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Intro. Statistics Week 2 Notes

by: Michelle H.

Intro. Statistics Week 2 Notes STAT 2000

Marketplace > University of Georgia > Statistics > STAT 2000 > Intro Statistics Week 2 Notes
Michelle H.
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About this Document

These notes are for week 2 of STAT2000 at UGA. The chapters covered are 3.1 and 2.1-2.4. Additionally, these notes contain summaries of in-class activities and material from the textbook not cover...
Intro Statistics
Georgia Gilbert
Class Notes
Math, Stats, Statistics, intro to statistics, uga




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This 5 page Class Notes was uploaded by Michelle H. on Thursday August 25, 2016. The Class Notes belongs to STAT 2000 at University of Georgia taught by Georgia Gilbert in Fall 2016. Since its upload, it has received 55 views. For similar materials see Intro Statistics in Statistics at University of Georgia.


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Date Created: 08/25/16
Introductory Statistics: Week 2     4.3: Good and Poor Ways to Experiment  ● Experimental unit:​ The individual whom is studied by the survey.  ● Treatment​: A condition applied to the subject.  ● Explanatory variable​: A variable in the study that explains or influences the changes in a  response variavle  ● Response variable:​ The variable or interest/what is measured by the study  ● Placebo​: “dummy” treatment given to the control group so they aren’t aware they aren’t  actually receiving the experimental treatment.  ● Double Blind​: Neither the researchers or the patients know which group is the control group  or the experimental group.  ● Single Blind​: The researchers know which group is the experimental or control, but the  patients don’t.  ● Confounding​: Multiple explanations can be given for a certain behavior/effect and a definite  cause cannot be determined  ○ If this occurs, it is impossible to determine a cause/effect relationship.  ○ The results of the experiment cannot be replicated.        4.4: Ways to Conduct Studies  ● Completely Randomized Design​: The experimental units are randomly assigned to the  treatments  ● Matched­Pairs Design​: The experimental units are related in some way before the  experiment takes place (twins, husband, wife, etc.)  ○ Most of the time, units in a matched­pair design are measured before and after the  experiment  ● Blocking​: A factor is used to create homogeneous groups called blocks  ○ Eg. Male group and female group  ○ The experiment is conducted separately in each group.      Example: New Drug  ● The experimental units were the 300 males whom were in the study  ● The response variable that was measured was the white blood cell count  ● The explanatory variable was the type of treatment each experimental group received. The  two treatments used were the experimental drug and the placebo  ● In this example, the experiment was a single blind study as the participants did not know  which treatment they received but the researchers did.              Exploring and Summarizing Data  ● Variable​:Any characteristic that is studied  ○ Eg. GPA, Height, etc  ○ For each variable, there is an expected level of variability. Variability are the  differences of data that are studied in statistics  ○ Experiments are created to measure, record, and explain variability  Types of Variables  ● Categorical Variables​: Observations that can be placed into a finite set of categories.  ○ Political parties, Gender, Yes or No questions  ○ Definite answers  ● Quantitative variables​: Numbers or other values that cannot fit into a set of categories  ○ Height, Weight, SAT Score  ○ Quantitative variables can be ay number. For example, people tend not to have the  exact same height as another  Ways Variables Can be Visually Represented  ● Bar Graph:​ A graph in which values are represented by the height of bars.  ● Pareto Graph​:​ A type of graph that contains both a line graph and a bar graph.  ○ Individual values, shown from largest to smallest, are shown in a bar graph.  ○ A line graph shows the cumulative total      ● Proportional Graph​:​ Values are organized from highest to lowest and the number on the  side is the proportion of answers that fall into each category  ● Pie Chart​:​ circle divided into sectors which display values in percentages of a whole.        Categorical Variables    ● Conditional Distributions​: Restricts variables in a way that shows the distribution of values  that satisfy a certain condition  ○ eg. A study may only show the statistics from a certain age range (such as 19­25)  even though the group surveyed contained many people who fell outside this range.                          Example    Male  Left Handed  Right  Total  Handed  Female  160  600  760  Total   300  1160  1460    Explanatory Variable: ​ Left column (Male/female)  Response: ​ Middle columns (left and right handed)  Denominator:​ Right column (total)        Left  Right Handed  Handed  Male    = 0.21    =0.79  Female    =0.20  =0.80    Relative Risk​: Calculated by the equation    When the relative risk is close to one, it means the variables have no relation to each other and and  considered to be independent.    Sample Problem  How much more likely is it for a male to be left handed than a female?  ● Proportion of left handed males: 0.21  ● Proportion of left handed females: 0.20  ●  = 1.05  In this case, you can say that a male is 1.05 times more likely to be left handed than a female.                  2.1: Quantitative Variables  ● All possible values the variable could possibly take on and how these values are distributed  (spread out)  Types of Graphs  Dot Plot​: A plot with dots.  ● Each dot represents an individual value  ● Not often used   Histogram​:​ A bar graph that is used to measure the count of values that fall into certain intervals  ● A frequency table is used to find these counts  ● No value can fall into two intervals and the intervals must be made of equal intervals    Group  Freq.  10­19  5  20­29  7        2.2: Shape of Distribution  ● Looking at the overall shape of the histogram allows us to observe the trends found in the  data  ● Skewed​: not symmetric, meaning the graph is not equal on both sides. Skewed histograms  are either right skewed or left skewed.  ● Symmetrical​: The graph shows equal distribution across the values  ● Mode​: The tallest bar in the graph, also known as a peak. Histograms can contain multiple  peaks  ○ If the graph has one peak, it is called ​unimodal  ○ Two peaks are ​bimodal​, three peaks are trimodal, ect.  ● Tails​: The collection of bars on either side of the mode  ○ Symmetrical graphs have tails of equal length  ○ Right skewed graphs have a longer tail on the right side  ○ Left skewed graphs have longer tails on the left side                    Describing Graphs                          The above histograms are described as:  ● A: Unimodal and right skewed  ● B: Unimodal and left skewed  ● C: Unimodal and symmetrical      2.3: Measuring the Center of Quantitative Data     Vocabulary  ● Mean​: The average, or the sum of all observed values divided by the number of values.   ○ The mean can also be thought of as a “fair share"  ○ For example, the mean could be used to equally divide the money made between  business partners.  ● Median​:​ The point in which the values are split into two when the values are arranged from  smallest to largest  ○ The median is the "middle number” of the set.  ■ In the set (1,1,​3​,4,5) the median is 3  ○ If the data set has an odd number of values, the median is the number in the middle  of the two values  ■ In the set (1,1,​3​,​5​,7,8), the two middle numbers are 3 and 5. The median  would be 4.         


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