1 / 13

Significance Testing

Significance Testing. Wed, March 24 th. Statistical Hypothesis Testing. Procedure that allows us to make decisions about pop parameters based on sample stats Example – mean aver salary of all workers = $28,985 (pop mean =  y)

omer
Download Presentation

Significance Testing

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Significance Testing Wed, March 24th

  2. Statistical Hypothesis Testing • Procedure that allows us to make decisions about pop parameters based on sample stats • Example – mean aver salary of all workers = $28,985 (pop mean = y) • Sample of 100 African Amer workers, mean salary = $24,100 (samp mean = ybar) • Is that a significant difference from the population? Or not enough of a difference to be meaningful?

  3. Steps of Hypothesis Tests • 1) State the Research & Null Hypotheses: • Research Hyp (H1): state what is expected & express in terms of pop parameter • Ex) y does not = $28,985 (Af Am salary doesn’t = pop salary; the groups differ) • Null Hyp (Ho): usually states there is no difference/effect (opposite of H1). • Ex) y = $28,985 (Af Am salary = pop salary)

  4. (cont.) • Note: Research Hyp (H1) also known as alternative hypothesis (Ha) • Null hypothesis is tested; we hope to reject it & find support for H1

  5. 1 & 2-tailed hypotheses • (Step 1 cont.) – possible to specify 1 or 2-tailed research hyp (H1) • 1-tailed is a directional hyp (expect  > some value or < some value) • 2-tailed is nondirectional (specify  is not equal to some value) • Use 1-tailed when you can rely on theory to know what to expect; 2-tailed if no prior expectation • Here, we could expect H1: y < $28,985 (1-tailed test that specifies a lower salary)

  6. Steps 2&3 : Select & Calculate the Appropriate Test Statistic • Here, a 1-sample z test to compare a sample mean to a known pop mean • Z = (Ybar – y) / ybar • Where ybar is std error and = y / sqrt N and ybar is sample mean; y is pop mean • Salary example: y = $28,985, y = $23,335ybar = $24,100 and N=100, so… • ybar =23,335 / sqrt(100) = 2,333.5

  7. Example (cont.) • Z = 24,100 – 28,985 / 2,333.5 = -2.09 • Step 4 – use unit normal table to make a probability decision • Look up z score of –2.09 (or 2.09) in column C (proportion beyond z), find .0183. • This is the prob of getting a sample result this extreme ($24,100) if the null hypothesis is true; called p value

  8. Step 4 (cont.): Decision • We define in advance what is sufficiently improbably to reject the null hypothesis • Find a cutoff point, called  (alpha) below which p must fall to reject null • Usually  = .05, .01, or .001 • Reject null when p <=  • Here, if choose  = .05, we reject null (p = .0183< .05  reject null)

  9. Interpretation • P = .0183 means there is only a 1.83% chance of finding a sample of 100 Afr Amer workers w/mean salary = 24,100 if there is really no difference from overall aver salary. (very unlikely) • Note: if p <  and we reject the null, we can say our findings are ‘statistically significant’; the groups differ significantly

  10. 2-tailed test interpretation • Our example used a 1-tailed test, if we’d made a 2-tailed H1 (y does not = $28,985), we need to adjust the p value • Look up z=-2.09 and find p=.0183, but need to multiple p x 2 if 2-tailed (.0183)x 2 = .0366 • P is still < , so still reject null

  11. Decision Errors • Possible to make 2 types of errors when deciding to reject/fail to reject Ho:

  12. Errors (cont.) • Type 1 error = probability of incorrectly rejecting a true Ho • Type 2 error = probability of failing to reject a false Ho • So when  = .05, we have a 5% chance of incorrectly rejecting Ho (Type 1) • Can be more conservative and use  = .01 (1% chance of Type 1), but then increases Type 2 chances…

  13. Lab 17 • Skip #5

More Related