him 3200 midterm review dr. burton. mid-term review types of data normal distribution variance...

HIM 3200Midterm Review

Dr. Burton

Mid-term review

• Types of data• Normal distribution• Variance• Standard deviation and z scores• 2 X 2 table• Hypothesis testing H0: HA:• t-test• Pearson r/Linear regression• Chi square

Measurements

• Frequency– Incidence

• The frequency of new occurrences of disease, injury, or death in the study population during the time being examined.

– Prevalence• The number of persons in defined population

that had a specified disease or condition– Point prevalence (at a particular point in time.)– Period prevalence (the sum of the point prevalence at

the beginning of the interval plus the incidence during the interval.)

Measurements• FrequencyFrequency

– IncidenceIncidence– PrevalencePrevalence

• Risk– “The proportion of persons who are

unaffected at the beginning of a study period but who undergo the risk event during the study period.”

• Risk event:– Death– Disease– Injury

• Cohort:– Persons at risk for the event .

Measurements• FrequencyFrequency

– IncidenceIncidence– PrevalencePrevalence

• RiskRisk– ““The proportion of persons who are uneffected at The proportion of persons who are uneffected at

the beginning of a study period but who undergo the the beginning of a study period but who undergo the risk event during the study period.”risk event during the study period.”

• Rates– “The frequency of events that occur in a defined

time period, divided by the average population at risk.”

Rates

Rate = ------------------- x Constant multiplierNumerator

The constant multiplier is usually 100, 1000, 10,000 or 100,000.

Types of ratesIncidence rates (i.e. Per 1000)Prevalence rates (Proportional i.e. 20%)Incidence density (frequency of new events per person time)

Denominator

• Equations for the most commonly used population data. – (Mortality) Table 1 – 10 p.18 Osborn text– (Morbidity) Table 1 – 11 p. 21 Osborn text

Differential and nondifferential error

• Bias is a differential error– A nonrandom, systematic, or consistent

error in which the values tend to be inaccurate in a particular direction.

• Nondifferential are random errors

Bias• Three most problematic forms of bias in medicine:

– 1. Selection (Sampling) Bias: The following are biases that distort results because of the selection process

• Admission rate (Berkson’s) bias– Distortions in risk ratios occur as a result of different

hospital admission rate among cases with the risk factor, cases without the risk factor, and controls with the risk factor –causing greatly different risk-factor probabilities to interfere with the outcome of interest.

• Nonresponse bias– i.e. noncompliance of people who have scheduled interviews

in their home.

• Lead time bias– A time differential between diagnosis and treatment among

sample subjects may result in erroneous attribution of higher survival rates to superior treatment rather than early detection.

Bias• Three most problematic forms of bias in medicine:

– 1. Selection (Sampling) Bias1. Selection (Sampling) Bias• Admission rate (Berkson’s) biasAdmission rate (Berkson’s) bias

• Nonresponse biasNonresponse bias

• Lead time biasLead time bias

– 2. Information (misclassification) Bias2. Information (misclassification) Bias• Recall biasRecall bias

– Differentials in memory capabilities of sample subjectsDifferentials in memory capabilities of sample subjects

• Interview biasInterview bias– ““blinding of interviewers to diseased and control subjects is blinding of interviewers to diseased and control subjects is

often difficult.often difficult.

• Unacceptability biasUnacceptability bias– Patients reply with “desirable” answersPatients reply with “desirable” answers

Bias• Three most problematic forms of bias in medicine:

– 1. Selection (Sampling) Bias• Admission rate (Berkson’s) bias

• Nonresponse bias

• Lead time bias

– 2. Information (misclassification) Bias• Recall bias

• Interview bias

• Unacceptability bias

– 3. Confounding3. Confounding• A confounding variable has a relationship with both the A confounding variable has a relationship with both the

dependent and independent variables that masks or dependent and independent variables that masks or potentiates the effect of the variable on the study.potentiates the effect of the variable on the study.

Neyman bias

• “late look bias” if it results in selecting fewer individuals with severe disease because they died before detection.

• “length bias” in screening programs which tend to select less aggressive cases for treatment.

2 X 2 Tablecomparing the test results of two observers

Positive Negative

Positive

Negative

Observer No. 1

ObserverNo. 2

aa bb

cc dd

a + ba + b

c + dc + d

a + ca + c b + db + d a+b+c+da+b+c+dTotal

Total

+ _ + A B A + B - C D C + D A + C B + D

Sensitivity = A/(A + C)Specificity = D/(B + D)False- positive rate = B/(B + D)False-negative rate = C/(A + C)Positive predictive value = A/(A + B)Negative predictive value = D/ (D + C)Accuracy = (A + D) / (A + B + C + D)

Types of Variation

• Nominal variablesNominal variables• Dichotomous (Binary) variables

• Ordinal (Ranked) variables

• Continuous (Dimensional) variables

• Ratio variables

• Risks and Proportions as variables

Nominal

AA

OOBB

ABAB

Social Security Number

123 45 6789312 65 8432555 44 7777

Types of Variation

• Nominal variables

• Dichotomous (Binary) variablesDichotomous (Binary) variables• Ordinal (Ranked) variables

• Continuous (Dimensional) variables

• Ratio variables

• Risks and Proportions as variables

Dichotomous (Binary) Dichotomous (Binary) variablesvariables

WNL

Not WNL

Accept

Reject

Normal

Abnormal

Types of Variation

• Nominal variables

• Dichotomous (Binary) variables

• Ordinal (Ranked) variablesOrdinal (Ranked) variables• Continuous (Dimensional) variables

• Ratio variables

• Risks and Proportions as variables

Ordinal (Ranked) variablesOrdinal (Ranked) variables

Strongly agree, agree, neutral, disagree, strongly disagree

Types of Variation

• Nominal variables• Dichotomous (Binary) variables• Discrete variables• Ordinal (Ranked) variables

• Continuous (Dimensional) variablesContinuous (Dimensional) variables• Ratio variables• Risks and Proportions as variables

Continuous (Dimensional) Continuous (Dimensional) variablesvariables

Height Blood Pressure Weight

Temperature32° F

Types of Variation

• Nominal variables• Dichotomous (Binary) variables• Discrete variables• Ordinal (Ranked) variables• Continuous (Dimensional) variables

• Ratio variablesRatio variables• Risks and Proportions as variables

Ratio variablesRatio variables

• A continuous scale that has a true zero point

Measures of Central Tendency• Mode: the value with the highest number of

observations in a data set.• Median: the middle observation when data

have been arranged from highest to lowest.• Mean: (arithmetic) the average value of all

observed values.

Mean = x (xi)

Ni

Sum = Observed values = xi

Total number of observations = Ni

Raw data and results of Cholesterol levels in 26 subjects p.115

Number of observations or N 26

Initial HDL values 31, 41, 44, 46, 47, 47, 48, 49, 52, 53, 54, 57, 58, 58, 60, 60, 62, 63, 64, 67, 69, 70,

77, 78, 81, 90 mg/dl

Highest values 90 mg/dl

Lowest value 31 mg/dl

Mode 47, 48, 58, 60 mg/dl

Median (57 + 58)/2 = 57.5 mg/dl

Sum of the values (xi) 1496 mg/dl

Means, x 1496/26 = 57.5 mg/dl

Percentiles (quantiles)

• The median is the 50%• The 75th percentile is the point where

75% of observations lie below and 25% are above. (3rd quartile, Q3)

• The 25th percentile is the point where 25% of observations lie below and 75% are above. (1st quartile, Q1)

• Interquartile range (Q3 – Q1)

Raw data and results of Cholesterol levels in 26 subjects p.115

Number of observations or N 26

Initial HDL values 31, 41, 44, 46, 47, 47, 48, 48, 49, 52, 53, 54, 57, 58, 58, 60, 60, 62, 63, 64, 67, 69,

70,

77, 78, 81, 90 mg/dl

Highest values 90 mg/dl

Lowest value 31 mg/dl

Mode 47, 48, 58, 60 mg/dl

Median (57 + 58)/2 = 57.5 mg/dl

Sum of the values (xi) 1496 mg/dl

Means, x 1496/26 = 57.5 mg/dl

Interquartile range 64 – 48 = 16 mg/dl

Measures of dispersion based on the Mean.

• Mean deviation =

• Variance =

• Standard deviation = s =

Degrees of Freedom

(xi - x )

N -1

2

(xi - x )

N -1s

22=

(|xi - x| )

N

Raw data and results of Cholesterol levels in 26 subjects p.115

Number of observations or N 26Initial HDL values 31, 41, 44, 46, 47, 47, 48, 48, 49, 52, 53,

54, 57, 58, 58, 60, 60, 62, 63, 64, 67, 69, 70, 77, 78, 81, 90 mg/dl

Highest values 90 mg/dl Lowest value 31 mg/dl Mode 47, 48, 58, 60 mg/dl Median (57 + 58)/2 = 57.5 mg/dl Sum of the values (xi) 1496 mg/dlMeans, x 1496/26 = 57.5 mg/dlInterquartile range 64 – 48 = 16 mg/dlSum of squares (TSS) 4,298.46 mg/dlVariance, “s” squared 171.94 mg/dlStandard Deviation, s 171.94 mg/dl = 13.1 mg/dl

Theoretical normal (gaussian) distribution

stands for the mean in a theoretical distribution

stands for the standard deviation in a theoretical population.

-3 -2 - + +2 +3-3 -3 -2 -2 -1-1 00 11 22 33

Z scores

Theoretical normal distribution with standard deviations

Three Common Areas Under the Curve

• Three Normal distributions with different areas

Process of Testing Hypotheses• Test are designed to determine the probability

that a finding represents the true deviation from what is expected.

• This chapter focuses on the justification for and interpretation of the p value designed to minimized type I error.

• Science is based of the following principles:– Previous experience serves as the basis for

developing hypotheses;– Hypotheses serve as the basis for developing

predictions;– Predictions must be subjected to experimental or

observational testing.

Hypothesis testingH0 True H0 False

Accept H0

Reject H0

Type I Error

Type IIError

Correct

Correct

Truth

Decision

aa bb

cc dd

Alpha error: rejecting the null H0 when it is true

Beta error: accepting the null H0 when it is false

The power of a test:

(probability that a test detects differences that actually exist) can be determined by using the formula 1 – beta (1 - )

80% is usually acceptable

Hypothesis Testing

1. State question in terms of:H0: no difference or relationship (null)

Ha: is difference or relationship (alternative)

2. Decide on appropriate research design and statistic

3. Select significance (alpha) level and “N”4. Collect data5. Analyze and perform calculation to get P-

value6. Draw and state conclusions by comparing

alpha with P-value

-3 -2 - + +2 +3-3 -3 -2 -2 -1-1 00 11 22 33

Z scores

Theoretical normal distribution with standard deviations

ProbabilityUpper tail .1587 .02288 .0013Two-tailed .3173 .0455 .0027

When is a specific test used?Student’s t –test: to compare the means of two small (n

< 30) independent samples.Paired t-test: to compare the means of two paired

samples (e.g. before and after)F – test: to compare means of three or more samples or

groups.Chi-Square test: comparing two or more independent

proportions.Correlation coefficient: measures the strength of the

association between two variables.Regression analysis: Provides an equation that estimates

the change in a dependent variable (y) per unit change in an independent variable (x).