Estimation and Hypothesis Testing

Estimation

process of finding likely value for a population parameter based on a sample

Point Estimate

single valued estimate of a population parameter like mean or proportion

Interval Estimate

range of values for population parameter with a 95% CI

PE ± margin of error

A better estimate is

narrow or tight estimate

lower variation or high sample size

A worse estimate is

wide or loose estimate

higher variation or less sample size

Calculate confidence interval for large n>120

µ = x̄ ± Z_0.95 σ/√n

Calculate confidence interval for small n<120

µ = x̄ ± t_0.95 s/√n

Standard Error or margin of error

estimation of the mean parameter in the population

Hypothesis Testing

uses a test statistic to check claims made about population parameters

Generate Hypothesis Testing

process of identifying something of concern then generating opposing hypothesis

Null hypothesis H₀

general belief about the investigation that is assumed true until tested

Alternative Hypothesis H₁/H_A

what the researchers want to show to negate the null implying this one is true

One-tailed test

test null hypothesis in which alternative only has one end

little sliver on graph 2.5%

One-tailed test Results

H₀ µ ≥ 12 and H₁ µ < 12 or H₀ µ ≤ 12 and H₁ µ > 12

Two-tailed Test

test of null in which alternative has two ends

both slivers on the graph 5%

Two-tailed Test Results

H₀ µ =12 or H₀ µ ≠ 12

If P-value < 0.05

reject the null or significant result

If P-value≥ 0.05

fail to reject (FTR) null or not significant

If CI includes null or 0

fail to reject (FTR) H₀ or not significant

If CI excludes null value or 0

reject the H₀ or significant

Type 1 or alpha error

incorrectly reject H₀ or false positive

Minimizing Type 1 errors

controlling bias in study design and adjusting for cofounding

Type 2 or beta error

incorrectly FTR H₀ or false negative

Minimizing Type 2 errors

increase the sample size to reject the null

One-Sample T-test

compare the sample mean to an expected population mean

One sample T-test variables

1 scale or quantitative variable is normally distributed

One-Sample T-test Null

mean of a population for a given variable equals to a numeric value

Reporting One Sample T-test

test value mean±SD P-value CI

Median or Runs

used if scale or quantitative variable is not normally disturbed

Reporting Runs Test

test value median (Q₁-Q₂) P-values