1 type error upper limit ALWAYS = 0.05
- p>0.05 accept H0 reject Ha, p<0.05 reject H0, accept Ha
- If the P is low H0 has to go!
H0 = null hypothesis, are: do not depend on one another, does not differ, does not affect, etc.
HA = alternative hypothesis, are: dependent on one another, differ, affects, etc.
Dependent value: the measured value (e.g. cm, concentration, ml)
Independent value: unaffected (e.g. age)
Statistical language
Comparing (differ)
𝐻0 : 𝑥𝑚𝑒𝑎𝑛𝐴 = 𝑥𝑚𝑒𝑎𝑛𝐵
𝐻𝐴: 𝑥𝑚𝑒𝑎𝑛𝐴 ≠ 𝑥𝑚𝑒𝑎𝑛𝐵
Correlation(dependent)
𝐻0 : 𝑟 = 0
𝐻𝐴: 𝑟 ≠ 0
Effect:
𝑟=1
2
𝐻0 : ∑ (𝑓0 − 𝑓𝑒𝑥𝑝) = 0; z=0
𝑟=4
𝑟=1
2
𝐻𝐴 : ∑ (𝑓0 − 𝑓𝑒𝑥𝑝) ≠ 0; z≠0
𝑟=4
Topic 1 (Comparing 2 Independent Samples)
-
-
Dispersion of data? Compare variance or range (larger variance/range = high
dispersion)
Symmetrical data distribution? Compare Skewness (closer to 0 = more symmetric;
skewness<0 => skewed more left; skewness>0 skewed more right; -0.5<skewness<0.5
=> fairly symmetric)
Flattened data distribution? Compare Kurtosis (low Kurtosis = more flat distribution)
Higher variability? Compare standard deviation (high SD = high variability)
Accurate estimate of mean? Compare SE (high SE = low accuracy of mean)
Leptokurtic? Compare Kurtosis (K>0)
Mesokurtic? Compare Kurtosis (K=0)
Platykurtic? Compare Kurtosis (K<0)
Normality
-
Shapiro-Wilk Test
- Descriptive Statistics → select variables → Normality → Shapiro-Wilk (unselect
the other box above) → Histogram
- If p-value is > (bigger) than 0.05 accept H0 = the data follows a normal
distribution (if p < 0.05 reject H0, accept HA)
Mann-Whitney Test (U-test)
-
Your data followed a NOT normal distribution!
If your data is not normal then you can no longer compare means and you must
compare U variables. Not mean variables!
If data doesn't fit normal distribution it is nonparametric (the parameters cannot be
expressed in a normal distribution)
Select Nonparametrics → Comparing 2 independent samples
Confident limits of mean (Upper and lower limit)
-
H0: mean = value given, HA: mean ≠ value given
Find upper and lower limits, is the mean of the variable within these limits?
Yes, accept H0.
- E.g. Value given in question 3
- Upper limit = 4.41, Lower limit = 2.83. Hence, mean of 2 values = 3.62
- In conclusion 3.62 = 3, so we accept H0
Homogeneity Test (Do samples have similar data trends? eg. similar
variance)
-
Levene’s Test = sample size is the same (Same N-Value)
- Descriptive Statistics → t-test, independent by group → options → Select
Levene’s Test → select test value, p-value
- Compare the p-value to 0.05 (H0 = homogenous, HA= not homogeneous)
-
Brown & Forsythe Test = different sample size (Different N-Value)
- Descriptive Statistics → t-test, independent by group → options → Select Brown
& Forsythe Test → select test value (F(1,df)), p-value
- Compare the p-value to 0.05 (H0 = homogenous, HA= not homogeneous)
T- Test: compares samples' means
Student-t-test (2 sample t-test)
-
Your sample was homogenous!
Descriptive Statistics → 2 sample t-test
Cochran-Cox test (t-test with separate variance estimates)
-
Your sample was NOT homogenous!
Descriptive Statistics → C-test
Topic 2 (Comparing Independent and Dependent
Samples)
-
Ordinal? Qualitative Data(language, detail) → Wilcoxon Test
Metric? Quantitative Data(numbers) → Normality test
Normality
-
Shapiro-Wilk Test
- Descriptive Statistics → select variables → Normality → Shapiro-Wilk (unselect
the other box above) → Histogram
- If p-value is > (bigger) than 0.05 accept H0 = the data follows a normal
distribution (if p < 0.05 reject H0, accept HA)
Wilcoxon Test
-
Your data is either qualitative or does NOT follow a normal distribution
One sample depends on other
Paired t-test
-
Your data follows a normal distribution
one sample depends on other
Descriptive Statistics → Dependent Sample → get test value (t) and p value
Compare to 1 type error upper limit 0.05 for a conclusion
Topic 3 (Correlation, r-value)
Scatter Graphs
-
Graphs → Scatter Graph
Analyze Line best fit of line (if the line is a good representative of the data points on the
graph)
Check if there are any obvious outliers (1 specific data point that really stands out from
the others)
R-Value
-
If ±0.6<r±0.8 => correlation is strong; ±0.4<r<±0.6 correlation is moderate
Descriptive Statistics → Correlation matrix → Select variables → Options (select the box
with value r) → collect r-value and p-value
Topic 4 (Correlation, dependent by group)
Scatter Graphs
-
Graphs → Scatter Graph
Analyze Line best fit of line (if the line is a good representative of the data points on the
graph)
Check if there are any obvious outliers (1 specific data point that really stands out from
the others)
R-Value
-
Descriptive Statistics → Nonparametrics → Correlation, dependent by group →
Compute: Detailed Report → Variables
Topic 5 (Chi-Squared Test)
2x2 Table
-
Nonparametrics → 2x2 Table → enter values from table into the 4 boxes
Values are ≤ 10 in table
-
Write down values of “Yates correction of chi-square”, and its p-value
Value are > 10 in table
-
Write down values of “Chi-squared (df1)”, and its p-value