Normal Distribution

• Bell shaped curve
• In normal distribution curve, Mean=Mode=Median
• Standard deviation = 1
• The shape of normal distribution depends on mean, standard deviation and the number and nature of observation.
• Total area of this bell–shaped curve =1
• Confidence interval =Mean ± Standard error
• 68.27% CI = Mean ± S.E
• 95.45% CI = Mean ± 2 S.E
• 99.73% CI = Mean ± 3 S.E

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Type of Errors

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>Type I Error (α): - the probability that difference shown occurred due to chance
It is known as level of significance / critical region / region of rejection
P [reject H0 when it is true]

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>Type II Error (β): - if a true difference of a stated magnitude existed but the study would not have picked up as statistically significant.
P [accept HA when it is false]

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>Power of Study (1 – β): - the probability that if a true difference of stated magnitude existed then the study would have picked up as statistically significant.

Test of Hypothesis

• Fix Null Hypothesis: there is no difference /  relation between the groups
• Fix Alternative Hypothesis : there is significant difference /  relation between the groups
• Level of Significance (α)
• Test of Significance  (ex) Z = | x1 – x2 | / SE (x1 – x2)
• If |Z|> Zα - if the computed value of test statistic is greater than the critical or significance value then we say that it is significant and the null hypothesis is rejected at level of significance α.

Test of Significance

Parametric Tests: -

• Mean and SD as Parameters
• Large Sample Size
• Followed Normal Distribution

Nonparametric Tests: -

• Followed not normal distribution
• Small sample size
• Use median / ranks

Parametric Tests: -

Paired t test

• Calculate the difference in each set of paired observation.
• Same people are sampled on 2 different occasions.(ex: glucose test before and after)

Unpaired / Independent t Test

Two groups of subjects are sampled in 1 occasion. (Ex: nutritional study (1 occasion) total 25 candidates are there, 13 are provided with normal diet vitamin supplements and 12 are provided with normal diet)

Correlation

• To find out if there is any correlation between the two variables under study.
• Karl pearson a British biometrician developed a formula for correlation.
• Correlation coefficient between two random variables X and Y usually denoted by r(X,Y) = Cov (X,Y) / xy
• X – Independent Variable, Y – Dependent Variable
• Its value ranges from -1 to +1

Regression Techniques

• The linear Regression Model: Y = a + b X ,
• Where Y is Dependent Variable, X is Independent variable
•  b is Slope
• a =  Y – b * X
• a = intercept for which X = 0
• The slope b will explain that for each unit change in x, y increase.

Non Parametric Tests

• U test : - test difference in ranks score of two different groups
• Wilcoxon Signed rank test: - within difference in ranks of two related groups
• Median Test:- To test difference b/w medians of two different groups
• Kruskal Wallis Test: - Difference in ranks of three or more independent groups
• Chi square test:- find difference b/w 2 categorical data

McNemar chi sq: - within difference in proportion for paired 2x2