Quantitative methods in life sciences

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Quantitative methods in life sciences

• Maria Parlinska, PhD
• Valencia 9 March 2007

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Topics of today

• Quantitative research and methods
• Types of data
• Purposes of Quantitative Data Analysis
• Measures of central tendency (various forms of
  averages)
• Frequencies/histograms
• Cross-tabulations

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Quantitative research

• Are used in the systematic scientific
  investigation of quantitative properties and
  phenomena and their relationships.
• Are widely used in both the natural and social
  sciences, from physics and biology to sociology
  and journalism.
• The objective is to develop and employ
  mathematical models, theories and hypotheses
  pertaining to natural phenomena.
• The process of measurement is central to
  quantitative research because it provides the
  fundamental connection between empirical
  observation and mathematical expression of
  quantitative relationships.
• The term quantitative research is most often used
  in the social sciences in contrast to qualitative
  research.

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Quantitative methods

• Are research methods dealing with numbers and
  anything that is measurable.
• Counting and measuring are common forms of
  quantitative methods.
• The modern tendency is to use eclectic
  approaches. Quantitative methods might be used
  with a global qualitative frame.
• Using quantitative methods, it is possible to
  give precise and testable expression to
  qualitative ideas

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Types of data Measurement scales

• Nominal names
• Male, female
• Could also use words or letters instead of
  numbers
• Ordinal - ordered with unequal intervals
• Baby, toddler, schoolkid, teenager, adult
• Interval equal intervals
• Calendar years (zero point is arbitrary)
• Ratio - equal intervals, zero point
• Length, weight, speed, exam marks etc.

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Types of data Qualitative and quantitative data

• Qualitative data is essentially non-numeric and
  arises from the use of nominal measuring scales,
• Examples Colour of eyes blue, green, brown etc
  Exam result pass or fail Socio-economic
  status low, middle or high.
• Quantitative data on the other hand, is numeric
  in character and arises from the use of either
  ordinal or interval/ratio scales
• e.g. a persons height might be measured as
  1.8.meters or their weekly income as 300 each
  of these measurements provides interval/ratio
  data and the data can be described as
  quantitative.

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Purposes of Quantitative Data Analysis

• Summarize or describe what you found Descriptive
  statistics
• Frequencies, histograms ( graphic representation
  of frequency distribution)
• Measures of central tendency
• Mean, median
• Dispersion or distribution around the mean
• Compare
• E.g. gender x condition
• Cross tabs (non-parametric test)
• T-test, Anova (parametric test)

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Frequencies

• Can be calculated for all types of data
  (including nominal data)Example Soft drinks
  industry wants to conduct stadistical test to
  determine level there is a relationship beteween
  preference for one of the regular or diet Pepsi
  drink.

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Frequencies - Distribution Table
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Frequencies - Histogram

• Normal distribution
• A distribution which describes many situations
  where observations are distributed symmetrically
  around the mean. 68 of all values under the
  curve lie within one standard deviation of the
  mean and 95 lie within two standard deviations.

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Measures of Central Tendency

• Mode indicates which score or value in a
  distribution occurs most frequently.
• Example consider the data below which relates to
  the number of hours of overtime worked in a
  particular week by 15 workers 1 2 2 2 3 4 4 5 5
  5 5 5 7 8 8
• The mode is thus, 5 because this value occurs
  more often than any other value
• Median divides a distribution exactly in half.
• Median the value of X(n1)/2
• Example if Xi represents the number of persons
  in each of seven households and these take the
  values
• X1 X2 X3 X4 X5 X6 X7
• 2 2 3 3 4 4 5
• then n 7 and (n1) /2 8/2 4, so X(n1)/2
  X4 and median 3

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Measures of Central Tendency

• Mean (sample mean, the arithmetic average).
• Sample mean ungrouped data
• X (? Xi)/n, n sample values
• Population mean ungrouped data
• µ (? Xi)/N, N size of the population
• Sample mean grouped data
• X (? Xi fi)/ ? fi, Xi is the midpoint of the
  ith class and fi is the frequency of the ith
  class.
• Example Suppose the percentage increase in sales
  in the past year for the five largest microchip
  suppliers are
• 80 65 75 50 60
• Then the mean increase in sales is simply
• (8065755060)/5 330/5 66 percent.

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Measures of Dispersion

• Range measures the distance between the highest
  and lowest scores in a distribution.
• Range ungrouped data
• Range largest value smallest value
• Range grouped data
• Range largest boundary value smallest
  boundary value
• Variance (S2) sum of deviation score (score
  mean) squared/N
• Standard Deviation (SD) the square root of the
  variance

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Measures of Centre and Spread

• Nominal
• Mode
• Ordinal
• Mode, Median
• Range
• Interval/Ratio
• Mode, Median, Mean
• Range, Variance, Standard Deviation

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Chi-Square Analysis

• The Chi-square statistic is a measure of
  association or test of independence between two
  variables consisting of nominal data.
• For example Gender and Type of Sentence
  (Community vs. Custodial).
• This analysis yields a table of observations
  concerning two sets of variables
• This is known as a Crosstabs in SPSS.

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CrosstabsTable
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Chi-square from Crosstabs

interpretation
from this
value
Chi-square value
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Chi-square Interpretation

• Ho - No association between Gender and Type of
  Sentence
• In a chi-square test the null hypothesis should
  state that there is no association between two
  variables.
• H1 - Is association between Gender and Type of
  Sentence
• The alternative hypothesis should state that the
  two variables are associated
• As the significance on the printout is below 0.05
  (i.e. .00000) you should reject the null
  hypothesis (at the 5 level) and accept the
  alternative (If it would have been greater than
  0.05 the reverse would be the case).

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Todays assignment

• Soft drinks industry wants to conduct stadistical
  test to determine level there is a relationship
  beteween preference for one of the regular or
  diet drink. A random of 120 people is selected
  their response are as follows