Students t test and Nonparametric Statistics

1
Students t test and Nonparametric Statistics

• OT 667

2
Hypothesis testing defined

• A method for deciding if an observed effect or
  result occurs by chance alone
• OR
• if we can argue the results found actually
  happened as a result of an intervention.

3
The Null Hypothesis

• In order to decide if the results of an
  experiment occur by chance or if the effects seen
  are the result of a treatment, researchers
  declare a null hypothesis (Ho) and an alternative
  or research hypothesis (Ha).

4
To test a hypothesis, researchers talk about
rejecting the null in order to demonstrate the
treatment has an effect.
5
When you reject the null, you say that there IS a
significant difference between the groups,
indicating the likelihood the treatment was
effective.
6
Decisions to reject or accept the null.

• Based on the alpha level or the probability that
  a certain outcome will be achieved
• By tradition, .05 is the most common alpha level
  used to make this decision

7
Students t test
8
What is the t test?

• A parametric statistical test which analyzes the
  difference between the means of scores between
  two groups.

9
Calculating a t test

• The formula for independent t tests
• The difference between the means divided by the
  variability within the groups

10
There are different formulas to calculate the t
statistic when variances within groups are equal
and when they are unequal
11
Assumptions

• There are assumptions about the data that need to
  be considered when using the t-test. These are
• the data is normally distributed
• the variances are homogenous or similar
• the groups are of equal size

12
The research question asked by the t test Is
there a difference between the two groups?
13
Two kinds of t tests

• t test for paired samples - when the subjects are
  measured on a variable, receive the treatment,
  then measured again. The pre and post-test means
  of the measures are compared
• t test for independent samples - comparison of
  means between 2 different groups after a
  treatment is administered

14
Example of an independent t test

• From the Case-Smith article, the difference
  between pre and post test means on various tests
  (DTVP, BOTMP) could have been compared between
  the IG and the CG.

15
Example of a Paired t test

• In the Case-Smith article, paired t tests were
  actually performed between pretest and postest
  means for the IG only.

16
Multiple t tests

• When you read a study where several t tests are
  used to test the same data, BEWARE
• For example, a researcher writes an article on
  the outcomes of a treatment used in persons with
  dementia. More than one measure is used to study
  the outcome. This means the risk of committing a
  Type I error (rejecting a true null or finding a
  difference when there isnt one) is increased.

17
Both point and interval estimates (confidence
intervals) can be calculated for t tests.
18
Solutions for the problem

• Perform an ANOVA
• Adjust the alpha level using a Bon Ferroni
  correction - to do this you half or lower the
  alpha level

19
Parametric Tests vs. Nonparametric Tests

• Parametric tests are based on assumptions made on
  the normal curve normal distribution of data
  and homogenous or similar variances
• Nonparametric tests are used when the data is not
  normally distributed or variances are dissimilar.
  

20
Criterion for Using Nonparametric Tests

• Assumptions of normality and homogeneity of
  variance cannot be made
• Data is ordinal or nominal
• Sample size is small (10 per group)

21
Comparable Parametric and Nonparametric Tests

• Mann-Whitney U test
• Wilcoxon Signed-Ranks Test
• Sign Test
• Kruskal-Wallis one way analysis of variance by
  ranks
• Friedman Two Way

• Independent samples t test
• Paired t tests
• One way ANOVA
• Factorial ANOVA

22
Hypothesis testing with nonparametric tests is
the same procedure as with parametric tests.
23
Test Power

• Parametric tests are seen as more powerful
• Are often used with inappropriate data because of
  this
• Need to assess the nature of the data carefully
  to decide if the appropriate test is being used