Two-Sample Between-Subjects Experiments and Independent-Samples t-Tests So far, we’ve talked about experiments in which we needed to take only one sample.

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Two-Sample Between-Subjects Experiments and Independent-Samples t-Tests So far, we’ve talked about experiments in which we needed to take only one sample of subjects. In these experiments, we only had one sample, and we compared the results obtained from that one sample against the data already known about a population of subjects. There are two key things about this population of subjects that we used as our comparison group (we sometimes referred to it as the null population): 1. The subjects in the null population had experienced a different level of the IV from that experienced by the experimental group; generally the level the population had experienced is the absence of a treatment For example, the null population had never taken an IQ pill 2. We had some information about how subjects in the null population performed at that different level of the IV (e.g., in the absence of a treatment). For example, we knew the μ and the σ, or we at least knew the μ, and could estimate the SD, of the population who had never taken an IQ pill. As I mentioned previously, it is only on rare occasions in psychology experiments that we will have the necessary info about a given population, so we will usually be comparing (at least) two groups to each other rather than comparing one group to a population. A comparison requires two things to work. If we don’t know anything about the outcomes (scores on the DV) in a population that has been measured under some level of the IV different from the level we plan to subject our experimental group to, then we have to take a second sample and measure the level of the outcomes in that sample under a different level of the IV from the one our first sample is going to be subjected to. So that’s what we’re going to talk about now: Two-sample experiments and the stats that we use to analyze findings from them

An Experiment Click here to try out the digit span test Randomly assign participants to one of two groups. In order to accomplish random assignment, I will count the total number of students, then I will measure out half that number of red chips and half that number of blue chips. All of the poker chips will be put into a box, from which each student will draw one chip without looking. Those who chose a blue poker chip would each get a peppermint, which they would be asked to consume immediately. Those who drew a red chip would be in the control group, which would not receive a peppermint. Once everyone had spent a few minutes consuming, or not consuming, a peppermint candy, I would administer the digit span test. The instructions for this test are as follows: “I am going to read a list of numbers and after I finish, you need to write them down in the order I said them. For example, if I say 5-3, you are going to write 5-3 in the same order. Do you have any questions? Please wait until I finish reading a set of numbers before you start writing them down.” I will read the numbers in the audio recording so that you can take the digit span test yourself. Click on the audio recording icon on the slide to listen. 3: 926 4: 2952 5: 48704 6: 185934 7: 9682473 8: 53294508 9: 953782064 10: 8592764032 11: 30586249481 12: 624067189530 After everyone in the room has given up (because no one can recall all the digits in the most recent number read), read the numbers back to the group to permit self-scoring. Your score is the highest number of digits you could recall perfectly, but you must have been able to complete all previous numbers of digits up to that point. In other words, if you could not recall the 8-digit number perfectly, your score is 7, even if you did recall 9 digits perfectly. In SPSS, we record the number of digits recalled by each person in the peppermint group and by each person in the no peppermint group. Using a two independent-samples t test, we determine whether there is a difference between the mean of each of the two groups. If there were a difference between the two groups, what are the two possible reasons for there being a difference between the two groups? This could happen because the peppermint affected the memory of the participants in the peppermint group. This could happen because sampling error led to a difference between the two groups before anyone ate the peppermints. What could account for the difference among participants within each group (e.g., different scores among those in the peppermint group)? The variability in scores among the members of a single group, all of whom experienced the same experimental condition, must be due to extraneous variables (any variable other than the variable being manipulated). These extraneous variables include all the characteristics of the participants (which are also known as individual differences) as well as any circumstances that are not identical among the participants in that group (e.g., being farther away from the researcher and therefore finding it harder to hear the numbers clearly). Click here to try out the digit span test

An Experiment IV ? Peppermint Levels of IV? 1 mint 0 mints DV? # of digits recalled (working memory capacity)

The Logic of Experimentation How was this study designed? Created two equivalent groups Treated them exactly the same, except for the IV Measured both groups on an outcome (DV) Any significant differences between the groups must be due to the difference in the treatment To conduct an experiment with one sample, we needed to know at least the mean of the population under a condition different from the one in the sample. Now we’re talking about experiments that use 2 samples because we don’t know the mean of the population. If we don’t know any population parameters to which we can compare a single sample, we need to take another sample so we have something to compare the first sample to. That was the first order of business in the experiment we just performed. Then we manipulated the IV, measured the DV, and inferred that the manipulation was responsible for any significant differences between the two groups.

The Logic of Experimentation How was this study designed? 1 - Created two equivalent groups How?

Random Assignment Random Assignment: A method of assigning research participants to groups so that each participant has an equal chance of being in any group. Random Assignment used to form comparable groups From a group of potential participants, you randomly assign individuals to either the experimental group or the control group. How? Pick red or blue chips from a box (as we did in our example) Flip a coin Use a random numbers chart

Random Assignment The Logic of Random Assignment: Individual differences (or differences in participant characteristics) should theoretically be equally distributed between groups The logic of random assignment is that individual differences (i.e., differences in subject characteristics) should, theoretically, be equally distributed between groups. So we say that subject characteristics that may potentially affect the outcome measure are balanced across conditions of the IV. This is good, because sometimes we don’t know what variables may potentially affect the outcome measure. If a variable had the potential to affect the outcome measure systematically, it would create a confound unless we balanced that variable across conditions. Think about our peppermint experiment: What variables might influence someone’s performance on the digit span test? IQ level Working memory ability There may be others that will also affect the outcome, that we might not predict For example, creativity level or bilingualism Imagine that we didn’t use random assignment. Imagine that the smartest people in the class tended to sit together, so they were concentrated on, let’s say, the left side of the room, and we split our groups into left and right halves of the room, giving peppermint to those on the left side. When our results showed significantly higher digit span scores on the left side of the room, could we confidently assert that peppermint was the cause? NO. Why not? Because it could just as likely be the difference in intelligence that was responsible. By using random assignment, we hope to balance extraneous variables across the groups in our experiment. At least in theory, random assignment would have resulted in equally smart participants in the peppermint group and the control group. The reality is that by chance, we may not actually end up with balanced characteristics.

Random Assignment Potential Problems with Random Assignment: May not actually balance participants’ characteristics/individual differences across groups Small sample size decreases likelihood of balancing participants’ characteristics across conditions There are potential problems that might arise when using random assignment: Random assignment may not actually balance subject characteristics/individual differences across groups. For example, just by chance, you could still end up with all or most of the high IQ folks in one group. Small sample size decreases the likelihood of balancing subject characteristics across conditions. Just as it’s more likely that you will toss a coin and get 5 heads out of 5 tosses than 50 out of 50, it’s more likely that you will get unbalanced characteristics if you have a small sample than if you have a large one. Fortunately, there are other ways to balance a limited number of characteristics among your groups. For example, you could match participants on IQ and randomly assign one of each matched pair to each group. However, this would be a different (dependent samples) design and it would use a different statistical test that we’ll talk about in the next unit.

The Logic of Experimentation How was this study designed? Created two equivalent groups What do we call these two groups? Back to the design of the peppermint and digit span experiment…

Two-Group Experiments Control Group: The group that does not receive any treatment or receives normal treatment. Experimental Group: The group that receives some form of treatment So you have 2 groups of subjects One that receives the treatment, and one that doesn’t What’s the name of the group that does not receive the treatment? control group  The group that does not receive any treatment or receives normal treatment In our example, this would be the group that does not receive the peppermint Sometimes, it is not possible or practical to give a zero level of the IV For example, temperature and aggression  can’t have no temperature, so use normal levels of the temperature What’s the name of the group that receives some form of treatment? experimental group  The group that receives some form of treatment In our example, this was the group that received the peppermint

Two-Group Experiments Between-Subjects Design Different groups of participants receive different levels of the IV Independent samples are used in each condition Participants are selected without regard to who is in the other condition Each participant serves in only one condition In our peppermint and digit span experiment, we used what is called a between-subjects design. You may best understand what we mean by “Participants are selected without regard to who is in the other condition,” by understanding what it means for samples to be dependent. In dependent samples, each person in the first group is matched up with someone in the second group with similar characteristics on one or more variables. Sometimes, that matching person is actually the same person participating in both the first group and in the second group at different points in time. Independent samples means that there is no matching up with some other participant, or with yourself, in the other condition. Who is in one group is completely separate from who is in the other.