ED 602

Statistical Research for Behavioral Sciences

Brian G. Smith, Ph.D.

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Homework - Lesson 12

Any student may may do the assignments from any area. You may run through this work an unlimited number of times. If you make errors, you will be referred to the appropriate area of the book for re-study.

Assessment - Lesson 12

You will have two options to take the quiz. If you fail to achieve 100% on the quiz, you will not able to advance to the next lesson. After failing on the second take, please email the instructor at ed602@mnstate.edu so remedial action can be taken.

1. Ask a question that can be answered empirically, through data or observations
2. Refine the question to form a hypothesis
3. Select a research design
4. Select participants
5. Assign participants to groups
6. Manipulate independent variable
7. Control extraneous variables
8. Measure dependent variable
9. Analyze data – is the difference between the groups more than can be accounted for by sampling error?
10. Form conclusions

• A test of significance
• Used to compare 2 independent groups
• A test for significant difference between sample means
• Uses degrees of freedom rather than sample size (N1+N2-2 for two groups)
• Measures the relative size of the difference between means
• Uses degrees of freedom to find significance levels
• Uses the formula
  

Significance levels in a two-sample t test

• Both two-tailed and one-tailed tests tables are on page 491
• Find your degrees of freedom
• Choose an a level of 0.05 or lower for most research
• Table lists only positive values, but t is significant if it is plus or minus that number

Assumptions of the one sample t test

• Subjects selected through random sampling
• The population has a normal distribution of scores
• Scores measured on an interval or ratio scale

Finding the confidence interval for the difference between means:

A 95% confidence interval uses the formula

In order to use this information for our BASC study, we need a second set of data, an independent group that was also randomly selected. If you remember back to the first lesson, we said that we sampled the Hispanic population at the school AND the non-Hispanic population. Now we can look at the BASC scores for these two groups to see if there is a significant difference in scores within our school.

First we need the formula for the t test for two independent groups

Now we can turn to the table on page 491, and use the two-tailed test column. We have 50 students in two groups so we have 48 degrees of freedom. We only need a rough estimate of the t being between 2.000 and 2.021 to reject the null hypothesis that there is no difference between groups. Our t of 0.28 is no where near high enough to reject the null hypothesis at the 0.05 alpha level.

We can also find the confidence level for the difference between these two means. We will use the formula

This tells us that we can be 95% certain that the true difference between the means of these two groups is between –5.29 and 6.97.

SPSS Tips:

Vocabulary

Between subjects design – An experiment in which two or more groups are created.

Random sampling – A sampling method in which individuals are selected so that each member of the population has an equal chance of being elected for the sample, and the selection of one member is independent of any other member of the population.

Convenience sampling – Obtaining participants from among people who are accessible or convenient to the researcher.

Equivalent groups – Groups of participants that are not expected to differ in any consistent or systematic way prior to receiving the independent variable of the experiment.

Random – A method of assigning participants to treatment groups so that any individual selected for the experiment has an equal probability of assignment to any of the groups, and the assignment of one person to a group does not affect the assignment of any other individual to that same group.

Level of an independent variable – One value of the independent variable. To be a variable, an independent variable must take on at least two different levels. For example there can be males and females as two levels, or there can be several levels of household income, etc.

Factor – an alternative name for independent variable.

One-factor between subjects design – A research design in which one independent variable is manipulated and two or more groups are created.

Extraneous variables – Any variables, other than the independent variable, that can affect the dependent variable in an experiment.

Confounded experiment – An experiment in which an extraneous variable is allowed to vary consistently with the independent variable.

Placebo control – A simulated treatment condition.

Sampling distribution of the difference between means – The distribution of differences when all possible pairs of samples of size n are selected from a population and found for each pair of samples.

Standard error of the difference between means – The standard deviation of a theoretical sampling distribution of values.

Estimated Standard error of the difference between means – The standard error of the difference between means obtained by using s2 to estimate &sigma 2.

Robustness – A term used to indicate that violating the assumptions of a statistical test has little effect on the probability of a Type I error.

Strength of effect – The strength of an independent variable as measured by one of the strength of effect statistics.

Within-subjects design – A research design in which one group of participants is exposed to and measured under each level of an independent variable. In a within-subjects design, each person receives each treatment condition.