Hypothesis Testing Flashcards
Hypothesis
Statement about one or more populations
Steps of hypothesis testing
- State hypothesis
- Identify appropriate test statistic and its probability distribution
- Specify significance level
- State decision rule
- Collect data and calculate test statistic
- Make statistical decision
- Make economic or investment decision
Describe and interpret choice of null and alternative hypotheses
Null - hypo to be tested
Alt - hypo accepted when null rejected (set up as suspected condition with one-sided test, or for neutrality use two-sided)
One tailed vs. two tailed tests
One tail - equals hypothesis (could be bigger or smaller)
Two tail - greater/less than or equal to hypothesis (halve significance level)
Test statistic
Quantity, calculated based on sample, whose value is basis for deciding whether or not to reject the null hypothesis
(sample statistic - value of hypo population parameter) / standard error of sample statistic
Std error = std dev / square root n
Type I error
Reject true null hypo. α is prob of type I error.
Type II error
Not reject false null hypo. β is prob of type II error.
Significance level and how used in hypothesis testing
Probability of committing a type I error - denoted with α
Decision rule
If test statistic is more extreme than given value based on certain significance level, reject null hypothesis
power of a test
Probability of correctly rejecting the null (inverse of significance level)
relationship of confidence intervals and hypothesis tests
In two tailed tests, (1-α) confidence intervals and hypothesis tests will produce the same results
Distinguish between statistical result and economically meaningful result
Statistically significant result requires rejection of null hypothesis
Explain and interpret p-value as it relates to hypothesis testing
Smallest level of significance at which null hypothesis can be rejected. Smaller the p-value, stronger the evidence against the null hypothesis (i.e. more sure of rejecting)
Test statistic and results interpretation re population mean of both large and small samples when population is normally or approximately distributed and variance KNOWN
z = x-μ / (σ / sq rt n)
Test statistic and results interpretation re population mean of both large and small samples when population is normally or approximately distributed and variance UNKNOWN
t (sub n-1) = X-μ / (s / sq rt n)
Test statistic and results interpretation re equality of population means of two at least approximately normally distributed populations based on independent random samples with EQUAL assumed variances
t = (x1-x2) - (μ1-μ2)
___________
(PE/n1+PE/n2)^1/2
PE = (n1-1)s1^2 + (n2-1)s2^2
_________________
n1+n2-2
df = n1+n2-2
Test statistic and results interpretation re equality of population means of two at least approximately normally distributed populations based on independent random samples with UNEQUAL assumed variances
Same t test formula, but use standard deviation in place of the pooled estimator. CALCULATE TEST STATISTIC FIRST b/c whether it’s significant might be obvious.
df = (s1^2/n1 + s2^2/n2) ^2
_________________
[(s1^2/n1)^2]/n1 + [(s2^2/n2)^2/n2
Test statistic and results interpretation re mean difference of two normally distributed populations (SAMPLES DEPENDENT)
t = d - μ
____
s
df = n-1 d = sample mean difference
Test statistic and result interpretation re variance of normally distributed population
χ^2 = (n-1)s^2
______
σ^2
Chi square test requires random sample and normally distributed population
df = n - 1
For less than hypotheses, lower α point is (1-α) on chi square chart
Test statistic and result interpretation re equality of variances of two normally distributed populations based on two independent random samples
F = sample1 variance / sample2 variance [FLIP TO LARGER]
df1 = n1-1 df2 = n2-1
Not equal to - reject if greater than upper α/2 point of f-distribution
greater/less than - reject if greater than upper α point of f-distribution
Parametric vs. nonparametric tests and when appropriate
Parametric tests concern parameters and rely on assumptions
Nonparametric tests not concerned with parameters or has minimal assumptions. Use when: data do not meet distributional assumptions, data given in ranks, when hypothesis addressing does not concern parameter
t-distribution
Symmetrical distribution defined by single parameter: degrees of freedom. Fatter tails than normal distribution.
