Chapter 6: Analysing the Data |

## Independent Samples t-TestIn this section, I illustrate how to test hypotheses involving the mean difference between two independent groups. We'll be working with an example from a reward and learning study wherein two groups of children have been scored on a Learning variable.. The data are replicated below in Figure 6.10, in a format that would be used to enter the data into SPSS. The condition to which a child was randomly assigned is coded in this table as the "Group" variable, with either a value of 1 or 2. If Group = 1, the child was assigned to the no-reward group. If Group = 2, the child was assigned to the reward group. The values under "Learning" are the number of letters the child correctly pronounced during the testing phase. The research hypothesis would be along the lines, that "Children who receive nonverbal reinforcement improve in their learning of the alphabet".
Figure 6.10 data for the independent groups t-test. The five steps of hypothesis testing as they apply to the independent samples t-test are as follows. ## Step 1: Stating the hypotheses
Again we have a two-tailed test and an alpha level of .05. Notice the research hypothesis is framed in the direction that you should expect, an improvement in learning. Nevertheless we will assess the hypothesis using a two-tailed test (!!) See your texts and earlier for the confusing rationale here. ## Step 2: Checking the assumptions
See Howell, p. 302-303 and 197-202. Note Howell does not specify Assumption 2. However, this is a necessary part of parametric analysis. The data need to be measured along some metric. If the data represent counts or ranks then nonparametric analyses must be performed. The first two assumptions are dealt with by design considerations (i.e., before the data are collected). To ensure that the observations are independent, the researcher needs to make sure that each participant contributes his or her own data uncontaminated by other people's scores, or views, or mere presence. The second two assumptions can only be dealt with once the data are in. Note the assumptions are worded in terms of ## Step 3: Calculate the test statisticSee Output 6.6 for the results of this analysis and the SPSS Screens and Output booklet for instructions. ## Output 6.6 Compare means -> Independent samples t-test## T-Test
The Confidence Interval information is also given. Notice the null hypothesis value (i.e., zero) does not fall within this interval. ## Step 4: Evaluate the resultThe output indicates that the observed difference in the means is significant t(18) = -2.247, p = .037. We reject H ## Step 5: Interpret the resultA significant increase in letters recalled occurred in the nonverbal learning group compared to the control group (t(18) = -2.247, p = .037, The broader view might be to consider what is the active ingredient in the new learning method. What is it about the nonverbal reinforcement that appears to have worked? Perhaps the new learning method can be applied to learning arithmetic tables? We are not given a lot of information about the study to comment much further on the broader implications. |

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