1. Logic of Hypothesis Testing
Inferential statistics:
Based on laws of probability
Used to estimate population parameters from sample statistics
When different researchers apply inferential statistics to the same data resulting conclusions likely to be the same

2. Basic Preparation Planning a Research Study
Identify problem
Review literature
Determine conceptual and operational definitions of variables
Select appropriate instruments

3. Basic Steps Making Inferential Decisions
Five basic steps in making inferential decisions:
State hypotheses
Select appropriate inferential statistic(s)
Specify alpha or level of significance
Data analysis
Decision-making

4. Basic Steps: Step 1 Step 1 Hypotheses: Prior to data collection:
Delineate study purpose
Prepare formal purpose statement in form of a hypothesis
Essential conditions for a testable hypothesis:
Must delineate a relationship between variables
Relationship must be empirically testable through the collection of data

5. Step 1 Essential Conditions for Testable Hypothesis:
Must make a clear statement regarding explicit nature or posited relationship between the variables
Decide before study conducted whether or not to use a directional hypothesis (one-tailed) or non directional (two-tailed)
Examples testable hypotheses
Null (HO): There is no difference between staff nurses participating in a mentoring program and those not participating with respect to job satisfaction

6. Step 1
Examples Testable Hypotheses: Directional research hypothesis (HA, alternate hypothesis): Staff nurses participating in a mentoring program will have significantly higher job satisfaction than staff nurses not participating in a mentoring program Non directional research hypothesis: There will be a significant difference between job satisfaction of staff nurses participating in a mentoring program and staff nurses not participating in a mentoring program.

7. Step 1 Testable Hypotheses Un testable Hypotheses
There is no significant relationship between age and blood pressure
There is no significant difference between students receiving and those not receiving instruction with respect to achievement scores
An individual’s blood pressure is a function of his age, weight and daily exercise regime
There is no significant difference between age and blood pressure
Administering instruction is the best way to increase student achievement scores
What is the relationship between an individual’s blood pressure and his age, weight and daily exercise regime ?

8. Step 1
Is the following hypothesis testable? Why or why not? A researcher hypothesizes that Group A is significantly better than groups B and C and group B is better than group C. Adapted from: Waltz,C.F. & Bausell, R.B. (1981) Nursing Research: Design, Statistics and Computer Analysis Philadelphia: F.A. Davis Company

9. Parametric tests are more powerful than nonparametric tests ,
Basic Steps: Step 2
Step 2 Selecting the appropriate inferential statistic(s) prior to data collection
Types of statistical tests: parametric & non parametric
Parametric tests have the following characteristics:
Involve estimation of a parameter
Require interval or ratio levels of measurement
Involve a set of assumptions to be met (e.g. that the variables are normally distributed in the population)
Parametric tests are more powerful
than nonparametric tests ,
thus are usually preferred

10. Step 2 Nonparametric tests Do not estimate parameters
Involve less restrictive assumptions about the distribution shape (referred to as distribution free tests)
Use when
Variables are not at the interval or ratio level
distribution is markedly skewed (i.e. not normal)
when sample size is small

11. Step 2 Research data is used to compute test statistics
Every test statistic is based on a related theoretical distribution
Value of the computed statistic is compared to values that specify critical limits for the underlying distribution
When beyond the critical limit the results are said to be statistically significant (vs clinically significant)
Stat significance means that the obtained results are not likely to have been a result of chance at some specified level, e.g., <.05 . A nonsignificant result could reflect chance fluctuations.

13. Factors considered in selecting a test statistic include:
Levels of measurement of the variables
Whether a parametric test is justified
Whether dependent or independent groups
Whether the focus is correlations or group comparisons and if so,
How many groups are being compared

14. Step 2 Types of comparisons: Between subjects design
Comparisons involve different subjects (e.g. experimental and control group) and
Statistical test is for independent groups
Within subjects design
Involve one group of subjects who are exposed to two or more treatments (e.g. staff nurse job satisfaction measured, same staff nurses participate in a mentoring program and job satisfaction measured again )
Comparisons are not independent because the same subjects used in both conditions, thus referred to as tests for dependent groups

15. Basic Steps: Step 3 Step 3 Specifying alpha or level of significance
Typically researcher sets alpha at 0.05.
However there are instances when researcher may decide to use a more stringent level of alpha , e.g
Alpha 0.05 indicates researcher willing to take up to 5% risk of making an error (Type I error) when deciding statistical significance.
Alpha 0.01 indicates researcher willing to take up to 1% risk of Type I error
Type I error occurs when a researcher rejects the null hypothesis when in fact it is true in the population.

16. Alpha, Beta, Power, Effect Size
Null is true
Null is false
Researcher calc and decides the null is false:
Reject null
Alpha
Type I error
False positive
1 – Beta
Power
CORRECT REJECTION
Researcher calc and decides the null is true:
Null accepted
1 – Alpha
CORRECT NON-REJECTION
Beta
Type II error
False negative
Alpha – Level of significance, p value often set at 0.05 or 0.01
Type I error-Reject a null hypothesis when it is true
Beta –Type II error-Fail to reject null hypothesis when it is false
One controls the risk of a type I error by selecting a level of significance. Reducing the alpha to .01 from .05 reduces type I error
Lowering the risk of Type I increases the risk of Type II.
Simplest way to reduce type II errors is to increase sample size.

17. Basic Steps: Step 4 Step 4 Data analysis
Data entered into computer in a DATA file
SPSS used to analyze the results
SPSS Printout includes all necessary descriptive / inferential statistics including level of significance or probability.

18. Step 4 Example : Data Analysis Suppose:
A researcher is interested in the correlation between subjects years of experience as a staff nurse and scores on a job satisfaction questionnaire (sample size, n=700) .
The researcher employs the Pearson correlation coefficient (rxy) for this analysis and the following SPSS results are obtained.

19. Correlations
Years exp. Job sat. Years exp. Correlation ** Sig. (1-tailed) .000 N _______________________________________ Job sat. Correlation .384** 1.00 Sig. (1-tailed) .000 N ** Correlation significant at 0.01 level (1-tailed)

20. Step 4 Example: Data Analysis
The p value (or level of significance) gives the probability of committing error if results are declared to be statistically significant.
In this example, Sig.(1-tailed) for the correlation between years of experience and job satisfaction <.001 (=.000), indicating the result is statistically significant.
Whether a test is 1-tailed or 2-tailed is determined on the basis of the hypothesis statement

21. Basic Steps: Step 5 Step 5. Making a decision involves:
Do you reject or fail to reject the null hypothesis?
The decision is made by examining the p level furnished by the computer.
Example: if the alpha level is set at .05, inferential statistics with p levels of .05 or less are statistically significant.
When this is the case , the HO is rejected and HA is supported.

22. Step 5
The researcher might report the results of the data analysis example as follows:
There was a significant correlation
(r=.38, p =.01, 1-tailed) between years of experience and job satisfaction for the 699 subjects.
In reporting correlation results the coefficient is rounded to 2 decimal places

23. Step 5
The inferential statistic employed is based on the data collected in the study.
This inferential statistic is referred to as the test statistic ( i.e. it tests the null hypothesis)
The test statistic is also called the obtained or calculated statistic.
Each inferential statistic ( e.g. t-test, chi-square) has a separate table of what are referred to as critical values (CVs).
The values of the computed test statistic are compared to expected values (critical values) provided in tables or calculated in the ‘memory’ of the computer

24. Step 5
The appropriate table of CVs can be found in most statistics text books.[appendix pgs ]
When employing the CV in the appropriate table for decision making, the general rule is:
If the test statistic calculated for the data in your study equals or exceeds the CV, then the result is determined to be statistically significant (p< .05 or .01)
CVs are usually not included in research reports, instead the p level is included in reports.

25. Step 5 Examples of decision making using CVs
Test statistic = 4.11; CV= 4.110; decision: result is statistically significant because it equals the CV
Test statistic = 4.11; CV = 4.120; decision: result not statistically significant because it is less than the CV
Test statistic = 4.11; CV = 3.98; decision: result is statistically significant because it exceeds the CV

26. Step 5 Ex: Interpreting and Reporting Hypothesis Testing Results
Given an alpha level of .01
Suppose the results are statistically significant, that is, p<.01. This means that getting this result by chance is less than 1 time in 100.
Therefore , the null hypothesis is rejected.
The evidence supports the research hypothesis
That is, if your were testing for a difference in group means , statistical significance would lead you to conclude that the difference is not due to chance.

27. Step 5
Suppose the results are non significant ( i.e. p> .01). This means that:
The null hypothesis cannot be rejected
The evidence fails to support the research hypothesis
That is, if you were testing a difference in group means , statistical non significance would lead you to conclude that the apparent difference in group means is presumably due to chance.
Non significantly different means are treated as if they were equal.

28. The actual situation is that the null hypothesis is:
Type I error (also known as alpha error): researcher REJECTs the null hypothesis (HO) when it is true in the population. Type II error (also known as beta error): researcher FAILS to reject the null hypothesis (HO) when it is FALSE in the population
The actual situation is that the null hypothesis is:
_____________________________________
True False
True Correct Type II Error
(Null accepted) Decision Beta
_______________________________________
False Type I Error Correct Decision
(Null rejected) Alpha

29. Step 5
Power refers to the probability that the statistical procedure will be able to reject a false null hypothesis.
That is, the probability that the researcher will not make a Type II error.
Power depends on Alpha :
for example, alpha set at .05 gives more power as compared to an alpha set at .01 or .001

30. ‘power’ Sample size: the larger the sample the more power
Effect size: strength of the study’s expected effect (in experimental research); expected difference (in descriptive comparative research); expected correlation (in descriptive correlational research ).
Parametric statistics are generally more powerful than nonparametric
For some statistics (e.g. t-test) , one-tailed hypotheses (tests) are more powerful than two-tailed tests , PROVIDED the researcher predicts the right direction
Power for a study should be at .80 or higher