To Pass Multi- variate Stats

1. To Pass Multi-variate Stats

2. 1. Problem (A) • “I wonder if the average time (minutes) for students coming to school tends to be greater than the average time (minutes) for students going home for students at Pakuranga College.” • It must contain •  Numerical Variable •  Group Variable •  Population •  Comparison • “I wonder if there is any difference between the average height (cm) for Year 9 students, and Year 13 students for students in the 2013 Census at Schools Database.”

3. 2. Plan (A) “My sample size is 30. I believe this is enough to be representative (characteristic) of the population, and will allows me to make a conclusion about the population based on my sample.”

4. 3. Data (A) “The data comes from the 2013 Census at Schools database. I assume it has been collected accurately and fairly. I have checked the data, and believe it is clean.”

5. 4. Analysis (A) Statistics Summary Table 2 Dot Plots and Box Plots calculate (calculator or by hand) good use of scale, and correctly under each other

6. 4. Analysis (A) Using “I notice…”, make comparing statements about your samples. Require at least 3 good statements supported with numerical and contextual support. (For merit/excellence must be contextual and reflective) Centre - median, mean Unusual Values - unusual, outliers, and extreme values Spread - IQR and range Shape - symmetry, modality (single, bi or other) Shift - relation of one 50% box to the other, or total data Overlap - how much overlap between the two 50% boxes

7. 4. Analysis Using “I notice…” statements describe in context your samples Centre – talk about the median,mean  “I notice that the median height (175cm) for boys tends to be greater than the median height for girls (167cm)”  “I notice that the difference between the mean and median for the boys height is quite large (20 cm), this is due to the 3 unusual values at the top end of the scale (187, 189, 194 cm), and also shows by the right skew on the dot plot”

8. 4. Analysis Using “I notice…” statements describe in context your samples Unusual Values – talk about any values that look strange or ordinary  To say they are outliers they need to be outside the 1.5xIQR  “I notice that there are 3 unusual values at the top end for the boys sample (187, 189, 194 cm). 1.5xIQR is 205cm, therefore these are simply unusual, and not outliers. A possible explanation is that they come from families where there is history of tallness”

9. 4. Analysis Using “I notice…” statements describe in context your samples Spread – talk about the differences in IQR and range between the samples  “I notice that the IQR for boys (35cm) is much larger than for girls (20cm). This means that the boys are less consistent in their middle 50% of data, as the variation is larger. I wonder if that is also evident in the population”  “I notice that there is no apparent difference in the IQR’s for Year 9’s and 13’s bag weight. This tells me that on average the middle 50% of Year 9’s and 13’s vary the same”

10. 4. Analysis Using “I notice…” statements describe in context your samples Shape – talk about symmetry, modality (single, bi or other)  “I notice that the boys distribution is non-symmetrical, with a long tail to the higher values, as compared to the girls data which is quite symmetrical about its median of 167cm”  “I notice that both sets of data shows two peaks (or bimodal). This could be explained by students walking to school for the longer times, and being dropped off by car for the shorter times”

11. 4. Analysis Using “I notice…” statements describe in context your samples Shift – talk about the relation of one 50% box to the other, or total data  “I notice that the boys middle 50% box is shifted towards higher heights than the middle 50% box for females. Could this mean that boys are taller than females back in the population?”

12. 4. Analysis Using “I notice…” statements describe in context your samples Overlap – how much overlap between the two 50% boxes  Calculate If >33% then “likely to be a difference”  None= “There is a difference in my samples …”  Overlap (1 median) = “There is likely a difference …”  Overlap (both medians) = “There is not like to be a difference …”  Complete = “There is no difference in my sample …”

13. 5. Conclusion Statement: (A) “My samples show that there is a difference…, this is shown by …” Answer Problem Question: (A) “Based on my investigation, it is safe to say that the average height of males is greater than the average height of females for my population (Year 11 students in NZ).” or “Based on my investigation, it is too close to say if the average weight of Year 9 school bags are heavier than Year 13 school bags…”

14. 5. Conclusion Sampling Variation: (M) “If I took another sample from the population, I would expect to get similar results to those I have investigated, however I have to remember these are samples, and will vary, and in some cases provide results which I wouldn’t expect” Sample Size: (M) “If I increased my sample size, I would expect to see results with approximately the same median, but with reduced spread, as an increase in sample size reduces the variability with more results within the middle 50% expected”

15. 5. Conclusion Reflection: (E)  Evaluate how good your conclusion is  Does it make sense given the context provided?  Is the inference (conclusion regarding population) realistic?  Would you expect the same results if you repeated with a different sample, or changed the sample size