Statistics Dictionary

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Binomial Probability Negative Binomial Random Variable Neyman Allocation Nominal Scale Nonlinear Transformation Non-Probability Sampling Nonresponse Bias Normal Distribution Normal Random Variable Null Hypothesis Null Set Observational Study One-Sample t-Test One-Sample z-Test One-stage Sampling One-Tailed Test One-Way ANOVA One-Way Table Optimum Allocation Ordinal Scale Orthogonal Comparisons Outer Product Outlier Paired Data Parallel Boxplots Parameter Pearson Product-Moment Correlation Percentage Percentile Permutation Placebo Planned Comparisons Point Estimate Poisson Distribution Poisson Experiment Poisson Probability Poisson Random Variable Population Post Hoc Comparisons Power Precision Probability Probability Density Function Probability Distribution Probability Sampling Proportion Proportionate Stratification P-Value Qualitative Variable Quantitative Variable Quartile Random Effects Model Random Factor Random Number Table Random Numbers Random Sampling Random Variable Randomization Randomized Block Design Randomized Block Experiment Range Ratio Scale Reduced Row Echelon Form Region of Acceptance Region of Rejection Regression Relative Frequency Relative Frequency Table Repeated Measures Design Replication Representative Residual Residual Plot Response Bias Row Echelon Form Row Vector Sample Sample Design Sample Point Sample Space Sample Survey Sampling Sampling Distribution Sampling Error Sampling Fraction Sampling Method Sampling With Replacement Sampling Without Replacement Scalar Matrix Scalar Multiple Scatterplot Scheffe Test Selection Bias Set Significance Level Simple Random Sampling Simple Regression Singular Matrix Skewness Slope Sphericity Standard Deviation Standard Error Standard Normal Distribution Standard Score Statistic Statistical Experiment Statistical Hypothesis Statistics Stemplot Strata Stratified Sampling Subset Subtraction Rule Sum Vector Sums of Squares Symmetric Matrix Symmetry Systematic Sampling T Distribution T Score T Statistic Test Statistic Transpose Treatment t-Test Two-Sample t-Test Two-stage Sampling Two-Tailed Test Two-Way Table Type I Error Type II Error Unbiased Estimate Undercoverage Uniform Distribution Unimodal Distribution Union Univariate Data Variable Variance Variance Inflation Factor Vector Inner Product Vector Outer Product Vectors Venn Diagram Voluntary Response Bias Voluntary Sample Y Intercept z-score

Null Hypothesis

There are two types of statistical hypotheses.

• Null hypothesis. The null hypothesis, denoted by H₀, is usually the hypothesis that sample observations result purely from chance.
  
  
• Alternative hypothesis. The alternative hypothesis, denoted by H₁ or H_a, is the hypothesis that sample observations are influenced by some non-random cause.

For example, suppose we wanted to determine whether a coin was fair and balanced. A null hypothesis might be that half the flips would result in Heads and half, in Tails. The alternative hypothesis might be that the number of Heads and Tails would be very different. Symbolically, these hypotheses would be expressed as

H₀: p = 0.5
H_a: p <> 0.5

Suppose we flipped the coin 50 times, resulting in 40 Heads and 10 Tails. Given this result, we would be inclined to reject the null hypothesis. That is, we would conclude that the coin was probably not fair and balanced.

See also:

Statistics Tutorial: Hypothesis Tests