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Parametric versus Nonparametric Statistics-when to use them and which is more powerful?. Dr Mahmoud Alhussami. Parametric Assumptions. The observations must be independent. Dependent variable should be continuous (I/R) The observations must be drawn from normally distributed populations
Dr Mahmoud Alhussami
e.g. Male X Female
Nurse X Physician
Manager X Staff
NO OVER LAP
Sending an innocent to jail for no significant reason
K Sample (i.e., >2)
Categorical or Nominal
Rank or Ordinal
Mann Whitney U
Wilcoxin Matched Pairs Signed Ranks
Kruskal Wallis H
Parametric (Interval & Ratio)
z test or t test
t test between groups
t test within groups
1 way ANOVA between groups
1 way ANOVA (within or repeated measure)
Factorial (2 way) ANOVASummary Table of Statistical Tests
When running a t test and ANOVA
When the assumptions are violated:
We use tests that are equivalent to t test and ANOVA
Must be a random sample from population
Data must be in raw frequencies
Variables must be independent
A sufficiently large sample size is required (at least 20)
Actual count data (not percentages)
Observations must be independent.
Does not prove causality.
The data must be in the form of frequencies
The frequency data must have a precise numerical value and must be organised into categories or groups.
The expected frequency in any one cell of the table must be greater than 5.
The total number of observations must be greater than 20.
e.g. treatment and disease
gender and mortality
Note: chi-square must be calculated on actual count data, not substituting percentages, which would have the effect of pretending the sample size is 100.
Grand total4. Calculating Test Statistics
Fe= Fr Fc / N
df = (R-1)(C-1)
Number of levels in column variable
Number of levels in row variable
Alpha of .05
= 40* 25/90
df = (R-1)(C-1) =(2-1)(3-1) = 2
through an example
1 = 72 hrs
2 = 96 hrs
from Polit Text: Table 8-1
Since the p > .05, we fail to reject the null hypothesis that the complication rate is unrelated to heparin lock placement time.
Smallest of number of rows or columns
Number of cases
A chi-square test of independence of the relationship between sex and marital status finds a statistically significant relationship between the variables.
Researcher often try to identify try to identify which cell or cells are the major contributors to the significant chi-square test by examining the pattern of column percentages.
Based on the column percentages, we would identify cells on the married row and the widowed row as the ones producing the significant result because they show the largest differences: 8.2% on the married row (50.9%-42.7%) and 9.0% on the widowed row (13.1%-4.1%)
Using a level of significance of 0.05, the critical value for a standardized residual would be -1.96 and +1.96. Using standardized residuals, we would find that only the cells on the widowed row are the significant contributors to the chi-square relationship between sex and marital status.
If we interpreted the contribution of the married marital status, we would be mistaken. Basing the interpretation on column percentages can be misleading.
You can conduct a chi-square test of independence in crosstabulation of SPSS by selecting:
Analyze > Descriptive Statistics > Crosstabs…
First, select and move the variables for the question to “Row(s):” and “Column(s):” list boxes.
The variable mentioned first in the problem, sex, is used as the independent variable and is moved to the “Column(s):” list box.
The variable mentioned second in the problem, [fund], is used as the dependent variable and is moved to the “Row(s)” list box.
Second, click on “Statistics…” button to request the test statistic.
First, click on “Chi-square” to request the chi-square test of independence.
Second, click on “Continue” button to close the Statistics dialog box.
In the table Chi-Square Tests result, SPSS also tells us that “0 cells have expected count less than 5 and the minimum expected count is 70.63”.
The sample size requirement for the chi-square test of independence is satisfied.
The probability of the chi-square test statistic (chi-square=2.821) was p=0.244, greater than the alpha level of significance of 0.05. The null hypothesis that differences in "degree of religious fundamentalism" are independent of differences in "sex" is not rejected.
The research hypothesis that differences in "degree of religious fundamentalism" are related to differences in "sex" is not supported by this analysis.
Thus, the answer for this question is False. We do not interpret cell differences unless the chi-square test statistic supports the research hypothesis.
X variable goes here
If all expected frequencies are the same, click this box
If all expectedfrequenciesare not the same, enter the expected value for each division here
expected frequencies are the same
expectedfrequenciesare not the same