Statistics Flashcards
case control or case referent studies.
biomedical studies looking backward in time are called case control or case referent studies.
surveys or cross-sectional studies.
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.
efficacy
whether the treatment is better than the control in treating the disease
toxicity
whether the treatment has fewer side effects or unwanted effects than the control
double-blind trial
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.
meta-analysis
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.
prospective trend studies
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.
prospective panel studies
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
prospective (panel) study
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
case control or case referent studies
the investigator begins with cases who already have the disease diagnosed (outcome) and looks back earlier in time for possible causes .
single-sample case studies
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.
retrospective case control studies
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.
NUMERICAL METHODS OF ORGANIZING DATA
1 An Ordered Array
2 Stem and Leaf Tables
3 The FrequencyTable
4 Relative FrequencyTables
GRAPHS
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
An ordered array
An ordered array is an arrangement of the observations according to size from smallest to largest.
An ordered array
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
Stem and Leaf Tables
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.
The FrequencyTable
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.
Relative FrequencyTables
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.
graph
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.
The Histogram: Equal Class Intervals
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.
The Histogram: Unequal Class Intervals
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.
Areas Under the Histogram
Areas Under the Histogram
The eye tends to compare the areas in a graph rather than the heights.
The Frequency Polygon
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.
mean
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.
The mean
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.
The median
The median, the number that divides the total number of ordered observations in half.
The median
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.
The mode
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.
MEASURES OF VARIABILITY
The Variance and the Standard Deviation
The sample variance
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
standard deviation.
The square root of the variance is also used. It is called the standard deviation.
