Final Project Significance Testing

1. Final ProjectSignificance Testing Excellent Student #1 Excellent Student #2 Don’t cry for me Canyon Crest A survey study about depression at CCA

2. Introduction Depression is very common among teenagers as well as adults. After finding some national statistics that suggested the rates of depression were around 20% among teenagers, we decided to survey students at CCA to compare our school’s statistics against national statistics about depression rates. Our questions were based off the underlying information provided by various national statistics, and asked about family history (if any immediate family members had ever suffered from depression), leading causes of depression, and whether the student had ever suffered from depression. By collecting yes or no survey answers to our six questions, we were able to conduct hypothesis testing to verify if students at CCA are actually less likely, or more likely to suffer from depression than other teens in the United States.

3. Background Information on Depression • In general, more teenage girls than boys are treated for depression. The leading explanation for this discrepancy has been linked to differing social expectations and norms of communication. Social factors often trigger depressive episodes in teenage girls. • Depression is commonly caused by environmental or school related stresses, traumatizing events, or conflicts between the teen and family, friends, or teachers. • Some major signs of depression are: faltering school performance, failing relationships, substance abuse, excessive sleeping, and changes in eating habits. • Only a small percentage of teens with depression are actually diagnosed and treated with either medication or therapy, although nearly 80% of teens suffering from depression could be successfully treated and later be less likely to suffer from depression in adulthood.

4. National Statistics We found four national statistics from the following websites: www.teendepression.org/articls5.html http://kidshealth.org/teen/your_mind/feeling_sad/depression.html. -20% of teens will experience depression before adulthood Question #1: Have you ever suffered from depression -Less than 33% of teens with depression get help Question #2: Have you ever been medically treated for depression? -30% of teens who suffer from depression also develop a substance abuse problem Question #4: Have you taken part in alcohol or drug consumption because of your depression? -Up to 45% of teens who suffer from depression have immediate family members who also suffer from depression. Question #3: Does anyone in your immediate family suffer from depression?

5. Randomization Design We used a systematic sampling design. Beginning with the last page of the master schedule, we selected every fourteenth teacher’s second period class. We sent e-mails to Caston, Haas, Nguyen, Simmons, Thow, Yates. We ended up surveying Mrs. Caston’s second period English Class, Ms. Simmons’ second period Chemistry class, and Ms. Yates’s second period dance class. Our total sample size was 73. 1. Have you ever suffered from depression? 2. Have you even been medically treated for depression? 3. Does anyone in your immediate family suffer from depression? 4. Have you ever taken part in drug or alcohol consumption due to depression? 5. Have you ever experienced depression from solely the atmosphere around you (community, family, and friends)? 6. Have you ever experienced depression but weren’t able to point to any particular sad or stressful event? Our surveys were environmentally friendly, we fit four surveys to a page.

6. Histogram of DataNational v. CCA Our national statistics were compiled by the National Institute of Health, and the websites mentioned before are sites which collect information so that teens and parents can educate themselves about depression and find treatment centers. National Statistic to Question: 1. 20% of teens suffer from depression. 2. Less than 30% get help. 3. Up to 45% have family members who suffer from depression. 4. 30% of teens have used drugs or alcohol because of depression. 5. 25% suffer from environmental depression. CCA is graphed as Series 1, the light purple. The national statistics are graphed in Series 2, the magenta bars.

7. Raw Data Analysis - CCA CCA Statistic to Question 1. 45.20% of teens surveyed have experienced depression. 2. 27.27% (of those who have had depression) have gotten help. 3. 35.62% have family members suffer from depression. 4. 16.44% (of those who have depression) have used alcohol or drugs because of their depression. 5. 50.68% (of those who have depression) suffer from environmental depression. Question #: Yes No 1. 33 40 2. 9 64 3. 26 47 4. 12 61 5. 37 36 We discarded question 6, because there was not an exact national statistic to compare our results with, however, 45.20% of CCA responses stated they had experienced depression but could not pin point a specific catalyst.

8. Requirements/Results The requirements for hypothesis testing are: 2 N I P – 2 results (yes or no), set number of trials (73 surveys), independent trials ( one survey did not influence another), set p value SRS – To do hypothesis testing the sample must be a simple random sample N * P is greater than or equal to 5, N * Q is greater than or equal to 5 All the requirements are met. Our sample size is larger than 30, so our results can be treated as a normal distribution. Our sample population was randomly selected, and both np and nq are greater than five. The binomial requirements are also met, as described above. In general, results from confidence intervals will not match results calculated if using the traditional or p-value method. The results from the p-value and the traditional method are equivalent, however confidence intervals use an estimated standard deviation based off of p-hat. The use of p-hat values changes the results. This will occur in our calculations as well, as the confidence intervals are constructed for p-hat estimations and values.

9. Hypothesis Testing Problem #1: A national statistic released from the National Institute of Health claims that the percentage of teens who suffer from depression is 20%. The results from our survey provided a sample statistic of a 45.20% rate of depression among teens. Test the claim that p is equal to 20%. • n = 73, p-hat = .4520, significance level = .05 • Ho: p = .20 • Ha: p > .20 • Z = p-hat – p / (√pq / n) • Significance Level = .05, right tailed  .025 Rejection Region begins at 1.96 Calculation Results: Z Test Stat = 5.38 P Value = 1-.999 = .0001 .0001 < .05 Reject Ho in favor of Ha. Sufficient evidence to support the claim that the percentage of teens with depression is higher than 20%. 95% Confidence Interval of P-Hat (.4025) We are 95% confident that, for our survey results, the true population proportion of teens with depression is between .3378 < p < .566. Reject the Ho, p of 0.20 is not w/in the interval 1.96 5.38

10. Hypothesis Testing • Problem # 2: A teen health and awareness website claims that less than 33% of teens who experience depression seek help or are medically treated. From a sample of 33 students, it was shown that only 9 of the students who suffered from depression received medical help. Test the claim that less than 33% of teens receive help. **Our total sample size was 73, however of those 73 students, 33 have suffered from depression. The sample size (n) for this problem has been reduced to 33 for statistical accuracy. We are attempting to test a claim that only pertains to students who have experienced depression, not of all students surveyed.** Ho: p = .33 p-hat = .27272727 significance level = .05 Ha: p < .33 n = 33 one tailed  -1.96 Calculation Results: Z Test Stat = -.701 P-Value = .2420 .2420 < .05 – Not less than Significance Level Fail to Reject the Ho. There is not sufficient evidence to support the claim that the % of teens who receive help is less than 33%. -1.96 -.70 We are 95% confident that the true population proportion is within: .2609 < p <.2845 Reject the Ho

11. Hypothesis Testing • Problem # 3: A national statistics claims that 25% of teens suffer from environmental depression, in general terms, a more severe form of mood swings triggered by interactions with family, friends, and school or work environments. From a sample size of 73 students, 37 claimed that they have experienced environmental depression. Test the claim that 25% of teens experience environmental depression using a two tailed test. • Ho: p = .25 Ha: p ≠ .25, n = 73, x = 37, significance level = .05 (1-alpha) • Rejection Region begins with + or - 1.645 Calculation Results: Z Test Stat = 5.068 P-Value = .0001 x 2 = .0002 .0002 < .05 Reject the Ho in favor of Ha. There is sufficient evidence to support the claim that p is not equal to 25%, that the percentage of teens who suffer from environmental depression is not equal to 25 %. We are 95% confident that p is w/in this interval: .41 < p < .60 – Reject Ho 1.645 5.068 As stated before, all the problems met the requirements for hypothesis testing, and the variation between the projected CI and p value method is a result of using sample statistics.

12. Conclusion Our survey results differed from the national statistics we found. Our results yielded that around 45% of teens have experienced depression, which is significantly higher than the national statistic of 20%. Only 27.27% of teens who suffered from depression received help, however this falls relatively close to the national average of less than 33% of teen treatment. 16.4% turned to alcohol or drugs as a result of depression. Our results are interesting and surprising, but not entirely accurate. However, it is clear that a small percentage of teens actually treat their depression. Our survey statistic and the national statistic were similar on this account. However, our results do not necessarily prove that depression is more common at CCA. Our survey did not define depression or explain how to recognize the signs of depression. Because a low number of students were actually medically treated for depression, our survey results depend of the accuracy of student interpretations of depression. It is possible that students answered yes to having suffered from depression when it could have been a mood swing or other condition.