SPSS

Part III

 

Hypothesis Testing

Hypothesis testing is a decision making process for evaluating claims about a population.

 

The researcher must:

o      Define the population under study

o      State the hypothesis that is under investigation

o      Give the significance level

o      Select a sample from the population

o      Collect the data

o      Perform the statistical test

o      Reach a conclusion

 

Examples include z-test, t-test, and correlation analysis to name a few.

 

My goal is to give you enough information to use SPSS to perform some different hypothesis tests without getting into the nitty gritty detail. To use this tool properly, you must have a statistics background; otherwise, chances are an incorrect test can be applied to a given set of data to name one problem.

 

Hypothesis testing is the formal statistical technique of collecting data to answer questions through the use of a statistical model.

 

Each question asked needs to be posed as a null hypothesis; the null hypothesis is that there are no differences of the dependent variables of your model that can be explained by the independent variables. 

ONE-SAMPLE T-TEST:

This is the easiest of the statistical tests to understand. Specifically, this test compares a sample mean (computed from a set of observed values) to a hypothesized mean and determines the likelihood that the observed difference between the sample and hypothesized mean occurs by chance. The chance is reported as the p-value.

 

A p-value close to 1 means that it is very likely that the hypothesized and sample means are the same (assuming that they are the same), and a small p-value (for example 0.01) means it is unlikely (only a one in 100 chance) that such a difference would occur by chance (again, assuming that the two means are the same).

 

Thus, the lower the p-value the more certain that we can be that there is a statistically significant difference between the observed and hypothesized mean. Most disciplines use an alpha value of 0.05; that is, if the p-value is less than 0.05 then the difference is regarded as statistically significant.

 

á      if p < 0.05, reject the null hypothesis

á      if p>= 0.05, accept the null hypothesis

Problem #1

Our first objective is to perform a one-sample t-test on data from blood lipid screening of medical students. Specifically, we will test whether the mean cholesterol level is significantly greater than 190, the point at which cholesterol levels may be unhealthy.  You will test the null hypothesis that the mean value for cholesterol is 190.

 

Null hypothesis: The mean value for cholesterol is 190.

 

 

Notice: In SPSS, the p-value is given in the box labelled Sig. (2-tailed).

You will notice that the mean is slightly higher than the hypothesized value of 190.  However, although the mean is in fact higher, this difference is well within the range of sampling variance. In particular, the p-value of 0.7373 indicates you would see a difference of this magnitude by chance more than 73% of the time. Thus the mean cholesterol level is not significantly greater than 190.

PAIRED T-TEST:

The most common use of the paired t-test is the comparison of two measurements (typically one measurement occurs before a "treatment" and the other after the "treatment") from the same individual or group. This test is used primarily to determine if the "treatment" had a statistically significant effect. As in the case of the one-sample t-test, the primary statistic of concern is the p-value, and thankfully the p-value has the same interpretation here as it did in the case of the one-sample t-test.

Problem #2

Again using the Lipid Data file we want to see if there is a statistically significant difference between Triglycerides and Trig-3.

 

Null hypothesis: There is no statistically significant difference between Triglycerides and Trig-3..

 

 

Question: Should we accept the null hypothesis in this case?

 

Problem #3

Go to the Web Site http://www.physics.csbsju.edu/stats/t-test.html and solve the problem under the heading Paired Data. Perform the Paired Student's t-test first by clicking on the link and then enter the data into SPSS and get the same results.

 

UNPAIRED T-TEST:

This test is very similar to the paired t-test, but instead of comparing two measurements within our entire population, we use only one measurement but break our population into two natural subgroups, testing whether there is a statistically significant difference between the means of these two subgroups. As in the case of the paired t-test, our primary statistic of concern is the p-value, and again it has the same interpretation.


Problem #4

Null hypothesis: There is no statistically significant difference between the price of houses near to and far from the Charles River.

 

 

 

Question: Should we accept the null hypothesis?

Problem #5

The dean of students wants to see whether there is a significant difference in age between resident students and commuting students. She selected a random sample of 10 students from each group.

 

The data follows:

 

Resident

Commuter

Students

Students

22

18

25

20

27

19

23

18

26

22

28

25

26

24

24

22

25

23

20

18

a) What statistical test should be used to solve this problem?

b) State the Null Hypothesis.

c) Create an SPSS dataset and perform the proper test.

d) State your conclusion.