Community Dental Health

1
Community Dental Health

• Review

2
Statistics

• Statistics is the field of study which concerns
  itself with the art and science of data analysis
• Planning, collecting, organizing, analyzing,
  interpreting, summarizing and presenting the data
• Statistics, when used in the plural form, refers
  to the specific bits of data which either have
  been or are about to be gathered.

3
Introduction To BIOSTATISTICS

• Biostatistics
• The mathematics of collection, organization and
  interpretation of numeric data having to do with
  living organisms.
• Techniques to manage data
• Descriptive
• Inferential

4
Facts About Data

• Two types of data
• Qualitative labels used to identify an item when
  it cannot be numerically identified.
• e.g. marital status, car colour, occupation
• (attributes)
• n.b. has absolutely nothing to do with the
  quality of the data
• Quantitative characteristics that can be
  expressed numerically. Any mathematical
  manipulation that is carried out on them will
  have meaning.
• e.g. height, length, volume, number of DMFTs
• (variates)

5
Data Management

• Grouping data to make it easier to understand.
• Descriptive Technique
• Used to describe and summarize a set of numerical
  data
• Tabular and graphical methods
• Apply to generalizations made about the group
  studied

6
Descriptive Data Display Types
An Array A group of scores arranged from lowest
to highest in value. e.g. Histology test results
24 students
19 28 30 44 41 41
25 33 39 49 42 38
26 35 41 38 33 40
30 38 44 31 36 46
Raw Data
Array 19, 25, 26, 28, 30, 30, 31, 33, 33, 35,
36, 38, 38, 38, 39, 40, 41, 41, 41, 42, 44, 44,
46, 49 / 50 total
7
Descriptive Data Display Types

• Arrays are bulky and hard to read, thus an
  alternative is
• Frequency Distribution
• An organization of scores from lowest to highest
  which includes the number of times each score
  value occurs in the data set.

8
Descriptive Data Display Types

• Frequency Distribution 3 Types
• Ungrouped
• Each possible score value of the variable being
  measured is represented in the display and the
  frequency of occurrence of the value is recorded.
  Sample

9
Descriptive Data Display Types
Frequency Distribution Ungrouped
Score F Score F Score F
50 40 1 30 2
49 1 39 1 29
48 38 3 28 1
47 37 27
46 1 36 1 26 1
45 35 1 25 1
10
Descriptive Data Display Types
2. Grouped Frequency Distribution When a broad
range of values on the measurement is possible
(i.e. gt 30), the range is collapsed by grouping
scores together into smaller value ranges.
Scores Grouped Cumulative
16-20 1 1
21-25 1 2
26-30 4 6
31-35 3 9
36-40 6 15
41-45 7 22
46-50 2 24
11
Descriptive Data Display Types
3. Cumulative Frequency Distribution Used with
score groupings where the frequency of any one
group includes all instances of scores in that
group plus all the groups of lower score values.
Scores Grouped Cumulative
16-20 1 1
21-25 1 2
26-30 4 6
31-35 3 9
36-40 6 15
41-45 7 22
46-50 2 24
12
Central Tendency

• Term in statistics that describes where the data
  set is located.
• Measures of Central Tendency
• Used to describe what is typical in the sample
  group based on the data gathered.
• Three Main Indicators
• Mean
• - Median
• - Mode

13
Central Tendency

• Mean arithmetic average of scores
• Mean symbol is ( x )
• Scores are all added then divided by the number
  of scores.
• The most common measure
• Data set 3, 7, 9, 4, 9, 16 48 / 6 8

14
Central Tendency

• Median
• Is the point that divides the distribution of
  scores into 2 equal parts 50 / 50
• With odd set of numbers, median is the datum in
  the middle
• i.e. 3, 7, 2, 5, 9 rearranged to 2, 3, 5, 7,
  9
• median 5
• With even set of numbers, median is the average
  of the two middle values
• i.e. 4, 7, 1, 3, 8, 2 rearranged to 1, 2, 3,
  4, 7, 8
• 3 4 7 / 2 median 3.5

15
Central Tendency

• Mode
• Is the most frequently occurring score in a
  distribution
• i.e. 4, 3, 4, 9, 7, 2 mode 4
• i.e. 3, 8, 4, 2, 4, 9, 7, 4, 9, 1, 9
• bimodal data set 4 and 9

16
BIOSTATISTICS Continued

• Previously discussed
• Descriptive statistical techniques
• The first measures of spread / central tendency
• Information about central tendency is important.
  Equally important is information about the spread
  of data in a set.

17
Variability/Dispersion

• Three terms associated with variability /
  dispersion
• Range
• Variance
• Standard Deviation
• (They describe the spread around the central
  tendency)

18
Variability/Dispersion

• Range
• The numerical difference between the highest and
  lowest scores
• Subtract the lowest score from the highest score
• i.e. c 19, 21, 73, 4, 102, 88
• Range 102 4 98
• n.b. easy to find but unreliable

19
Variability/Dispersion

• Variance
• The measure of average deviation or spread of
  scores around the mean
• - Based on each score in the set
• Calculation
• Obtain the mean of the distribution
• Subtract the mean from each score to obtain a
  deviation score
• Square each deviation score
• Add the squared deviation scores
• Divide the sum of the squared deviation scores by
  the number of subjects in the sample

20
Variability/Dispersion

• Standard Deviation of a set of scores is the
  positive square root of the variance
• - a number which tells how much the data is
  spread around its mean
• Interpretation of Variance and Standard Deviation
  is always equal to the square root of the
  variance
• The greater the dispersion around the mean of
  the distribution, the greater the standard
  deviation and variance

21
Normal Curve (Bell)

• A population distribution which appears very
  commonly in life science
• Bell-shaped curve that is symmetrical around the
  mean of the distribution
• Called normal because its shape occurs so often
• May vary from narrow (pointy) to wide (flat)
  distribution
• The mean of the distribution is the focal point
  from which all assumptions may be made
• Think in terms of percentages easier to
  interpret the distribution

22
Research Techniques

• Inferential Statistics
• (Statistical Inference)
• Techniques used to provide a basis for
  generalizing about the probable characteristics
  of a large group when only a portion of the group
  is studied
• The mathematic result can be applied to larger
  population

23
Definitions Relating To Research Techniques

• Population
• Entire group of people, items, materials, etc.
  with at least one basic defined characteristic in
  common
• Contains all subjects of interest
• A complete set of actual or potential
  observations
• e.g. all Ontario dentists or all brands of
  toothpaste
• Sample
• A subset (representative portion) of the
  population
• Do not have exactly the same characteristics as
  the population but can be made truly
  representative by using probability sampling
  methods and by using an adequate sample size (5
  types of sampling)

24
Definitions Relating To Research Techniques

• Parameters
•  Numerical descriptive measures of a population
  obtained by collecting a specific piece of
  information from each member of the population
• Number inferred from sample statistics
•  
• E.G. 2,000 women over age 50 with heart disease

25
Definitions Relating To Research Techniques

• Statistic
•  A number describing a sample characteristic.
  Results from manipulation of sample data
  according to certain specified procedures
•  A characteristic of a sample chosen for study
  from the larger population
• e.g. 210 women out of 500 with diabetes have
  heart problems

26
Sampling Procedures

• 5 Types of Samples
• A random sample by chance
• A stratified sample categorized then random
• A systematic sample every nth item
• A judgment sample prior knowledge
• A convenience sample readily available

27
Concept Of Significance

• Probability P (symbol)
• When using inferential statistics, we often deal
  with statistical probability.
• The expected relative frequency of a particular
  outcome by chance or likelihood of something
  occurring
• Coin toss

28
Probability

• Rules of probability
• The (P) of any one event occurring is some value
  from 0 to 1 inclusive
• The sum of all possible events in an experiment
  must equal 1
• Numerical values can never be negative nor
  greater than 1
• 0 non event
• P 1 event will always happen

29
Probability

• Calculating probability
• Number of possible successful outcomes
• / Number of all possible outcomes
• E.G. Coin flip
• 1 successful outcome of heads
• / 2 possible outcomes P .5 or 50
• E.G. Throw of dice
• 1 successful outcome
• / 6 possible outcomes P .17 or 16.6

30
Hypothesis Testing

• The first step in determining statistical
  significance is to establish a hypothesis
• To answer questions about differences or to test
  credibility about a statement
• e.g. ? does brand X toothpaste really whiten
  teeth more than brand Y ?

31
Hypothesis Testing

• Null hypothesis (Ho) there is no statistically
  significant difference between brand X and brand
  Y
• Positive hypothesis brand X does whiten more
• Ho most often used as the hypothesis
• Ho assumed to be true
• Therefore the purpose of most research is to
  examine the truth of a theory or the
  effectiveness of a procedure and make them seem
  more or less likely!

32
Hypothesis Characteristics

• Hypothesis must have these characteristics in
  order to be researchable.
• Feasible
• Adequate number of subjects
• Adequate technical expertise
• Affordable in time and money
• Manageable in scope
• Interesting to the investigator
• Novel
• Confirms or refutes previous findings
• Extends previous findings
• Provides new findings

33
Hypothesis Characteristics

• Ethical
• Relevant
• To scientific knowledge
• To clinical and health policy
• To future research direction

34
Significance Level

• A number (a alpha) that acts as a cut-off point
  below which, we agree that a difference exists
  Ho is rejected. Alpha is almost always either
  0.01, 0.05 or 0.10.
• Represents the amount of risk we are willing to
  take of being wrong in our conclusion
• P lt 0.10 10 chance
• P lt 0.01 1 chance (cautious)
• P lt 0.05 5 chance
• Critical value cut-off point of sample is set
  before conducting the study (usually P lt 0.05)

35
Degree Of Freedom (D.F.)

• Most tests for statistical significance require
  application of concept of d.f.
• d.f. refers to number of values observed which
  are free to vary after we have placed certain
  restrictions on the data collected
• d.f. usually equals the sample size minus 1
• e.g. 8, 2, 15, 10, 15, 7, 3, 12, 15, 13 100
• d.f. number (10) minus 1 9
• Takes chance into consideration
• A penalty for uncertainty, so the larger the
  sample the less the penalty