Statistics

• cosists of metods for organizing and summarizing information
• ex. construction of graphs, charts, tables...

The collection of all individuals or items under cosideration in a statistical study

That part of the population from which inforamtion is obtained

consists of methods for drawing and measuring the reliability of conclusions about a population based on information obtained from a sample of the population

• The study is descriptive - If the purpose of the study is to examine and explore information for its own intrinsic interest only. ( can be performed on both sample and pupulation)
• The study is inferential - if information is obtained from a sample of a population and the purpose of the study is to use that information to draw conclusions about the population.

observing of characteristics and take measurements, as ina sample survey.Can reveal only association.

researchers impose treatments and controls and then observe characteristics and take measurements. Can help establish causation

Obtaining information for the entire pupulation of interest. However, it is time consuming and might be impossible.

Sampling and experimentation

• Sim. Ran. Sampling - A sampling procedure for which each possible sample of a given size is equally likely to be the one obtained.
• S.. R. Sample - A sample obtained by simple random sampling
• There are 2 types of Simple Random Sampling
• 1. Simple random sampling with replacement - a member of pup. can be selected more, than once
• 2. ----without the replacement - can be selected at most once.

• Step 1: Divide the populati1on size by the sample size and round the result down to the nearest whole number, m.
• Step 2: Use a random - number table (or a similar devise) to obtain a number, k, between 1-m.
• Step 3: Select for the sample those members of the population that are numbered, k, k+m, k+2m, k+3m..

• useful when the members of the population are widely scattered geographically.
• Step1: Divide the population into groups (clusters)
• Step 2: Obtain a simple random sample of the clusters
• Step 3: Use all the members of the clusters obtained in step 2 as the sample.

• more reliable than cluster sampling. First divided into subpopulations, called strata. Then sampling is done from each sratum. Uses proportions called stratifeid random Sampling with proportional allocation
• Step 1: Divide the population into subpopulations (srata)
• Step 2: From each sratum, obtain a simple random sample of size proportional to the size of the stratum; that is, the sample size for a stratum equals the total sample size times the stratum size divided by the populations size.
• Step 3: Use all the members obtained in Step 2 as the sample.

• -Experimental Units or subjects - those on whom performed the experiment. IF on humans -experimental units, if non humans - subjects.
• -Control - who is given the placebo
• -treatment group - who is given the treatment
• - Randomization - The exper. units shold be randomly divided into groups to avoid unintentional selection bias in constituting the groups
• - Replication - A sufficient number of experimental units should be used to ensure that randomization creates groups that resemble each other closely and to increase the chances of detecting any differences among the treatments.
• Treatment - experimental condition

• response variable - experimental outcome that is to be measured or observed.
• Factor - types of variables whose effect on the response variable in the experiment (ex. Ph and irrigation regime)
• Levels - The possible values of a factor ( ex. with p4, no P4, light, none, med...)
• Treatment - Each experimental condition. For one-factor experiments, the treatments are the levels of the single factor. (ex. 10 treatments, no p4/none, no p4/light, with p4/none....)

all the experimental units are assigned randomly amon all the treatments.

experiemtanl units that are similar in ways that are expected to affect the response variable are grouped in blocks. Then the random assignment of experimetanl units to the treatments is made block by block. The experimental units are assigned randomly among all the treatments separately withing each block.

A characteristic that varies from one person or thing to another

A nonnumerically vallued variable

• A numerical valued variable
• Two types:
• 1. Discrete
• 2.Continuous

a quantitative variable whose possible values can be listed (ex. # of siblings,)

A quantitative variable whose possible values form some einterval of numbers. A measurement of something, height of a person, weight of a newborn, lengh of time a battery lasts.

values of variable (info collected, organized, and analyzed by statisticians is data)

each individual piece of data

collection of all observations fora paritcular variable.

• categories of grouping methods.
• ex. group data by 10s, 1st class 30<- 40 from 30 days, but not including 40 days.
• <- simble means "up to, but not including"
• number of classes should be between 5-20

The number of observations that fall in a particular class. Ex. the frequency of the class 50<-60 is 8.

a listing of all classes and their frequencies.

• the ratio of the frequency of a class to the total number of observations. To find the pecentage, frequency of a class devide by total number of observations and then multiply the result by 100.
• 8/40=0.20 or 20% . The relative frequencies should add up to 1 (100%)

a list of all classes and their relative frequencies.

the smallest value that could go into a class

the smallest value that could go in the next higher class(or the lower cutpoint of the next higher class)

the middle of a class, found by averaging its cutpoints ex. 50<-60 (50+60)/2=55

The difference between the cutpoints of a class. 60-50=10

A table that provides the classes, frequencies, relative frequencies and mid-points of a data set.

• Make 8 classes
• 1. Find max value (45)
• 2. Min value ( 155)
• 3. Range between Max and min =Max-Min (155-45) =110
• 4. Width - 110/8=13.75~14 is the width between lower and upper cutpoints 45<-59

A graph that displays the classes on the horizonal axis and the frequencies of the classes on the vertical axis. The frequency of each class is represented by a vertical bar whose height is qual to the frequency of the class.

A graph that displays the classes on the horizontal axis and the relative-frequencies of the classes on the vertical axis. The relative frequency of each class is represented by a vertical bar whose height is equal to the relative frequency of the class.