Hypothesis testing about means (HtestAboutMeans
)¶
-
class
cerebunit.statistics.hypothesis_testings.aboutmeans.
HtestAboutMeans
(observation, prediction, test_statistic, side='not_equal')¶ Hypothesis Testing (significance testing) about means.
1. Verify necessary data conditions.
Statistic Interpretation sample size, n experiment/observed n optionally: raw data experiment/observed data array Is \(n \geq 30\)?
If not, check if data is from normal distribution.
If both returns NO, you can’t perform hypothesis testing about means. Instead use sign test.
If either of the above two question returns YES continue below.
2. Defining null and alternate hypotheses.
Statistic Interpretation sample statistic, \(\mu\) experiment/observed mean null value/population parameter, \(\mu_0\) model prediction null hypothesis, \(H_0\) \(\mu = \mu_0\) alternate hypothesis, \(H_a\) \(\mu \neq or < or > \mu_0\) - Two-sided hypothesis (default)
- \(H_0\): \(\mu = \mu_0\) and \(H_a\): \(\mu \neq \mu_0\)
- One-side hypothesis (left-sided)
- \(H_0\): \(\mu = \mu_0\) and \(H_a\): \(\mu < \mu_0\)
- One-side hypothesis (right-sided)
- \(H_0\): \(\mu = \mu_0\) and \(H_a\): \(\mu > \mu_0\)
3. Assuming H0 is true, find p-value.
Statistic Interpretation sample size, n experiment/observed n standard error, SE experiment/observed SE = \(\frac{SD}{\sqrt{n}}\) or or standard deviation, SD experiment/observed SD t-statistic, t test score, \(t = \frac{\mu - \mu_0}{SE}\) degree of freedom, df \(df = n - 1\) z-statistic, z (standard) test score, \(z = \frac{\mu - \mu_0}{SD}\) Using t and df look up table for t-distrubution which will return its corresponding p. If the denominator is
SD
then value of z is seen in a normal distribution to return its corresponding p.4. Report and Answer the question, based on the p-value is the result (true H0) statistically significant?
Answer is not provided by the class but its is up to the person viewing the reported result. The results are obtained calling the attributed
.statistics
and.description
. This is illustrated below.ht = HtestAboutMeans( observation, prediction, score, side="less_than" ) # side is optional score.description = ht.outcome score.statistics = ht.statistics
Arguments
Argument Representation Value type first experiment/observation dictionary that must have keys; “mean” and “sample_size” second model prediction float third test score/z or t-statistic dictionary with key; “z” or “t” fourth sidedness of test string; “not_equal” (default) or “less_than”, “greater_than” The constructor method generates
statistics
andoutcome
(which is then assigned todescription
within the validation test class where this hypothesis test class is implemented).-
static
alternate_hypothesis
(side, symbol_null_value, symbol_sample_statistic)¶ Returns the statement for the alternate hypothesis, Ha.
-
static
null_hypothesis
(symbol_null_value, symbol_sample_statistic)¶ Returns the statement for the null hypothesis, H0.
-
test_outcome
()¶ Puts together the returned values of
null_hypothesis()
,alternate_hypothesis()
, and_compute_pvalue()
. Then returns the string value for.outcome
.