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Hypothesis Testing and Statistical Inference - Coggle Diagram
Hypothesis Testing and Statistical Inference
Standard Normal Distribution
The standard normal distribution is a specific case of the normal (Gaussian) distribution
Mean (μ) = 0
SD (σ) = 1
Used extensively in z-tests and probability calculations
Z- Score
x = identified score
u = population mean
alpha = standard deviation
Z value tells how many standard deviations the identified score is away from the mean
Standard Normal Distribution
68% of values lie within ±1 SD
95% within ±2 SD
99.7% within ±3 SD
Z-score used in conjunction with the standard normal table
This gives the total amount area in the graph to left side of Z score
Normal distribution is a density curve and total area under = 1 or 100%
https://www.youtube.com/watch?v=2tuBREK_mgE
Statistical Tests
alpha (α) - probability of commiting type 1 error. Also the significance level
Beta (β) - probability of committing type 2 error
Power - probability of correctly rejecting the null hypothesis when it is false (1 - β)
one tail vs two tail
P- VALUE
The p-value is the probability of obtaining a test statistic equal to or more extreme than what was actually observed, under the assumption that the null hypothesis is true.
Types of Statistical Tests for Continuous data
T-test
Paired T-Test
ANOVA
Parametric and equivalent
One Sample T-Test = Wilcoxon Signed Rank Test
Two Sample T-Test = Wilcoxon Rank Sum/Mann Whitney U Test
ANOVA = Kruskal Wallis Test
Paired Two Sample T test = Wilcoxon Signed Rank Sum Test
Remember non-parametrics dont use means but rather medians
T-Tests
One Sample T Test
Is there a difference between a group and the population
x bar = sample mean
Mew 0 = fixed mean (population)
s = sample SD
n = sample size
df = n-1
t-value (after doing calculation) = the number of SDs away from the mean the value is.
Independent Sample T Test/ Two sample t test
Is there a difference between 2 groups
Uses different formulas for equal or unequal variances.
Equal Variance
df = n1 + n2 - 2
Students T
Unequal Variance
df very difficult
Welches Test
Paired Sample T Test
Is there a difference between the same group at different points in time
D bar is the difference.
Null hyp = no difference in means of the two groups.
Df = n-1
Parametric and Numerical. tests means. tests 2 statistics. If more use ANOVA for parametric.
Student's T vs Wleches test
Student T when the two samples have the same variance
ANOVA
Used for more than 2 groups that are parametric.
Null hypothesis = no difference in all the means
tests means
Requires equal variances
Types of Statistical Tests for Categorical Data
Z - Test
Requires assumptions
n.p = or more tnan 10
p(1-n) + or more than 10
Looks at proportions
Chi Squared test
2x2 tables NB
Nulll hypothesis = column and row variables are independent
Alt Hypothesis = columb and row are associated
Use yates continuity if one of the expected values is less than 5
