Post on 23-Dec-2015
Types of Inferential Statistics• Inferential Statistics: estimate the value of a population
parameter from the characteristics of a sample• Parametric Statistics:
– Assumes the values in a sample are normally distributed
– Interval/Ratio level data required• Nonparametric Statistics:
– No assumptions about the underlying distribution of the sample
– Used when the data do not meet the assumption for a nonparametric test (ordinal and nominal data)
Choosing Statistical Procedures
Two Independent Variables
Interval or RatioIndependent
t-testDependent
t-testOne-Way ANOVA
Repeated Measures ANOVA
Two -Factor ANOVA
Two-Factor ANOVA
Repeated Measures
OrdinalMann-
Whitney UWilcoxon
Kruskal-Wallis
Friedman
Nominal Chi-Square Chi-Square Chi-Square
Factorial Designs
Independent Groups
Dependent Groups
Measurement Scale of the Dependent
Variable
One Independent Variable
Two Levels More than 2 Levels
Two Independent
Groups
Two Dependent
Groups
Multiple Independent
Groups
Multiple Dependent
Groups
Mann Whitney U Test• Nonparametric equivalent
of the independent t test– Two independent groups– Ordinal measurement of the
DV– The sampling distribution of
U is known and is used to test hypotheses in the same way as the t distribution.
Mann Whitney U Test• To compute the Mann
Whitney U:– Rank the scores in both
groups (together) from highest to lowest.
– Sum the ranks of the scores for each group.
– The sum of ranks for each group are used to make the statistical comparison.
Income Rank No Income Rank25 12 27 1032 5 19 1736 3 16 2040 1 33 422 14 30 737 2 17 1920 16 21 1518 18 23 1331 6 26 1129 8 28 9
85 125
Non-Directional Hypotheses
• Null Hypothesis: There is no difference in scores of the two groups (i.e. the sum of ranks for group 1 is no different than the sum of ranks for group 2).
• Alternative Hypothesis: There is a difference between the scores of the two groups (i.e. the sum of ranks for group 1 is significantly different from the sum of ranks for group 2).
Computing the Mann Whitney U Using SPSS
• Enter data into SPSS spreadsheet; two columns 1st column: groups; 2nd column: scores (ratings)
• Analyze Nonparametric 2 Independent Samples
• Select the independent variable and move it to the Grouping Variable box Click Define Groups Enter 1 for group 1 and 2 for group 2
• Select the dependent variable and move it to the Test Variable box Make sure Mann Whitney is selected Click OK
Interpreting the OutputRanks
10 12.50 125.00
10 8.50 85.00
20
Income StatusIncome Producing
No Income
Total
Equal Rights AttitudesN Mean Rank Sum of Ranks
Test Statisticsb
30.000
85.000
-1.512
.131
.143a
Mann-Whitney U
Wilcoxon W
Z
Asymp. Sig. (2-tailed)
Exact Sig. [2*(1-tailedSig.)]
Equal RightsAttitudes
Not corrected for ties.a.
Grouping Variable: Income Statusb.
The output provides a z score equivalent of the Mann Whitney U statistic.
It also gives significance levels for both a one-tailed and a two-tailed hypothesis.
Generating Descriptives for Both Groups
• Analyze Descriptive Statistics Explore
• Independent variable Factors box
• Dependent variable Dependent box
• Click Statistics Make sure Descriptives is checked Click OK
Wilcoxon Signed-Rank Test• Nonparametric equivalent of
the dependent (paired-samples) t test– Two dependent groups
(within design)– Ordinal level measurement of
the DV.– The test statistic is T, and the
sampling distribution is the T distribution.
Wilcoxon Test• To compute the Wilcoxon T:
– Determine the differences between scores.
– Rank the absolute values of the differences.
– Place the appropriate sign with the rank (each rank retains the positive or negative value of its corresponding difference)
– T = the sum of the ranks with the less frequent sign
Pretest Posttest Difference Rank36 21 15 1123 24 -1 -148 36 12 1054 30 24 1240 32 8 732 35 -3 -350 43 7 644 40 4 436 30 6 529 27 2 233 22 11 945 36 9 8
Non-Directional Hypotheses
• Null Hypothesis: There is no difference in scores before and after an intervention (i.e. the sums of the positive and negative ranks will be similar).
• Non-Directional Research Hypothesis: There is a difference in scores before and after an intervention (i.e. the sums of the positive and negative ranks will be different).
Computing the Wilcoxon Test Using SPSS
• Enter data into SPSS spreadsheet; two columns 1st column: pretest scores; 2nd column: posttest scores
• Analyze Nonparametric 2 Related Samples• Highlight both variables move to the Test Pair(s) List
Click OKTo Generate Descriptives:• Analyze Descriptive Statistics Explore• Both variables go in the Dependent box • Click Statistics Make sure Descriptives is checked
Click OK
Interpreting the OutputRanks
10a 7.40 74.00
2b 2.00 4.00
0c
12
Negative Ranks
Positive Ranks
Ties
Total
POSTTEST - PRETESTN Mean Rank Sum of Ranks
POSTTEST < PRETESTa.
POSTTEST > PRETESTb.
POSTTEST = PRETESTc.
Test Statisticsb
-2.746a
.006
Z
Asymp. Sig. (2-tailed)
POSTTEST -PRETEST
Based on positive ranks.a.
Wilcoxon Signed Ranks Testb.
The T test statistic is the sum of the ranks with the less frequent sign.
The output provides the equivalent z score for the test statistic.
Two-Tailed significance is given.