Statistics

Question 0

case control or case referent studies.

Answer 0

biomedical studies looking backward in time are called case control or case referent studies.

Question 1

surveys or cross-sectional studies.

Answer 1

In terms of time, we can examine data taken at an “instant in time”; we can look forward in time or we can look backward in time. The studies that theoretically take place in an instant of time are usually called surveys or cross-sectional studies. The types of studies that look forward in time are often called (1) experiments, (2) clinical trials,(3)field trials,or (4)prospective orpanel orfollow-upstudies.

Question 2

efficacy

Answer 2

whether the treatment is better than the control in treating the disease

Question 3

toxicity

Answer 3

whether the treatment has fewer side effects or unwanted effects than the control

Question 4

double-blind trial

Answer 4

Random assignment to treatment is still the recommended procedure, and methods of performing the assignment have been devised to fit the needs of clinical trials. If possible, it is recommended that neither the patient nor the professionals who interact with the patient or evaluate the outcome know whether the patient is getting the new treatment or the control treatment. When this can be accomplished, the clinical trial is called a double-blind trial.

Question 5

meta-analysis

Answer 5

When a number of researchers have already performed clinical trials on the same topic, such as the comparison of two specific treatments for a given medical condi- tion, a meta-analysis can be considered.

Question 6

prospective trend studies

Answer 6

repeated samples of different individuals can be taken at intervals over time from a dynamic population where some of the individuals in the population may change over time. Such studies have been used to study voting intentions as an election approaches.

Question 7

prospective panel studies

Answer 7

In prospective panel studies, repeated measures are made on the same individ- uals over time. This is the type of prospective study most used in biomedical studies.Also called as cohort studies ,prospective studies

Question 8

prospective (panel) study

Answer 8

a cohort of disease-free individuals are measured for exposure to the causal factor(s) at the beginning of the follow-up period. Then, at subsequent examinations, exposure can be remeasured and disease status (outcome) must be measured

Question 9

case control or case referent studies

Answer 9

the investigator begins with cases who already have the disease diagnosed (outcome) and looks back earlier in time for possible causes .

Question 10

single-sample case studies

Answer 10

no controls without the disease are used. Here the investigator typically searches a medical record system for all the cases or patients who have a particular disease outcome in a fixed time period, say the last 2 years. Then, a search is made through the records to see if some prior exposure occurred, more than would be expected considering the group of patients involved. One difficulty with this type of study is that it is difficult to evaluate the levels of the exposure factor and decide what is high or low, since only cases are studied.

Question 11

retrospective case control studies

Answer 11

In case/control studies, the investigator starts with the cases after they are diagnosed or treated. These studies are also called retrospective since the investigator is look- ing backward in time. This often involves taking a chunk sample at one or more institutions that have medical records that the investigator can search to find cases that meet the eligibility criteria for a particular disease. Sometimes the study is per- formed solely from available records. Otherwise, the investigator must contact the case, obtain the person’s consent to enter the study, and interview or examine him.

Question 12

NUMERICAL METHODS OF ORGANIZING DATA

Answer 12

1 An Ordered Array
2 Stem and Leaf Tables
3 The FrequencyTable
4 Relative FrequencyTables

Question 13

GRAPHS

Answer 13

1 The Histogram: Equal Class Intervals
2 The Histogram: Unequal Class Intervals
3 Areas Under the Histogram
4 The Frequency Polygon
5 Histograms with Small Class Intervals
6 Distribution Curves

Question 14

An ordered array

Answer 14

An ordered array is an arrangement of the observations according to size from smallest to largest.

Question 15

An ordered array

Answer 15

The simplest arrangement of the data is an ordered array. An ordered array is an arrangement of the observations according to size from smallest to largest. It can be done easily by hand for small sets of data

Question 16

Stem and Leaf Tables

Answer 16

Stem and Leaf Tables
The basic idea in making a stem and leaf table is to present the first digit or digits of each observation in the first column and the rest of the digits in the second column. Each line is called a called a stem and the information on the stem is called the leaf.

Question 17

The FrequencyTable

Answer 17

The FrequencyTable
To make a frequency table, we find the interval that includes the smallest and largest observation in the data set (here 12.2-26.2) and decide on some convenient way of dividing it into intervals called class intervals or classes. The number of observa- tions that fall in each class interval are then counted; these numbers form a column headed frequency.

Question 18

Relative FrequencyTables

Answer 18

Relative FrequencyTables
If the numbers in the frequency table are expressed as proportions of the total number in the set, the table is often somewhat easier to interpret. These proportions are computed by dividing the frequencies in each class interval by the total sample size. Often, these proportions are converted to percentages by multiplying by 100. The table may then be called a table of relative frequencies, or it may still be called a frequency distribution or frequency table. Relative frequency tables are especially helpful in comparing two or more sets of data when the sample sizes in the two data sets are unequal.

Question 19

graph

Answer 19

In making a graph, we draw a picture of the situation, and we may lose even more of the fine details. A well-done graph is usually easier to read and interpret than the table.
Two ways of grafting a sample of continuous data are given here: the histogram and the frequency polygon.Some graphs are described that can be used to display measures of the center and spread of a set of observations.

Question 20

The Histogram: Equal Class Intervals

Answer 20

The Histogram: Equal Class Intervals
When the class intervals in the frequency distribution are equal, a histogram can be drawn from it directly, using the frequencies, proportions, or percentages. Two lines, one horizontal, the other vertical, are all that is needed; one line is called the horizontal axis and the other, the vertical axis.

Question 21

The Histogram: Unequal Class Intervals

Answer 21

The Histogram: Unequal Class Intervals
When drawing a histogram from a set of data with unequal class intervals, we must first adjust for the length of the class intervals in order to avoid a graph that gives a misleading impression.

Question 22

Areas Under the Histogram

Answer 22

Areas Under the Histogram

The eye tends to compare the areas in a graph rather than the heights.

Question 23

The Frequency Polygon

Answer 23

The Frequency Polygon
Instead of a histogram a frequency polygon is often made from a frequency distri- bution. It is made in the same way, except that instead of a bar of the proper height over each class interval, a dot is put at the same height over the midpoint of the class interval. The dots are connected by straight lines to form the frequency polygon.

Question 24

mean

Answer 24

The number most often used to describe the center of a distribution is called the average or arithmetic mean. Here, we call it the mean to avoid confusion.

Question 25

The mean

Answer 25

The mean for a sample is defined as the sum of all the observations divided by the number of observations. In symbols, if n is the number of observations in a sample, and the first, second, third, and so on, observations are called X I .X2,X 3 , …, X,, thenx= (XI+X2 +X3 +…+X,)/n.

Question 26

The median

Answer 26

The median, the number that divides the total number of ordered observations in half.

Question 27

The median

Answer 27

To find the median of the same data set of observations used in Section 5.1.1 ( 8, 1, 2, 9, 3, 2, 8, 1, 2), we order them to obtain 1, 1, 2, 2, 2, 3, 8, 8, 9. With nine observations, n is an odd number and the median is the middle or fifth observation. It has a value of 2. If n is odd, the median is the numerical value of the ( n + l ) / 2 ordered observation. If the first number were not present in this set of data, the sample size would be even and the ordered observations are 1, 2, 2, 2, 3, 8, 8, 9; then the median is the mean of the fourth and fifth number observations, or (2 +3)/2 = 2.5. In general, for n even, the formula for the median is the mean of the n/2 and ( n / 2 )+ 1 observations.

Question 28

The mode

Answer 28

The mode is the value of the variable that occurs most frequently. In order to contrast the numerical values of the mean, mode, and median from a sample that has a distribution that is skewed to the right (long right tail), let us look at a sample of n = 11 observations. The numerical values of the observations are 1 , 2 , 2 , 2 , 2 , 3 , 3 , 4 , 5 , 6 , 7 . The mode is 2, since that is the value that occurs most frequently. The median is 3,since that is the value of the sixth or(n+1)/2 observation. The mean is 3.36. Although small, this sample illustrates a pattern common in samples that are skewed to the right. That is, the mean is greater than the median, which in turn is greater than the mode.

Question 29

MEASURES OF VARIABILITY

Answer 29

The Variance and the Standard Deviation

Question 30

The sample variance

Answer 30

The sample variance is defined as the sums of squares of the differences between each observation in the sample and the sample mean divided by 1 less than the number observations,but for now it is sufficient to remark that n - 1 is part of the definition of the variance. The variance of the sample is usually denoted by s2and the formula is written as
s2 = £(X- X)2 /n-1

Question 31

standard deviation.

Answer 31

The square root of the variance is also used. It is called the standard deviation.