Quantitative Analysis unit 1

Data

collection of observations such as measurements, genders, or survay responses

Statistics

The science of planning studies and experiments, obtaining data and organizing, summarizing, presenting, analyzing, and interpreting that data, and then drawing conclusions

Population

The complete collection of all measurements or data that are being considered

Census

The collection of data from every member of a population

Sample

a subcollection of members selected from a population

Voluntary response sample/self selected sample

where the respondents decide whether to be included

statistical significance

achieved in a study if the likelihood of an event occurring by chance is 5% or less

practical significance

Some treatment or finding is effective, but common sense might suggest that the treatment or finding does not make enough of a difference to justify its use as practical

misleading conclusions

When forming a conclusion based on a statistical analysis, we should make statements that are clear even to those who have no understanding of statistics

Why is it better to do your own measurements?

People may not report truthfully

loaded questions

If the survey results are not worded carefully, the results of a study can be misleading

Order of questions

Sometimes survey questions are unintentionally loaded by the order of the items considered

Nonresponse

A nonresponse occurs when someone refuses or is unable to respond

Parameter

A numerical measurement describing some characteristic of a population

Statistic

A numerical measurement describing some characteristic of a sample

Quantitative data

consists of numbers representing counts or measurements

Qualitative (categorical) data

Consists of names or labels

Discrete data

result when the data values are quantitative, and the number of values is finite

Continuous data

Result from infinitely many possible quantitative values, where the collection of values is not countable

Nominal

Characterized by data that consists of names, labels, or categories only, and the data cannot be arranged in some order

Ordinal level

Involves data that can be arranged in some order, but the differences between data values either cannot be determined or are meaningless

Interval level

Involves data that can be arranged in order, and the differences between data values can be found and are meaningful; however, there is no natural zero starting point at which none of the quantity is present

Ratio level

Data can be arranged in order, differences can be found and are meaningful, and there is a natural zero starting point. Differences and ratios are both meaningful

Big data

Refers to data sets so large and so complex that their analysis is beyond the capabilities of traditional software tools. Analysis of big data may require software simultaneously running in parallel on many different computers.

Data science

Involves the application of statistics, computer science, and software engineering, along with some other relevant fields

Completely random missing data value

If the likelihood of it being missing is independent of its value or any of the other values in the data set

Experiment

Apply some treatment, then observe its effects on the individuals

Observational study

observing and measuring specific characteristics without attempting to modift the individuals being studied

Replication

The repetition of an experiment on more than one individual

Blinding

A technique in which the subject doesn’t know whether they are receiving a treatment or a placebo, prevents the placebo effect

Double Blind experiment

Neither the subject nor the experimenter knows who is receiving the treatment or the placebo

Randomization

Used when subjects are assigned to different groups through a process of random selection

Simple Random Sample

A sample of n subjects is selected in such a way that every possible sample of the same size n has the same chance of being chosen

Systematic Sampling

Select a starting point and select every kth element in the population

Convenience Sampling

using data that is very easy to get (teacher only sampling their students)

Stratified sampling

Divide the population into at least 2 different subgroups (strata) so that the subjects within the same subgroup share the same characteristics, then draw a sample from each subgroup (stratum)

Cluster sampling

Divide the population area into sections, then randomly select some of those clusters, and choose all the members from those selected areas

Cross sectional study

data is observed, measured, and collected at one point in time

Retrospective study

Data is collected from a past time period

Prospective

Data is collected in the future from groups sharing common factors

Confounding

Occurs in an experiment when the experimenter is not able to distinguish between the effects of different factors

Completely randomized experimental design

Assign subjects to different treatment groups through a process of random selection

Randomized block design

A block is a group of subjects that are similar, but blocks differ in ways that might affect the outcome of he experiment

Matched pairs design

Compare 2 treatment groups by using subjects matched in pairs that are somehow related or have similar characteristics

Rigorously controlled design

Carefully assign subjects to different treatment groups, so that those given each treatment are similar in ways that are important to the experiment

Sampling error

occurs when the sample has been selected with a random method, but there is a discrepancy between a sample result and the true population result

Nonsampling error

Is the result of human error, including such factors as wrong data entries, computing errors, biased questions, and false data

Nonrandom sampling error

Is the result of using a sampling method that is not random

Frequency distribution

shows how data are partitioned among several classes by listing categories along with the frequency of data values in each of them

lower class limits

the smallest numbers that can belong to each of the different classes

upper class limits

the largest numbers that can belong to each of the different classes

class boundaries

The numbers used to separate the classes, but without the gaps created by class limits

class midpoint

The value in the middle of classes is found by taking the average of the upper and lower class limits

class width

The difference between 2 consecutive lower limits in a frequency class

relative frequency

frequency for a class/sum of all freqencies

% of a class

relative frequency x 100

cumulative frequency

the sum of that class’s frequency plus the frequency of all previous classes

Histogram

a graph of qualitative data consisting of bars of equal widths drawn adjacent to each other

SOCS

shape, outliers, center, spread

CVDOT

center, variation, distribution, outliers, time

what are the types of distribution

bell shaped, uniform, skewed to the right, skewed to the left

What is normal distribution

The pattern of the points in the normal quantile plot is reasonably close to a straight line, and the points don’t show any other systematic pattern that is not a straight line