Question

In a meaningful and substantive manner, do you agree or disagree with the ways the choice to deal with the outliers(a, b, c)? Explain your position at length.

(a) A participant estimating ordinary people’s heights estimates one woman’s height to be “84 inches” tall.

The participant may have got confused and said an incorrect number. Using raw data to double check her height and make sure that this has been accurately recorded. This number is really high and unbelievable. This is an outlier and I think this participants data is unusable but if she is actually 7 foot than we can keep this data just in case.

(b) In a study of memory for ordinary objects, one participant scores 0 out of 15.

This participant may not have understood and resulted in a low score. Using raw data to double check this and deciding whether to keep this 0 or not. I don't think this should be kept in the data because it seems like this participant purposely scored a zero and didn't put in an effort, this result would severely drop the average scores. This is an outlier that should be stored away from the data.

(c) In response to a question about how many “close friends” she has, one participant, writes “32.”

This participant may have a different understanding of close friends or she may feel like she has a lot of close friends. Use raw data to double check this number and decide whether to keep this or not. I would not include this number because it is obviously too high and I don't think it's possible to have 32 close friends. This number would increase the average score of all the participants.

Answer 1

a) The height of the woman, though might actually be 7 ft, is definitely an outlier as can be seen by comparing with other people's heights. If we are estimating ordinary people's heights, we should be interested in the average heights and not unusually outlier heights. Hence, it makes sense to either do a significance test for this observation, or use median as a measure of central tendency as this data point will distort the mean.

b) The memory for ordinary objects should not be unusually low number like 0. This can be easily concluded looking at a sample of raw data. However, removing this from the sample means we are inadvertently trying to bump up the mean. Though this does not look like representative of the sample, it should still be kept and not ignored so that we can later address such serious cases of possible memory problems. Percentile scores can definitely be used to ensure such outliers do not distort the average, and we can also present the relative positioning this way. A Zero percentile doesn't always mean the score was 0, it just means that score was the lowest.

c) 32 friends could be possible for a person extremely well-versed in social and networking skills, but it definitely looks to be an overstatement that they are all close friends. This can be considered an outlier if we are only interested in the average "close friends" score of the participants. To take care of the outlier, one can use the mode or the median number of close friends as the average.