Fisher invented a statistical way to compare data sets.
This sample difference between the female mean of 5.
However, the gender difference in this particular sample is not very important. What is important is whether there is a difference in the population means. In order to test whether there is a difference between population means, we are going to make three assumptions: The two populations have the same variance.
This assumption is called the assumption of homogeneity of variance. The populations are normally distributed.
Each value is sampled independently from each other value. This assumption requires that each subject provide only one value. If a subject provides two scores, then the scores are not independent. The analysis of data with two scores per subject is shown in the section on the correlated t test later in this chapter.
The consequences of violating the first two assumptions are investigated in the simulation in the next section. For now, suffice it to say that small-to-moderate violations of assumptions 1 and 2 do not make much difference. It is important not to violate assumption 3.
We saw the following general formula for significance testing in the section on testing a single mean: In this case, our statistic is the difference between sample means and our hypothesized value is 0.
The hypothesized value is the null hypothesis that the difference between population means is 0. We continue to use the data from the "Animal Research" case study and will compute a significance test on the difference between the mean score of the females and the mean score of the males.
For this calculation, we will make the three assumptions specified above. The first step is to compute the statistic, which is simply the difference between means.
The next step is to compute the estimate of the standard error of the statistic. In this case, the statistic is the difference between means, so the estimated standard error of the statistic is. Recall from the relevant section in the chapter on sampling distributions that the formula for the standard error of the difference between means is: Since we are assuming the two population variances are the same, we estimate this variance by averaging our two sample variances.
Thus, our estimate of variance is computed using the following formula:one pound, two pounds or three pounds. Students are randomly assigned to clipboards and are unaware of any difference in the clipboards. After the data are collected, guesses are entered into a computer program and grouped according to the weights of the clipboards.
The mean guess for each group is computed and the output is shown in Table Statistical methods for comparing multiple groups Continuous data: comparing multiple means Analysis of variance To compare the means in 2 groups, just use the methods we learned to conduct a hypothesis test for the equality of two population means (called a t-test).
With studies involving group differences, effect size is the difference of the two means divided by the standard deviation of the control group (or the average standard deviation of both groups if you do not have a control group).
Reading Assignment An Introduction to Statistical Methods and Data Analysis, (see Course Schedule).. Inferences About the Difference Between Two . You then collect data from the two groups about how well they liked the song on a scale of For your analysis, you compute the mean of each group and find that the experimental group's mean is , while the control group's mean is Use the two-sample t-test to determine whether the difference between means found in the sample is significantly different from the hypothesized difference between means.
Analyze Sample Data Using sample data, find the standard error, degrees of freedom, test statistic, and the P-value associated with the test statistic.