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# Quantitative Data Analysis

Principles of Scientific Investigation

by

Tweet## Sophie Hunt

on 1 May 2011#### Transcript of Quantitative Data Analysis

A researcher should be looking at the best ways to present data only in terms of what gives the clearest, least ambiguous picture of what was found in a research study.

Hence we typically see descriptive statistics and graphs.

In quantitative studies, look for similarities, differences, groupings, patterns of particular significance, anomalies In quantitative studies, look for similarities, differences, groupings, patterns of particular significance, anomalies. Central Tendency Mathematical average of a

series of numbers Median Middle value of a distribution range The most commonly occurring value in a series Mode Mean The mean can be distorted by Anomalies …findings which seem at odds with the general trend Darren Moore 2009 Let’s start with… Percentage

A proportion expressed as

hundredth parts What percentage of HE students

own their own car? In presenting statistics numerically, first consider: Diagrammatical Representations Exercise Quantitative Data Analysis Principles of Scientific Investigation Pie chart Tables Bar charts Used to compare numerical data

Flexible

Simple in structure Simple to read

More than 10 categories makes it confusing to read Incorporates the components of the total for a category

Compare different sets of data Stacked bar charts They show simply the proportions of each Present data as segments of a pie Important segments can be extracted from the pie category that make up the total Dispersion Standard deviation

How wide is the spread of data?

How even is the spread of data? Students’ grades improve every year Data 2005:

44, 67, 21, 65, 43, 55, 68, 41, 52, 59, 51, 70

2006:

56, 56, 73, 45, 80, 71, 45, 49, 51, 50, 60

2007:

66, 69, 51, 64, 55, 58, 65, 67, 51, 49, 73, 45

2008:

59, 43, 67, 68, 70, 64, 55, 52, 41

2009:

54, 67, 77, 45, 65, 78, 43, 65, 67, 30, 54, 72, 62, 61, 55, 70

Hypothesis Now produce a bar chart showing the same things

Produce a table showing the mean and median, year by year (three types of averages) Range The difference between the highest and lowest values E.g if we take two sequences of numbers: 5, 6, 7, 8, 9

3, 5, 7, 9, 11 In each case the mean is 7, but dispersion

around the mean varies. To calculate Standard Deviation First find the mean of the sequence

Mean of :

5, 6, 7, 8, 9 = 7 Then subtract the mean from each

number in the sequence:

5 - 7 = -2

6 - 7 = -1

7 - 7 = 0

8 - 7 = 1

9 - 7 = 2 Square the results:

-2 x -2

-1 x -1

0 x 0

1 x 1

2 x 2 Now add up the results of the squares:

4 + 1 + 0 + 1 + 4 = 10 Divide this number by the number of values in the sequence

10 / 5 = 2

and finally find the square root of this… Square root of 2 = 1.4142 = 4

= 1

= 0

= 1

= 4 Standard deviation for :

5, 6, 7, 8, 9

is 1.4142 Standard deviation for :

3, 5, 7, 9, 11

is ? 2.8284

Uses all of the values to calculate how far in general the values tend to be

spread out around the mean. http://www.mathsrevision.net/gcse/pages.php?page=42 Six easy steps to find the distribution using all of the values. Example: 10 subjects were asked how many

hours of TV they watched yesterday. = 2,2,3,1,8,6,1,1,3,2 Responses Re-arrangement Range Mean Median Mode = 1,1,1,2,2,2,3,3,6,8 = 2.9 = 2 = 1 and 2 = 7 hours = 1,1,1,2,2,2,3,3,6,8 = 7 hours = 2.9 = 2 = 1 and 2 Range = 7 hours Example: 10 subjects were asked how many

hours of TV they watched yesterday. Mode = 2,2,3,1,8,6,1,1,3,2 Median Responses Re-arrangement = 1,1,1,2,2,2,3,3,6,8 = 1 and 2 Mean = 2 = 2.9 Diagrammatical Representations

Full transcriptHence we typically see descriptive statistics and graphs.

In quantitative studies, look for similarities, differences, groupings, patterns of particular significance, anomalies In quantitative studies, look for similarities, differences, groupings, patterns of particular significance, anomalies. Central Tendency Mathematical average of a

series of numbers Median Middle value of a distribution range The most commonly occurring value in a series Mode Mean The mean can be distorted by Anomalies …findings which seem at odds with the general trend Darren Moore 2009 Let’s start with… Percentage

A proportion expressed as

hundredth parts What percentage of HE students

own their own car? In presenting statistics numerically, first consider: Diagrammatical Representations Exercise Quantitative Data Analysis Principles of Scientific Investigation Pie chart Tables Bar charts Used to compare numerical data

Flexible

Simple in structure Simple to read

More than 10 categories makes it confusing to read Incorporates the components of the total for a category

Compare different sets of data Stacked bar charts They show simply the proportions of each Present data as segments of a pie Important segments can be extracted from the pie category that make up the total Dispersion Standard deviation

How wide is the spread of data?

How even is the spread of data? Students’ grades improve every year Data 2005:

44, 67, 21, 65, 43, 55, 68, 41, 52, 59, 51, 70

2006:

56, 56, 73, 45, 80, 71, 45, 49, 51, 50, 60

2007:

66, 69, 51, 64, 55, 58, 65, 67, 51, 49, 73, 45

2008:

59, 43, 67, 68, 70, 64, 55, 52, 41

2009:

54, 67, 77, 45, 65, 78, 43, 65, 67, 30, 54, 72, 62, 61, 55, 70

Hypothesis Now produce a bar chart showing the same things

Produce a table showing the mean and median, year by year (three types of averages) Range The difference between the highest and lowest values E.g if we take two sequences of numbers: 5, 6, 7, 8, 9

3, 5, 7, 9, 11 In each case the mean is 7, but dispersion

around the mean varies. To calculate Standard Deviation First find the mean of the sequence

Mean of :

5, 6, 7, 8, 9 = 7 Then subtract the mean from each

number in the sequence:

5 - 7 = -2

6 - 7 = -1

7 - 7 = 0

8 - 7 = 1

9 - 7 = 2 Square the results:

-2 x -2

-1 x -1

0 x 0

1 x 1

2 x 2 Now add up the results of the squares:

4 + 1 + 0 + 1 + 4 = 10 Divide this number by the number of values in the sequence

10 / 5 = 2

and finally find the square root of this… Square root of 2 = 1.4142 = 4

= 1

= 0

= 1

= 4 Standard deviation for :

5, 6, 7, 8, 9

is 1.4142 Standard deviation for :

3, 5, 7, 9, 11

is ? 2.8284

Uses all of the values to calculate how far in general the values tend to be

spread out around the mean. http://www.mathsrevision.net/gcse/pages.php?page=42 Six easy steps to find the distribution using all of the values. Example: 10 subjects were asked how many

hours of TV they watched yesterday. = 2,2,3,1,8,6,1,1,3,2 Responses Re-arrangement Range Mean Median Mode = 1,1,1,2,2,2,3,3,6,8 = 2.9 = 2 = 1 and 2 = 7 hours = 1,1,1,2,2,2,3,3,6,8 = 7 hours = 2.9 = 2 = 1 and 2 Range = 7 hours Example: 10 subjects were asked how many

hours of TV they watched yesterday. Mode = 2,2,3,1,8,6,1,1,3,2 Median Responses Re-arrangement = 1,1,1,2,2,2,3,3,6,8 = 1 and 2 Mean = 2 = 2.9 Diagrammatical Representations