Hypothesis Testing

1
Hypothesis Testing

• HED 489 Biostatistics

2

• The purpose of inferential statistics is to test
  hypotheses. A researcher makes inferences from
  samples to populations. A hypothesis is an
  educated-guess regarding the answer to a research
  question.  More than one hypothesis is called
  "hypotheses." Experimental research will have at
  least two hypotheses a null hypothesis and an
  alternative hypothesis. In other words, there is
  an effect, or there is not an effect.
• You'll learn how to construct hypotheses in a
  research methods class. For this class, what you
  want to know is that there are several forms of
  hypotheses, and they go along with various types
  of inferential statistics
• There are hypotheses that posit a difference
  between groups
• There are hypotheses that posit a difference
  within groups
• There are hypotheses that posit a relationship
  between two or more variables
• There are hypotheses that posit the fit of a
  model of variables.

3
Null Hypothesis

• The null hypothesis is often noted as H0
  (H-sub-zero). What does "null" mean? Often
  researchers test what is called the nil null
  hypothesis. It means "nothing," "empty," "zero,"
  "zilch." In research terms, it means "no effect,"
  "no difference," "no relationship." If, at the
  end of our study, we conclude that the null
  hypothesis has the best chance of being true, we
  mean that "nothing happened. The null
  hypothesis could be set to other values as well.
• Think of this as a jury trial.  We gather
  evidence. We assume the person is innocent
  (the null hypothesis is correct). The evidence
  helps us to test our assumption of innocence. 
  The same goes with research.  Research always
  tests that the null hypothesis (being innocent')
  is true. Due to probability and error, there is
  always a chance that our conclusion is wrong,
  however.
• Remember that researchers conclusions have
  consequences.
• Fortunately, there are ways to understand the
  probability of errors in hypothesis testing.

4
Alternative Hypothesis

• The alternative hypothesis is usually noted as Ha
  (H-sub-a) or H1 (H-sub-one). If there's more than
  one alternative hypothesis, the second would be
  H-sub-b," or H-sub-2," etc. I like the 1, 2,
  style, because it helps me keep them straight.
• The alternative hypothesis asserts that
  "something happened" (there is a difference or
  that there is a relationship). The alternative
  hypothesis is the one you'd like to accept as
  being true, since it would suggest that your
  program worked.
• One does not directly test the alternative
  hypothesis one either rejects or fails to reject
  the null hypothesis.
• Just so you get a little more experience, here
  are the two hypotheses for my cholesterol
  reduction program
• H0 There was no difference in mean cholesterol
  between the start and end of the cholesterol
  reduction program (the means were equal).  
• H1 There was a difference in mean cholesterol
  between the start and end of the cholesterol
  reduction program (the means were not equal).

5

• This section assumes you have only one null
  hypothesis and one alternative hypothesis. As a
  beginning researcher, you should make sure this
  is true!
• What you're using inferential statistics for is
  to take your best guess as to which hypothesis is
  true. Only one of them can be true based on the
  evidence. Another way of looking at it is that
  your cholesterol reduction program either worked
  or it didn't people either reduced cholesterol
  or they didn't.
• It's really important for you to understand this,
  so let's go into a bit more detail.
• You cannot accept as true both the null and the
  alternative hypothesis. You cannot conclude,
  simultaneously, that your program worked and
  didn't work.
• You cannot reject as true both hypotheses,
  either. Either the program was effective or it
  wasn't. You either reject the null or fail to
  reject the null.
• If you fail to reject the null hypothesis, then
  the value of the null is tenable based on your
  evidence. Practically, you would be saying that
  your program didn't work based on the data that
  there was no difference, no relationship, no
  cause-effect.
• If you reject the null hypothesis, the value of
  the parameter being estimated is not value in the
  null hypothesis. This indicates that your
  program worked that there was a difference, a
  relationship, a cause-effect.

6
Statistical Error

• Because inferential statistics work only because
  of our acceptance of the laws of probability, you
  have a chance of being wrong.
• A statistical error occurs when our statistical
  evidence does not correspond with reality. There
  are two basic types of statistical errors Type 1
  and Type 2 error.
• Type 1 error Reject the null hypothesis when the
  null hypothesis is really true. That is, you
  claim your program is effective when it really
  isn't.

7
Type I Error and Type II Error
8
(No Transcript)
9

• Type 2 error Fail to reject the null hypothesis
  when it should be rejected. In this case, you say
  your program isn't effective when it really is.
  So, you assume that the red sample, close to the
  mean, represents your data when, really, the blue
  is more accurate.

10
(No Transcript)
11
Caution in Evaluating Problems of Error

• Sometimes a Type 1 error is worse than a Type 2
  error, whereas other times it is the opposite.
• Other times it is difficult to say exactly which
  error is better or worse
• For example, missing that someone has HIV, when
  in fact they do has negative consequences.
  Further, concluding that someone has HIV when in
  fact they do not also has negative consequences.

12
Other Cautions Statistical Error

• Warning the sum of the probabilities of Type 1
  and Type 2 error does not necessarily and most
  likely will not sum to 1.0. It's common to accept
  .05 as the critical value (Type 1 error value)
  for statistical significance. If your program is
  effective at the .05 level, it means that the
  researcher accepts that the null hypothesis will
  be rejected by chance 5 of the time. Type 1
  error is relatively easy to calculate and set. A
  researcher sets the Type 1 error value a priori
  (before the analysis), usually .05 in social
  science research.

13

• The only way you can minimize your risk of
  committing a Type 1 error is to accept a smaller
  alpha or critical value. In other words, move
  your yardstick further out on the tail of the
  distribution. You don't have to accept .05, you
  could accept .01, or even .005 as a critical
  value. See how your confidence in the
  effectiveness of your program increases as your
  critical value decreases?
• Is there a downside to all of this? Yes, indeed!

14
Interrelated Error

• Type 2 error is more difficult to calculate than
  Type 1 error.
• Type 2 error is influenced by Type 1 error.
• The smaller the Type 1 error, the larger the Type
  2 error
• The larger the Type 1 error, the smaller the Type
  2 error.

15
More about Type 2 Error

• Type 2 error decrease as sample size increases
• The further away the true parameter value from
  the value hypothesized in the null hypothesis,
  the lower the Type 2 error.
• (1-Type 2 error)Power

16
Introduction of Inferential Statistics

• We use inferential statistics whenever our
  project has a hypothesisthat is, we're going to
  try to change something. The thing we try to
  change, whether it's weight, attitude toward safe
  sex, smoking behavior, or whatever, is the
  dependent variable.
• The thing we use to try to produce change is
  known as the independent variable. In the case of
  a cholesterol-reduction program, the independent
  variable might be an exercise program. We might
  compare the cholesterol reduction of two groups
  of peopleone that exercised and one that didn't.
  The group that received our program, generically
  known as the treatment, is called an experimental
  group. The group that didn't get the treatment is
  called a control group.
• Beyond a treatment, other independent variables
  sometimes are included in a project. These might
  be things that occur naturally but which we
  influence. So, in our weight-loss program, we
  might want to see if the exercise program is any
  more effective for females than males. Now we
  would compare cholesterol reduction between males
  and females, and between our experimental and
  control group. While we can't influence whether a
  person is male or female, we could decide to
  include either gender or both genders in our
  project.

17
Review of Descriptive Statistics

• Remember, there are two bodies of
  statisticsdescriptive and inferential. When we
  conduct a research study or a health promotion
  program, we use descriptive statistics to
  describe the sample. When dealing with humans, we
  might use descriptive statistics to summarize
  some of the independent variablesthe number or
  percent of males and females, education level,
  race or ethnicity, or income things like that.
  We'd report on whatever variables were important
  to our study or program. We'd also use
  descriptive statistics to report central tendency
  and dispersion of our dependent variable. For
  example, in the case of the male/female,
  experimental/control group cholesterol reduction
  project, we'll likely report mean beginning and
  ending weight for males in the experimental
  group, males in the control group, and the same
  for females. The purpose of this is just to make
  it easier for our readers to understand the
  results of our project.

18
Inferential Statistics

• We use inferential statistics to infer the
  results of our study. We infer from a sample(s)
  to a population(s). We cannot be completely
  positive of the outcome because of probability.
  However, because of probability we can
  conditionally accept our findings within a
  certain level of confidence. Because of the
  uncertainty inherent in sample-based studies, you
  must never say that your results "prove"
  something. Proving something removes uncertainty,
  and that's not possible to do completely when
  working with samples of people. Your results are
  evidence or support but not proof.
• There are two types of inferential
  statisticsparametric and non-parametric. As I
  touched on earlier, parametric statistics require
  interval, ratio, normally-distributed data.
  Non-parametric statistics can be used with
  nominal, ordinal, or interval data, and can work
  with skewed data. Non-parametric statistics are
  also more conservative (less power) than their
  parametric equivalents. This means that if you
  calculate a non-parametric statistic and the
  value you calculate reaches statistical
  significance, you can put more confidence in it
  than if you calculated a parametric test. We'll
  cover both types before this course is over.

19
Types of Statistical Tests

• Under parametric difference statistics, you
  commonly see two testst-test and analysis of
  variance. Generally speaking, you use t-test when
  you have only one or two groups of data, and
  analysis of variance when you have more than two
  groups.
• Correlations test the linear association among
  variables. Technically, this test, using
  interval or ratio data, is known as "Pearson
  Product Moment Correlation," but most people call
  it "correlation."
• Linear regression generates the correlation above
  as well as other statistical coefficients.
  Regression" typically assumes directionality of
  relationships meaning that a variable(s) predict
  another variable.
• All of these tests above fall under the General
  Linear Model.

20
Inferential Difference Tests

• As noted, there are two inferential, difference
  testst-test and analysis of variance, usually
  shortened to "ANOVA." What you want to know with
  these tests is whether one or more sample mean
  values are different either from an assumed
  population mean or from each other.
• The question with a difference test is how far
  away from either the mean or from each other do
  the calculated values fall? Here's a new concept
  for you what you really want to know is whether
  the values you calculated came from the same or
  different populations! If they fall beyond your
  critical valuesay plt.05you might be able to
  conclude that they come from a different
  population of values.

21
Assignment 9Hypothesis Testing
22
For each of the following, write a null
hypothesis and an alternative hypothesis

• You are finding out whether a group of boys are
  fatter than a group of girls
• You are wondering whether the group you are
  working with has higher blood pressure than the
  national average.

Send to kitt_at_siu.edu