1 COMMUNITY DENTAL HEALTH Jan Ladas

Algonquin College - Jan Ladas2 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.

Algonquin College - Jan Ladas3 VARIABILITY/DISPERSION Three terms associated with variability / dispersion:  Range  Variance  Standard Deviation (They describe the spread around the central tendency)

Algonquin College - Jan Ladas4 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

Algonquin College - Jan Ladas5 VARIABILITY/DISPERSION Variance: The measure of average deviation or spread of scores around the mean - Based on each score in the set Calculation: 1.Obtain the mean of the distribution 2.Subtract the mean from each score to obtain a deviation score 3.Square each deviation score 4.Add the squared deviation scores 5.Divide the sum of the squared deviation scores by the number of subjects in the sample

Algonquin College - Jan Ladas6 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”

Algonquin College - Jan Ladas7 KURTOSIS Kurtosis of a data set relates to how tall and thin, or short and flat the data set is.  Leptokurtic = tall and thin  Mesokurtic = normal, about average  Platykurtic = short and flat

Algonquin College - Jan Ladas8 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

Algonquin College - Jan Ladas9 THE NORMAL CURVE Most used frequency distributions in biostatistics. Characteristics: 1.Total area under the curve is equal to 1.00 or 100% 2.Mean = mode = median 3.The area under the curve is broken into equal segments which are one standard deviation in width 4.The proportion of area under the curve between: A the mean and 1 SD (+ or -) 34.13% B the 1 st and 2 nd SD 13.59% C the 2 nd and 3 rd SD 2.21%

Algonquin College - Jan Ladas10 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

Algonquin College - Jan Ladas11 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”)

Algonquin College - Jan Ladas12 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

Algonquin College - Jan Ladas13 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

Algonquin College - Jan Ladas14 DEFINITIONS RELATING TO RESEARCH TECHNIQUES Statistics:  Characteristics of samples used to infer parameters (characteristics of populations)  A set of tools for collecting / organizing, presenting and analyzing numerical facts or observations Survey:  The process of collecting descriptive data from a population

Algonquin College - Jan Ladas15 SAMPLING PROCEDURES 5 Types of Samples: 1.A random sample – by chance 2.A stratified sample – categorized then random 3.A systematic sample – every nth item 4.A judgment sample – prior knowledge 5.A convenience sample – readily available

Algonquin College - Jan Ladas16 RANDOM SAMPLE 1. A random sample is one in which every element in the population has an equal and independent chance of being selected. This method is preferred when possible because it equalizes the effect of variables not under investigation but which may influence the observations. It also controls possible selection bias on the part of the researcher. Sample = 1000 / 5000 students from 50 universities Lottery numbers or names in a hat

Algonquin College - Jan Ladas17 STRATIFIED RANDOM SAMPLE 12. Stratified random sampling is employed when it may be necessary to select elements of the population according to certain sub groups or categories e.G. Age or gender. This method allows for the control of the variable on which categorization is made. Sample subjects are then randomly chosen from the population making up each category. E.G.: List of names per university – random selection 1/5 of names

Algonquin College - Jan Ladas18 SYSTEMATIC SAMPLE 3. Systematic samples are selected by deciding to observe every nth item in the population. This method is not random because not every element in the population has an equal and independent chance for selection. Every 5 th from a list – odd or even numbers

Algonquin College - Jan Ladas19 JUDGEMENT SAMPLE 4. A judgement sample has characteristics similar to that of a stratified random sample. It is sample selection done when the researcher, with prior knowledge of the population or question under investigation, arbitrarily chooses certain criteria for representation E.G.: Income, educational levels, place of residence etc. Could be biased.

Algonquin College - Jan Ladas20 CONVENIENCE SAMPLE 5. A convenience sample is chosen because it is most readily available. It may or may not be representative of the larger population. Convenience samples are often chosen on the basis of geographical accessibility. Reliability is questionable – could be biased.

Algonquin College - Jan Ladas21 VARIABLES The items of a study that are measured. Independent Variable(s) (intervention):  All the factors that influence the characteristics which are under investigation  Some of the Independent Variables will be manipulated as part of the study or experiment = “controlled” i.e.: age, gender, type of oral hygiene aid, amount of drug administered

Algonquin College - Jan Ladas22 VARIABLES Independent Variable(s) (intervention): “Uncontrolled” variables can not be manipulated:  Subject’s prior experience  Subject’s knowledge base  Subject’s emotional state  Subject’s values, beliefs i.e.: dental hygienist evaluating tooth brushing method for children = “controlled variable”

Algonquin College - Jan Ladas23 VARIABLES Dependant Variable(s)  The measurable result or outcome which the researcher hopes will change or not change as a result of the intervention  Their values are determined by all of the independent variables operational at the time of the study (both controlled and uncontrolled) n.b.: called dependant because result depends on independent variable e.g.: subject’s plaque scores / gingival condition (measured before and after) Result depends on method used.

Algonquin College - Jan Ladas24 POTENTIAL PATHOGENS ON NON-STERILE GLOVES 1.Method = experimental - Brief outline of experiment 2.Independent variables = items of a study that are measured = the intervention 3.- Gloves – material and origin - Petri dishes with growth substances - Time and temperature of incubation - Testing methods for identification - Soap – type, amount and use - Air exposure etc.

Algonquin College - Jan Ladas25 POTENTIAL PATHOGENS ON NON-STERILE GLOVES Dependant = measurable result = The types and numbers of micro- organisms found on the tested gloves

Algonquin College - Jan Ladas26 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

Algonquin College - Jan Ladas27 PROBABILITY Rules of probability: 1.The (P) of any one event occurring is some value from 0 to 1 inclusive 2.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

Algonquin College - Jan Ladas28 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%

Algonquin College - Jan Ladas29 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 ?

Algonquin College - Jan Ladas30 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!

Algonquin College - Jan Ladas31 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

Algonquin College - Jan Ladas32 HYPOTHESIS CHARACTERISTICS Ethical Relevant  To scientific knowledge  To clinical and health policy  To future research direction

Algonquin College - Jan Ladas33 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  Represents the amount of risk we are willing to take of being wrong in our conclusion P < 0.10 = 10% chance P < 0.01 = 1% chance(cautious) P < 0.05 = 5% chance  Critical value cut-off point of sample is set before conducting the study (usually P < 0.05)

Algonquin College - Jan Ladas34 ERRORS Type I (Alpha):  Is made when we reject the null hypothesis when, in fact, it is true, therefore could lead to practicing worthless treatments that do not work. Type II (Beta):  Is made when we do not reject the null hypothesis when, in fact, it is false, therefore could lead to overlooking a promising treatment. e.g.: the law – “innocent” or “guilty”

Algonquin College - Jan Ladas35 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