- Statistics Tutorial
- Home
- Adjusted R-Squared
- Analysis of Variance
- Arithmetic Mean
- Arithmetic Median
- Arithmetic Mode
- Arithmetic Range
- Bar Graph
- Best Point Estimation
- Beta Distribution
- Binomial Distribution
- Black-Scholes model
- Boxplots
- Central limit theorem
- Chebyshev's Theorem
- Chi-squared Distribution
- Chi Squared table
- Circular Permutation
- Cluster sampling
- Cohen's kappa coefficient
- Combination
- Combination with replacement
- Comparing plots
- Continuous Uniform Distribution
- Cumulative Frequency
- Co-efficient of Variation
- Correlation Co-efficient
- Cumulative plots
- Cumulative Poisson Distribution
- Data collection
- Data collection - Questionaire Designing
- Data collection - Observation
- Data collection - Case Study Method
- Data Patterns
- Deciles Statistics
- Dot Plot
- Exponential distribution
- F distribution
- F Test Table
- Factorial
- Frequency Distribution
- Gamma Distribution
- Geometric Mean
- Geometric Probability Distribution
- Goodness of Fit
- Grand Mean
- Gumbel Distribution
- Harmonic Mean
- Harmonic Number
- Harmonic Resonance Frequency
- Histograms
- Hypergeometric Distribution
- Hypothesis testing
- Interval Estimation
- Inverse Gamma Distribution
- Kolmogorov Smirnov Test
- Kurtosis
- Laplace Distribution
- Linear regression
- Log Gamma Distribution
- Logistic Regression
- Mcnemar Test
- Mean Deviation
- Means Difference
- Multinomial Distribution
- Negative Binomial Distribution
- Normal Distribution
- Odd and Even Permutation
- One Proportion Z Test
- Outlier Function
- Permutation
- Permutation with Replacement
- Pie Chart
- Poisson Distribution
- Pooled Variance (r)
- Power Calculator
- Probability
- Probability Additive Theorem
- Probability Multiplecative Theorem
- Probability Bayes Theorem
- Probability Density Function
- Process Capability (Cp) & Process Performance (Pp)
- Process Sigma
- Quadratic Regression Equation
- Qualitative Data Vs Quantitative Data
- Quartile Deviation
- Range Rule of Thumb
- Rayleigh Distribution
- Regression Intercept Confidence Interval
- Relative Standard Deviation
- Reliability Coefficient
- Required Sample Size
- Residual analysis
- Residual sum of squares
- Root Mean Square
- Sample planning
- Sampling methods
- Scatterplots
- Shannon Wiener Diversity Index
- Signal to Noise Ratio
- Simple random sampling
- Skewness
- Standard Deviation
- Standard Error ( SE )
- Standard normal table
- Statistical Significance
- Statistics Formulas
- Statistics Notation
- Stem and Leaf Plot
- Stratified sampling
- Student T Test
- Sum of Square
- T-Distribution Table
- Ti 83 Exponential Regression
- Transformations
- Trimmed Mean
- Type I & II Error
- Variance
- Venn Diagram
- Weak Law of Large Numbers
- Z table
- Statistics Useful Resources
- Statistics - Discussion

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

A statistical hypothesis is an assumption about a population which may or may not be true. Hypothesis testing is a set of formal procedures used by statisticians to either accept or reject statistical hypotheses. Statistical hypotheses are of two types:

**Null hypothesis, ${H_0}$**- represents a hypothesis of chance basis.**Alternative hypothesis, ${H_a}$**- represents a hypothesis of observations which are influenced by some non-random cause.

suppose we wanted to check whether a coin was fair and balanced. A null hypothesis might say, that half flips will be of head and half will of tails whereas alternative hypothesis might say that flips of head and tail may be very different.

$ H_0: P = 0.5 \\[7pt]
H_a: P \ne 0.5 $

For example if we flipped the coin 50 times, in which 40 Heads and 10 Tails results. Using result, we need to reject the null hypothesis and would conclude, based on the evidence, that the coin was probably not fair and balanced.

Following formal process is used by statistican to determine whether to reject a null hypothesis, based on sample data. This process is called hypothesis testing and is consists of following four steps:

**State the hypotheses**- This step involves stating both null and alternative hypotheses. The hypotheses should be stated in such a way that they are mutually exclusive. If one is true then other must be false.**Formulate an analysis plan**- The analysis plan is to describe how to use the sample data to evaluate the null hypothesis. The evaluation process focuses around a single test statistic.**Analyze sample data**- Find the value of the test statistic (using properties like mean score, proportion, t statistic, z-score, etc.) stated in the analysis plan.**Interpret results**- Apply the decisions stated in the analysis plan. If the value of the test statistic is very unlikely based on the null hypothesis, then reject the null hypothesis.

Advertisements