assumptions……………seriously..! assumptions of parametric data normal distribution parametric...
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Assumptions……………Seriously..! Assumptions of parametric data
◦ Normal distribution Parametric test --- Nonparametric data
= Wrong Conclusion Why? Test Selection Be a Critic Impress your seniors
Four basic assumptions Normally distribution
◦ Different meaning in different context Sampling distribution/error distribution
Homogeneity of variance◦ Same variance of data◦ Groups comparison (same variance of groups)◦ Correlational design (stable variance of a variable across all
levels of other variable) Interval data Independence
◦ Participants data independent of each other and uncorrelated errors (correlational desgin)
◦ Between conditions non-independent b/w participants independent (Repeated Measure design)
Frequency distribution◦ Values of skewness and kurtosis (Sig s = s/s.e◦ P–P plot (Analyze Descriptives P-P plot
cumulative probability of a variable against the cumulative probability of a particular distribution
Z-score of rank orders of data against their own z-scores A diagonal distributed data Normal distribution
Kolmogorov–Smirnov test (K–S test) Shapiro–Wilk test (more power than K-S)
◦ Analyze descriptive statistics explore Normality Plots with tests Non-significant (p > .05) = Normal Distribution
◦ Reporting results: D(df) = test-statistic, p > .05
D = (Symbol for K-S), df = degree of freedom (sample size), test-statistic = K-S Statistic
Limitations◦ Large sample sizes Always Significant
Equal variance◦ In groups data – at least one variable is categorical
All groups have equal variance◦ In correlation – both or all variables are continuous
A variable has equal variance for all levels of other
Levene’s test◦ Analyze descriptive statistics explore◦ Spread vs. level with Levene’s test
Non-significant (p > .05) = Equal Variance◦ Reporting results:
F(df1, df2) = 7.37, p < .01. F = (Symbol for Levene’s test), df = degree of freedom
(categories, sample size), test-statistic = F Statistic Hartley’s Fmax (Variance ratio)
◦ VR= largest group variance/the smallest◦ Smaller than the critical values
Remove the case
Transform the data
Change the score (a lesser evil)
◦ The next highest score plus one
◦ X = (z × s) + X = (mean + 3sd)
◦ The mean plus two standard deviations
Transforming data◦ Doesn’t change relationship b/w variables◦ Changes difference b/w variables
Choosing a transformation◦ trial and error◦ Levene’s test (Use Transformed option)
Types:◦ Log transformation (log(Xi))◦ Square root transformation (√Xi)◦ Reciprocal transformation (1/Xi)◦ Reverse score transformations
Evils of Transformation
Non-parametric tests
Robust methods
◦ Trimmed mean
◦ Bootstrap