Analyzing Results of Quantitative Research

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Analyzing Results of Quantitative Research
Descriptive Statistics and Statistical
Significance

• S. Kathleen Kitao
• Kenji Kitao

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• Keywords
• descriptive statistics
• range
• average
• mean
• standard deviation
• statistical significance

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• will discuss
• a few basic statistical procedures and
  statistical terms that you might find useful
• statistical significance

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Calculating Statistics

• In order to better understand what statistical
  calculations mean and how they work, you might
  sometimes find it useful to do at least some of
  the simple calculations by hand.
• Some of the simpler statistical formulas will be
  provided here.
• However, you will probably usually use statistics
  programs to calculate the results of most of your
  research.

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• Your school's computer center may have
  statistical programs available.
• SPSS (Statistical Package for the Social
  Sciences) is one of the well-known programs.
• If your school does not have such programs, you
  can use statistical programs that are available
  on web pages, such as http//glass.ed.asu.edu/stat
  s/analysis/basic.html.

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Descriptive Statistics

• Descriptive statistics are used to describe what
  a characteristic is like
• how high or low the characteristic is
• how strong or weak it is
• what the highest and lowest values are

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• Range
• The range is the distance from the lowest score
  to the highest score.
• You calculate the range by subtracting the lowest
  score from the highest score.
• If the highest score is 15, and the lowest score
  is 5, then the range is 10.

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• Average
• There are three types of average, but one that is
  usually used in statistics is called the mean,
  which is what you probably think of when you
  think of an average.
• The mean (which is called "x bar") is calculated
  by adding up the scores and dividing the total by
  the number of scores.

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• Example
• imagine that your study involves measuring the
  heights of three people.
• One of the people is 160 centimeters tall, one is
  170 centimeters tall, and one is 180.
• To get their average height, you
• add the three numbers
• divide the total (510 centimeters) by the number
  of people (3)
• you find that the mean is 170 centimeters

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• Standard Deviation
• The standard deviation is a statistic that is
  used to describe how much a characteristic
  differs within the group.
• That is, the standard deviation tells you whether
  all the members of the group are fairly similar,
  or whether they are very different from one
  another.

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• If the standard deviation is low, then most of
  the scores are near the mean, and the members of
  the group do not differ much.
• If it is high, then scores are spread out from
  the mean, and the members of the group are more
  different from each other.

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• Example
• Imagine that you are doing a study that includes
  asking participants to rate their ability in
  English on a scale from 0 to 10.
• Imagine that the mean is 5, and the standard
  deviation is 1.
• In that case, about 68 of the ratings would be
  within 1 point (one standard deviation) above or
  below the mean.
• That is, about 68 would be between 4 points and
  6 points.

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• In addition, about 95 of the scores would be
  within two points (two standard deviations) of
  the mean.
• That is, about 95 of the scores would between 3
  and 7 points.
• If the standard deviation is 1 point on a
  measurement that has a range of 10 points, then
  the responses are fairly close to each other.
• That is, the participants' ratings of their
  ability in English are fairly similar to one
  another.

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• If, on the other hand, the standard deviation is
  2, then 68 of the participants rated their
  English between 3 and 7 (two points above or
  below the mean, or one standard deviation), and
  95 between 1 and 9 (four points above or below
  the mean, or two standard deviations).
• The scores are more spread out, and the
  participants' scores are not as similar to each
  other.

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Statistical Significance

• You can also use statistics that compare
  different values.
• First, however, you have to understand
  statistical significance.
• When you are comparing two values, you need to
  find out whether they are really different or
  not.

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• Example
• Imagine that you are giving an English test to
  two groups of five students.
• Group As scores are higher.
• Can you be sure that on average, Group As
  English is better?
• Maybe the members of Group B were just having a
  bad day.

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• So you decide to give the test to the two groups
  100 times.
• You find that Group A got a higher score 95 times
  out of 100.
• Now you can feel fairly confident that Group As
  English is, on average, better.
• Of course, you couldnt really do this.
• However, you can use a statistical calculation to
  figure out, if you gave the test 100 times, how
  what percentage of the time you would get a
  different result.

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• Example
• You have asked participants to rate their English
  ability on a scale of 0 to 10.
• The ratings of one group of participants have a
  mean of 5, and the mean of the other group is 6.
• Is this difference just the result of chance, or
  is there a real difference between these two
  groups?
• In technical terms, the question is whether the
  difference is significant.

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• Whether the difference is real depends on
• 1) the size of the difference (that is, a
  difference of 5 points is more likely to be
  significant than a difference of one point)
• 2) the number of people in the groups (the larger
  the group, the more likely a difference in means
  is significant)
• 3) the size of the standard deviation (if there
  is a small standard deviation, it is more likely
  that the difference in means is significant)

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• Significance is reported in terms of probability
  (p), that is, the likelihood that two groups or
  two scores are different as a result of chance.
• The value of p is between 0.00 and 1.00.
• P tells you what percentage of the time you would
  get a different result.

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• Generally, in social science, a p of less than
  .05 is considered significant.
• That means that the difference can be considered
  real rather than as a result of chance.
• If p is equal to or less than .05, it means that
  in 5 or fewer out of 100 cases, the results would
  have been different -- but in 95 out of 100
  cases, there is a real difference between the two
  groups.

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• If p is less than .01, then in less than one out
  of 100 cases, a different result would have been
  found.
• The lower p is, the more confidence you can have
  that that difference is real and did not happen
  by chance.
• If the statistical significance is greater than
  .05, then there you cannot say that there is a
  real difference between the two groups or values.

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Conclusion

• Once you have gathered information for your
  quantitative study, you need to use statistics to
  analyze your results.
• You use descriptive statistics such as the mean
  and the range to describe the characteristics of
  the sample.
• When you compare two sets of numbers, you also
  need to find out if the difference you see is
  significant.