SW318 Social Work Statistics Slide 1

1
Five-step model for Testing Hypotheses

• The five-step model used for all hypothesis tests
  contains the following steps
• Step 1. Evaluating assumptions.
• Step 2. Stating the research hypothesis and the
  null hypothesis and setting alpha
• Step 3. Selecting the sampling distribution and
  the test statistic
• Step 4. Computing the test statistic
• Step 5. Making a decision about hypotheses

2
Evaluating Assumptions

• All hypothesis tests assume the sample is
  representative of the population assured by
  random sampling
• Assumptions about the distribution of variables.
  e.g. normality, equal variances
• Assumptions about sample size, e.g. no cell with
  expected frequency less than 5

3
Hypotheses

• The research hypothesis states relationship we
  think is true, e.g. mean of one group higher than
  other, or two variables are related
• The null hypothesis contradicts research
  hypothesis, e.g. means of all groups are the
  same, or two variables are independent. Usually a
  statement of equality or no difference.
• Both hypotheses are statements about the
  population that will be tested on sample data.

4
Alpha

• Alpha is the probability that we could make an
  error in rejecting the null hypothesis and
  supporting the research hypothesis.
• Alpha is the risk that we will make a Type I
  error a true null hypothesis is rejected.
• We can also make an error when the null
  hypothesis is false, but we fail to reject it a
  Type II error.
• When alpha is higher, it is easier to reject the
  null hypothesis and the chances that we may be
  making a mistake are larger.

5
Alpha

• We choose alpha based on the consequences of
  making a Type I error or a Type II error.
• If rejection of null hypothesis leads to action
  with serious side effects, we set alpha lower
  (making it harder to reject null) so that we do
  not risk the side effects too easily. Type I
  error is less likely.
• If rejection of the null hypothesis lead to an
  action that may be helpful and has no serious
  side effects, we set alpha higher (making it
  easier to reject null) so that we take advantage
  of helpful action. Type II error is more likely.

6
Selecting Test Statistic

• We choose the statistical test based on the
  research question and the conformity of the
  variables to the assumptions for the test.
• First, we eliminate statistical tests for which
  we cannot satisfy the level of measurement
  requirements and other assumptions.
• Second, we choose the statistical test that
  treats the variables at the higher level of
  measurement. For example, we could test the
  relationship between two ordinal variables with
  either regression analysis or with a chi-square
  test of independence. We would choose the
  regression analysis, because the variables are
  treated as interval rather than nominal.

7
Making a decision based on test statistic

• If the p-value of the test statistic is less than
  or equal to alpha, we reject the null hypothesis
  and find that our research hypothesis is
  supported.

8
Testing Hypotheses Evaluating Assumptions
Independent samples t-test Chi-square test of independence One-way ANOVA Hypothesis test of r2
Level of measurement Dependent Interval (ordinal) Dependent Nominal (dichotomous, ordinal, grouped interval) Dependent Interval (ordinal) Dependent Interval (ordinal)
Independent (dichotomous) Independent Nominal (dichotomous, ordinal, grouped interval) Independent Nominal (dichotomous, ordinal, grouped interval) Independent Interval (ordinal)
Assumptions Normality Equal variances Minimum sample size no expected frequency lt 5 Normality Equal variances Normality Linearity Equal variances
9
Testing Hypotheses Hypotheses and Alpha
Independent samples t-test Chi-square test of independence One-way ANOVA Hypothesis test of r2
Null Hypothesis Group means are equal Variables are independent (Expected frequencies observed frequencies) Means of all groups are equal Variables are not related (r2 0)
Research Hypothesis Group means are different Variables are related (Expected frequencies ltgt observed frequencies) Mean of one or more groups is different Variables are related (r2 gt 0)
Alpha 0.05, unless otherwise indicated 0.05, unless otherwise indicated 0.05, unless otherwise indicated 0.05, unless otherwise indicated
10
Testing Hypotheses Sampling Distribution and
Test Statistic
Independent samples t-test Chi-square test of independence One-way ANOVA Hypothesis test of r2
Sampling distribution t X2 F F
Test statistic t X2 F F
11
Testing Hypotheses Compute Test Statistic
Independent samples t-test Chi-square test of independence One-way ANOVA Hypothesis test of r2
Compute Test Statistic Run SPSS, identify test statistic and p-value Run SPSS, identify test statistic and p-value Run SPSS, identify test statistic and p-value Run SPSS, identify test statistic and p-value
12
Testing Hypotheses Decision about Hypotheses
Independent samples t-test Chi-square test of independence One-way ANOVA Hypothesis test of r2
P-value lt alpha Reject null hypothesis (risk type I error) Support research hypothesis Reject null hypothesis (risk type I error) Support research hypothesis Reject null hypothesis (risk type I error) Support research hypothesis Reject null hypothesis (risk type I error) Support research hypothesis
P-value gt alpha Fail to reject null hypothesis (risk type II error) No support for research hypothesis Fail to reject null hypothesis (risk type II error) No support for research hypothesis Fail to reject null hypothesis (risk type II error) No support for research hypothesis Fail to reject null hypothesis (risk type II error) No support for research hypothesis
13
Testing Hypotheses Post Hoc Tests

• Chi-square test of independence supports the
  existence of relationship between variables. It
  does not tell us about strength or direction of
  relationship, i.e. which cells produce the
  difference. For this we use post hoc test of
  standardized residuals.
• One-way ANOVA identifies that one or means are
  different, but does not indicate pattern of
  differences between groups. To identify which
  means are different from one another, we use a
  post hoc test, such as Tukey HSD test.