Biology - Anatomy Assignment 5
Paris04
2 years ago
15
files (4)Assignment5-ANOVA.doc
significance.ppt
- goggles.sav
- divorce.sav
Assignment5-ANOVA.doc
significance.ppt
*
The Real Differences
*
We test SAMPLE to draw conclusions about POPULATION
If two SAMPLES (group means) are different, can we be certain that POPULATIONS (from which the samples were drawn) are also different?
Is the difference obtained TRUE or SPURIOUS?
Will another set of samples be also different?
What are the chances that the difference obtained is spurious?
Cont…
*
We do not need a test of significance:
- when we can measure the height of all of the subjects in the population
Statistically different? = Truly different?
Not just apparently different!!!
*
Inferential Statistics
- Estimation: This includes point and interval estimation of certain characteristics in the population(s).
- Testing Hypothesis about population parameter(s) based on the information contained in the sample(s).
Important Statistical Terms
- Population: A set which includes all measurements of interest to the researcher
- Sample: Any subset of the population
- Parameter of interest: The characteristic of interest to the researcher in the population is called a parameter.
Students please read the article on the following link http://pareonline.net/getvn.asp?v=4&n=5 before you continue with the PowerPoint presentation
*
Null Hypothesis
Null hypothesis (statistical hypothesis) states that there is no difference between groups compared.
Alternative hypothesis or research hypothesis states that there is a difference between groups.
In spite of the fact that the researcher is working with a sample from a population, the null hypothesis is always stated for the population. The null is always stated in terms of parameters, therefore, using Greek symbols
*
- Mean =
- Standard deviation =
- Proportion = π “pi”
- Correlation coefficient = “rho”
*
Consider a researcher is interested in determining if thereis a difference in the mean academic performance in writing, as evidenced by a standardized assessment, between a group of students that are using graphic organizers as a prewriting strategy and those that don’t. The null hypothesis is
µ1 =µ2;
where µ1 is the mean writing test outcome for students using graphic organizer and µ2 is the mean for those that are not using the organizers. Thus, the null hypothesis concerns the parameter µ1 - µ2 and the null hypothesis is that the parameter equals zero.
The level of significance ()
- The alpha level is the level of confidence designated by the researcher to evaluate the findings from the results obtained after analyzing the data. The researcher is asserting that the odds of obtaining that statistic, by chance only, are sufficiently low (one out of twenty) that it reasonable to conclude that the results are not due to chance. In the social sciences, an alpha level of .05 is generally considered "acceptable.“
P-value
- An indicator which measures the likelihood of observing values as extreme as the one observed based on the sample information, assuming the null hypothesis is true.
- P-value is also known as the observed level of significance.
Type I and Type II errors
- Type I error is committed when a true null hypothesis is rejected.
- is the probability of committing type I error.
- Type II error is committed when a false null hypothesis is not rejected.
- is the probability of committing type II error.
7.*
State of Affairs in the Population
Decision Made by
the Researcher
Based on the
Statistical Test
Value
Type I Error
(false positive)
(probability =
Alpha)
Correctly not
rejected:
no error
Correctly
rejected:
no error
(probability =
power)
Type II Error
(false negative)
(probability =
Beta)
Reject the
Null
Hypothesis
No Effect:
Null True
Effect Exists:
Null False
Fail to Reject the
Null Hypothesis
*
- A statistical value which is computed based on
the information contained in the sample under
the assumption that the null hypothesis is true.
- The sampling distribution of the test statistic is compared to the obtained statistical value to determine the likelihood of observing extreme values for the test statistics in a given situation.
- Or the researcher evaluates the p value obtained using a statistical software package.
How to interpret P?
If P < alpha (0.05), the difference is statistically significant
If P>alpha, the difference between groups is not statistically significant / the difference could not be detected.
When p<0.05, it shows that the chances of obtaining a false difference is less than 5% (1 in 20) [p<0.01 – 1 in 100; p<0.001 – 1 in 1000]
Since we consider 5% P is small, therefore, the difference between groups is TRUE
Truth is something which is most likely to be true and 100% certainty is impossible.
*
Selecting the Statistical Test
The researcher must determine:
- Aim of the study –
- Parameter to be analyzed -
- Data type- Continuous, Discrete, Rank, Score,
- Analysis type-Comparison of means, association, prediction
- No. of groups to be analyzed -
- No. of data sets to be analyzed -
- Distribution of data - normal or non-normal
- Design - paired or unpaired
Once these determinations have been made, then the appropriate statistical test can be selected.
*
Table downloaded from www.graphpad.com
Statistical Test Decision Matrix
*
Table downloaded from www.graphpad.com
*
The SPSS “Thinking Process”
SPSS analyses the data (numbers) submitted (by the researcher) to calculate the chances of obtaining a difference when there is none i.e. probability of obtaining a spurious difference.
It does not indicate
- whether your design is right or wrong
- whether the type of data is correct or wrong
(c) the magnitude of the difference
(d) whether the difference will be practically useful
All it can point out is whether the obtained difference between two groups is REAL or FALSE within a certain degree of confidence….
*
SPSS will….
- Process the data entered or submitted by the researcher
- Analyze the data as requested by the researcher
- Release a P value
*
Power of a test
- The power of a test is the probability that a false null hypothesis is rejected.
- Power = 1 - , where is the probability of committing type II error.
- More powerful tests are preferred. At the design stage one should identify the desired level of power in the given situation.
Factors influencing the Power
- The power of a test is influenced by the magnitude of the difference between the null hypothesis and the true parameter.
- The power of a test could be improved by increasing the sample size.
- The power of a test could be improved by increasing .
Minimum Required Sample Size
- Usually a Sample size calculation formula is available for most of the well known study designs. Some software packages such as Epi-Info could also be utilized for the sample size calculation purpose.
- It is extremely important to consult a biostatistician at the design phase to ensure adequate sample is considered for the study.
How to test statistical significance?
The Researcher will:
- State Null hypothesis
- Set alpha (level of significance)
- Identify the variables to be analyzed
- Identify the groups to be compared
- Choose a test
The Statistical Software will:
- Calculate the test statistic
- Find out the P value
The Researcher will:
Interpret the P value : A Decision
If the P value is less than the alpha value then null hypothesis is rejected i.e. the difference between groups is not due to chance
*
- Strategic Management DB 5
- biology homework2
- Due Sunday
- Comparing and Contrasting Theories of Learning
- CIS 500 UCERTIFY Quiz: 6. The Other Service Design Proc.
- Leadership in Nursing Practice: 5-6 Page Paper
- Can anyone do a case study?
- Special-Needs Children: Transitioning to Adulthood
- health class assignment
- Office protocols and medical ethics both refer to doing the right thing; however, the two terms are different in other ways. Compare and contrast the two terms by using examples in your discussion. Use a quote or two from you weekly reading to support you
