of levels in each IV o 2 x 2 = 4 o 3 x 3 = 9 o 3 x 4 x 2 = 24 Example: 2 x 2: Study of mood and memory. Participants are randomly assigned to a positive or a negative mood induction and to read and recall a list of positive or negative words - IV1: Mood induction (positive or negative) - IV2: Valence of words (positive or negative) Positive Mood Negative Mood Positive Word List Condition 1 Condition 2 Negative Word List Condition 3 Condition 4 Interactions: - 2 x 2 design = 1 interaction o Mood induction by Valence of words - 2 x 2 x 2 design = 4 interactions o Mood induction by Valence of words o Mood induction by Depression level of participant o Valence of words by Depression level of participant o Mood induction by Valence of words by Depression level of participation Sample size: - More levels/more IVs means more complexity…but results in smaller cell sizes and reduced power o Less of a problem in repeated measures designs - Example: Mood and recall, n=108 o 2 x 2 o 3 x 3 (harder to find statistical significant effect…) o 3 x 3 x 2 (even harder/smaller sample) Illustrating Main and Interaction Effects Tables o Useful for exact numbers o Harder to interpret Figures o Bar o Line Best to demonstrate interactions In general, the less parallel the lines are, the greater the likelihood of a meaningful interaction If they do cross, that’s likely an interaction Why interactions can’t be interpreted: Ceiling Effect: Performance on the DV reaches a maximum Floor Effect: Performance on the DV reaches a minimum **In either case, can’t interpret interaction(s).