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Pharmacometrics 541 PHL By: Asma Al-OneaziSupervised by Dr. Amal Fatani

Statistics:

Branch of mathematics concerned with collection, classification, analysis, and interpretation of numerical facts, for drawing inferences on the basis of their quantifiable likelihood (probability).

Statistics can interpret aggregates of data too large to be intelligible by ordinary observation because such data (unlike individual quantities) tend to behave in regular, predictable manner.

Statisticians improve the quality of data with the design of experiments and survey sampling.

Statistics also provides tools for prediction and forecasting using data and statistical models.

To understand statistics should be understand: Type of statistics.Data, and their types.Populations.Sample.Probability.Frequency distribution.Relative frequency.

Types of statistics 1) Descriptive statistics2) Inferential statistics (predictive statistics) Descriptive statistics: Generally describes a set of data elements by graphically displaying the information or describing its central tendencies and how it is distributed. This is useful in research, when communicating the results of experiments.Descriptive statistics can be representing as: 1) Numerical statistics: are numbers, but clearly, some numbers are more meaningful than others. E.g. the average (or mean) of the two value would be the important statistic. 2) Pictorial statistics: Taking numerical data and presenting it in pictures or graphs, showing data in the form of a graphic can make complex and confusing information appear more simple and straightforward.

Inferential statistics Patterns in the data may be modeled in a way that accounts for randomness and uncertainty in the observations, and are then used to draw inferences about the process or population being studied. Inference is a vital element of scientific advance, since it provides a prediction (based in data) for where a theory logically leads.

Data

Data they are facts or figures from which conclusions may be drawn. Datum is the singular form of the noun data. Data can be classified as either numeric or nonnumeric. Specific terms are used as follows:1) Qualitative data:(Catagorical data) They are nonnumeric. E.g. {Poor, Fair, Good, Better, Best}, colors, and types of material {straw, sticks, bricks}.

2)Quantitative data: They are numeric. Quantitative data are further classified as either discrete or continuous.

Discrete data are numeric data that have a fixed number of possible values.E.g. the counting numbers, {1,2,3,4,5} perhaps corresponding to {Strongly Disagree... Strongly Agree}.Continuous data have infinite possibilities: 1.4, 1.41, 1.414, 1.4142, 1.141421...E.g. Physically measureable quantities of length, volume, time, mass, etc. are generally considered continuous. Population:The complete set of data elements is termed the population. The term population will vary widely with its application.Examples could be any of the following: animals; primates; human beings; U.S. people; who are high school students.

Parameter: A parameter is a characteristic of the whole population.

Sample: A sample is a portion of a population selected to represent the population for further analysis.

The sample must be random.

A random sample is one in which every member of a population has an equal chance to be selected.

Sampling variability:

Sampling variability is the tendency of the same statistic computed from a number of random samples drawn from the same population to differ.Example, suppose that ten different samples of 100 people were drawn from the population, instead of just one. The income means of these ten samples would not be expected to be exactly the same.Normal distribution: is a frequency distribution in which the graph of the distribution is a bell-shaped curve (a.k.a. a normal curve).

Statistical Probability:A probability is a numerical measure of the likelihood of the event.(it is a number that we attach to an event)

A probability is a number from 0 to 1.

Summarizing data with Frequency Tables & Histograms

There are two ways to describe a data set (sample from a population):Pictorial GraphsTables of Numbers. Both are important for analyzing data.

A frequency distribution: It is a display of the number (frequency) of occurrences of each value in a data set.

A relative frequency: distribution is a display of the percent (ratio or frequency to sample-size) of occurrences of each value in a data set.

A percentile is the value of a variable that devides the real line into two segments - the left one caontaining certain percent (say 13%) of the observations for the specific process, and the righ interval containing the complement peecent of observations (in this case 87%). The 30th percentile is the value (measurement) that abounds above 30% and below 70% of the observations from a process. The (three) quartiles are the special cases of percentiles for Q1=25%, Q2=50% (median) and Q3=75%.

ExampleThe table below shows the stage of disease at diagnosis of breast cancer in a random sample of 2092 US women.

StageFrequencyRelative Frequency 01970.09I6910.33II7030.34III3140.15IV1870.09Total20921

Graphic Displays Used in Statistics Bar Chart:Pie Chart

If knowing about a part of the whole is an important consideration, then a pie chart is a good choice for showing particular data.

Frequency Histogram

One of the more commonly used pictorials in statistics is the frequency histogram, which in some ways is similar to a bar chart and tells how many items are in each numerical category.

Frequency Polygon

Relative frequencies of class intervals can also be shown in a frequency polygon. In this chart, the frequency of each class is indicated by points or dots drawn at the midpoints of each class interval. Those points are then connected by straight lines.

Frequency Distribution:

Frequency distributions are like frequency polygons; however, instead of straight lines, a frequency distribution uses a smooth curve to connect the points and, similar to a graph, is plotted on two axes: The horizontal axis from left to right (or x axis) indicates the different possible values of some variable. The vertical axis from bottom to top (or y axis) measures frequency or how many times a particular value occurs.

Box Plot (BoxandWhiskers)

Box plots, sometimes called box-and-whiskers, take the stem-and-leaf one step further. A box plot will display a number of values of a distribution of numbers: The median valueThe lower quartile (Q1) The upper quartile (Q3) The interquartile range or IQR (distance between the lower and upper quartiles) The symmetry of the distributionThe highest and lowest values

Box Plot (BoxandWhiskers)

Scatter Plot Sometimes you want to display information about the relationship involving two different phenomena. For example, suppose you collected data about the number of days that law school candidates studied for a state bar examination and their resulting scores on the exam.

Variables: Variables are things that we measure, control, or manipulate in research. They differ in many respects, most notably in the role they are given in our research and in the type of measures that can be applied to them.

Levels of Measurement

The experimental (scientific) method depends on physically measuring things. The concept of measurement has been developed in conjunction with the concepts of numbers and units of measurement.

Statisticians categorize measurements according to levels. Each level corresponds to how this measurement can be treated mathematically. Nominal: Nominal data have no order and thus only gives names or labels to various categories. Ordinal: Ordinal data have order, but the interval between measurements is not meaningful. Interval: Interval data have meaningful intervals between measurements, but there is no true starting point (zero). Ratio: Ratio data have the highest level of measurement. Ratios between measurements as well as intervals are meaningful because there is a starting point (zero).

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