Exam 1: Biostatistics Flashcards
(99 cards)
1
Q
Descriptive Statistics
- Involves
- Purpose
A
Involves: Collecting, Presenting, and Characterizign Data
Purpose: Describe Data
2
Q
Inferential Statistics
- Involves
- Purpose
A
Involves: Estimation and Hypothesis Testing
Purpose: Make decisions about population characteristics
***Allows us to describe a population based on a sample***
3
Q
Variable
A
A symbol of an event, act, characteristic, trait, or attribute that can be measured and to which we can assign some values
4
Q
Categorical Variable
A
Consists of some numeric or character codes that represent either:
- The presence or absence of something that is of research interest
- The relative weight or rank of the thing that is of research interest
5
Q
Quantitative Variable
A
Variable that holds the numerical result of some measurement
6
Q
Process
A
Series of actions or operations that transforms inputs to outputs; generates output over time
7
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Characteristics of Variables: Nominal Scale
A
Simplest level of measurement - categories without order
8
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Characteristics of Variables: Ordinal Scale
A
Nominal variables with an inherent order among the categories
9
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Characteristics of Variables: Interval Scale
A
Measruable difference or interval or distance between observations
10
Q
Characteristics of Variables: Ratio
A
Same as interval but with an absolute reference point (such as “0”)
11
Q
Data Presentation: Qualitative Data
A
Summary Table –> Either a Bar Graph or Pie Chart
12
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Data Presentation: Quantitative Data
A
Dot Plot, Stem and Leaf Display,
or
Frequency Distribution –> Histogram
13
Q
Class
A
One of the categories into which qualitative data can be classified
14
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Class Frequency
A
Number of observations in the data set falling into a particular class
15
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Class Relative Frequency
A
Class frequency divided by the total numbers of observations in the data set
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Class Percentage
A
The class relative frequency multipled by 100
17
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Bar Graph
A
Classes (Bars) have heights equivalent to class frequency, class relative frequency, or class percentage
(Unlike Histogram –> just class frequency and class relative frequency, bars are touching)
18
Q
Pie Chart
A
Classes are in slices proportional to the class relative frequency
19
Q
Central Tendency
A
Tendency to cluster/center about certain numerical values
20
Q
Variability
A
Spread of the data
21
Q
What symbols represents Sample/Population Mean and Size?
A
X bar should be lower case x
22
Q
Which is used for both quantiative and qualitative data, mean, median, or mode?
Which is not effected by extreme values?
A
Mode
Median and Mode
23
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Summary of Mean, Median, and Mode
A
24
Q
Variance and Standard Deviation
A
- Measures of dispersion ***More reliable than Range***
- Most common measures
- Consider how data are distributed (unlike Range)
- Show variation about mean
25
What does **Normal Distribution** mean?
Mean = Median = Mode
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What does the **mean** equal in the standard normal curve and what is the first standard deviation?
**Mean = 0**
First SD is +/- 1
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**Standard Notation** (Sample vs. Population)
1. Mean
2. Standard Deviation
3. Variance
4. Size
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When do you use **n-1** vs. **n** in the denominator of the Variance Formula?
**n-1** = Sample Variance
**n** = Population Variance
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Shape of Curve: Mean vs. Median
## Footnote
**1. Left-Skewed**
Left Skewed
Mean \< Median
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Shape of Curve: Mean vs. Median
1. Right-Skewed
Right-Skewed
Mean \> Median
31
**The Empirical Rule**
1. Applies to
2. What percentage of the measurements lie within 1, 2, and 3 SDs of the mean? What are their **Z-scores**?
**Applies to**: Data sets that are **mound-shaped** and **symmetric** (i.e. **_Normal Distributions_**)
**68%** of measurements lie within **one** SD of the mean (x-s to x+s) **z-score = b/w -1 and 1**
_95%_ of measurements lie within _two_ SDs of the mean (x-2s to x+2s) **z-score = b/w -2 and 2**
*99.7%* of measurements lie within *three* SDs of the mean (x-3s to x+3s) **z-score = b/w -3 and 3**
32
If you scored in the 58th percentile, what percentage of test takers scored **lower**/**higher** than you?
**Lower:** 58%
**Higher:** 42%
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Numerical Measures of Relative Standing: **Z-Scores**
1. Describes...
2. Measures...
Describes the relative location of a measurement compared to the rest of the data
Measures the **number of standard deviations** away from the mean a data value is located
34
What is the **Frequentist** definition of **Probability?**
If an experiment is repeated **n times** under identical conditions and if the event **A** occurs **m** times, then as **n** grows, the ratio of m/n approaches a fixed limit called the probability of **A**
P(A) = m/n
**"Law of Large Numbers"**
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**Probability** Equation
Frequency of times an outcome occurs **divided by** the total number of possible outcomes (symbolized as *p*)
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**Random Event**
Any event where the outcomes observed in that event involves uncertainty or the outcome can vary
(predicted by **Probability**)
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When is probability unnecessary to calculate?
For a **fixed event**
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**An Event** (Two Definitions)
1. An occurrence due to nature
2. A collection of one or more outcomes of an experiment
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**Simple vs Compound Probabilities**
Simple = Single occurrence
Compound = Result of operations
-Define relationships between or combination of event occurrences
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What are the **three operations** that can be used to create **compound events**?
1. Intersection
2. Union
3. Complement
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**Intersection**
The intersection is defined as **"both A and B"**
Represented by **A Π B**
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**Union**
Union is defined as **"either A or B or both A and B"**
**A Ü B**
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**Complement**
Defined as **"Not A"**
Denoted by **AC or -A**
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**The Additive Law: _Special_ Rule of Addition**
Two events A and B that **cannot** occur simultaneously are said to be **mutually exclusive or disjoint**
e.g. The probability of a newborn weightin under 2000 grams is 0.025 and over is 0.043
\*\*\*simply would **add the probabilities of the individual events**\*\*\*
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**The Additive Law: _General_ Rule of Addition**
This is used when there is a **common region**; must **_subtract out common region_**
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Two-Way Table Example
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Probabilities Example
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**Independent Events**
Two **unrelated** events
\*\*\*When expressing the joint probabilit of independent events, the general rule of **multiplication** _does not hold_
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**The Special Rule of Multiplication**
e.g. tossing a coin
Second toss has nothing to do with the first
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Questions about **Mutual Exclusiveness...**
1. If events are **mutually exclusive...**
2. If events are **_not_** mutually exclusive...
Use **"or"** and the **additive rule**
1. ME: add them all up
2. Not ME: Subtract out **common region**
51
Questions about **indpendence...**
1. Independent events...
2. Not independent...
Use **"and"** and the **multiplication rule**
1. Multiply them all together
2. P (A and B) = P(A|B) x P(B)
P (B and A) = P(B|A) x P(A)
52
**Bayes' Theorem**
1. When is it used
2. P(A) vs P(B|A)
3. Importance
1. When **multiplicative** events are **not independent**
2. P(A) = prior probability (**_known before_** calculation)
P(B|A) = posterior probability (only **_known after_** calculation)
3. Helps investigators determine the other pertinent probability when only one is known
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How do you figure out the **population mean?**
You can use a sample and will be **very close**
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**Unbiased vs. Biased Estimates**
**Unbiased:** if the sampling distributino of a sample statistic has a mean **equal to** the population paramater that the statistic is intended to estimate
**Biased:** if the mean of the sampling distribution is **not equal to** the parameter
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**Central Limit Theorem**
As sample size gets **large enough**, the **sampling distribution** becomes _almost normal_
\*\*\***Justifies Inferential Statistics**\*\*\*
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Confidence Interval for a Population Mean: Normal (z) Statistic
1. Finds what?
Finds the **range** over which the population parameter **MIGHT** be found
\*\*\*A **range of plausible values** for the **population parameter**\*\*\*
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What does a **95% Confidence Level** indicate?
In the long run, 95% of our confidence intervals will contain **u** (the **population mean**) and 5% will not
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What are **2 conditions** required for a Valid Confidence Interval for u?
1. A **Random Sample** is selected from the target population
2. The sample size **n** is **LARGE**
- Due to the **Central Limit Theorem** this condition guarantees that the sampling distribution of x(bar) is approximately normal
Also, for large n, s will be a good estimator of o- (population standard deviation)
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**Student's t-statistic**
Has a sampling distribution very much like that of the **z-statistic** (mound shaped, symmetric, with mean 0)
\*\*\*Primary difference is that t-statistic is more variable than z-statistic\*\*\*
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**Degrees of Freedom (df)**
Actual amount of **variability** in the sampling distribution of **t** depends on the **sample size, n**
T-statistic has **(n-1)** degrees of freedom
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What happens as **Degrees of Freedom (df)** go _down_?
The t-distribution **flattens out**
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**Sampling Error**
A way of expressing the **reliability** associated with a confidence interval for the population mean, u
**Sampling Error (SE)** is equal to **half-width** of the **confidence interval**
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What is a **Hypothesis**?
A statment about the **numerical value** of a _population parameter_
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**Null Hypothesis (H0)**
The hypothesis that will be accepted unless the data provide convincing evidence that it is false. This usually represents the **"status quo"** or some claim about the population parameter that the researcher wants to test
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**Alternative Hypothesis (Ha)**
The hypothesis that will be accepted only if the data provide convincing evidence of its truth. This usually represents the values of a population parameter for which **the researcher _wants to gather evidence to support_**
\*\*\***Opposite** of the null hypothesis\*\*\*
66
When do we use **Hypothesis Testing**?
1. **_Observational Studies_**
- Find the **"true" population parameter**
(e. g. what is the prevalence of AIDs in some community)
**\*\*\*1 sample\*\*\***
2. **_Clinical Trials_**
- Compare Group 1 to Group 2 or
- Compare Baseline state to post-intervention state
**\*\*\*2 sample tests - _Independent Samples_\*\*\***
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**Test Statistic**
A sample statistic, computed from information provided in the sample, that the researcher uses to **_decide between_** the null and alternative hypotheses
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**Type I Error**
Occurs if the researcher reject the null hypotehsis in favor of the alternative when, in fact, the **null hypothesis is _true_**. The probabilit of committing a Type I error is denoted by **a (alpha)**
\*\*\*The level of a is usually small and is referred to as the **level of significance** of the test\*\*\*
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**Rejection Region**
The set of possible values of the test statistic for which the researcher will reject **H0** in favor of **Ha**
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**Type II Error**
Occurs if the researcher **accepts the null hypothesis** when, in fact, it is **false**. Probabiility of committing a Type II error is denoted by **B (beta)**
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How do you identify the null hypothesis?
It will always have an **equality sign**
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What is a **p-value**?
The **observed significance level** for a specific statistical test is the probability (assuming H0 is true) of observing a value of the test statistic that is at least as contradictory to the null hypothesis, and supportive of the alternative hypothesis, as the actual one computed from the sample data
## Footnote
**\*\*\*Used to make _rejection decision_\*\*\***
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What does a p-value \> or = to a mean?
**DO NOT** reject H0
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What does a p-value \< a mean?
**REJECT** H0
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Where is the **Confidence** in hypothesis testing?
Confidence is in the **testing process, _NOT_** in the particular result of a single test
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Strength of Correlation
Reflects how consistently scores for each factor change
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Regression Line
The **best fitting straight line** to a set of data points. A best fitting line is the line that minimizes the distance of all data points that fall from it
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Numerical Measure of Correlation: **Pearson Correlation Coefficient**
**The Pearson (product moment) correlation coefficient (r)-** used to measure the _direction_ and _strength_ of the linear relationship of two factors in which the data for both factors are measured on an interval or ratio scale of measurement
Numerator --\> **Covariance** (extent to which X and Y axis vary _together_)
Denominator --\> "" _independently_ or _separately_
79
Regression Analysis
Statistical procedure used to determine the equation of a regression line to a set of data points and to determine the **extent to which the regression equation can be used to predict values of one variable**, given known values of a second factor in a population
- One quantitative dependent variable
- One or more quantitative or qualitative (**binary**) variables
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Regression Analysis --\>
Logistic Regression --\>
Regression Analysis (**Quant**itative DV)
Logistic Regression (**Qual**itative DV)
-Yes or no, Male or Female
81
What do rows and columns represent in a data table?
Rows = **Cases**
Columns = **Variables**
82
What type of data do proportions summarize?
**Nominal** and **Ordinal**
| (i.e. **Qual**itative data)
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How are rates different from proportions?
They are similar to proportions EXCEPT a **multiplier (e.g. 100, etc.) is used**
\*\*\*They have a **time reference** - are computed over a known/given period of time\*\*\*
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Vital Statistics Rates
Also known as **demographic measures**
\*\*\*Describe the **health status of a population**\*\*\*
e.g. Mortablity Rates (Crude, Specific) and Morbidity Rates
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Crude Mortality Rate
Number of **all deaths** in a given geography over a given year **divided by** the total population of the geography durnig the same year
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**Specific Mortality**
Relates to **specific populations** within the geographic region
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What is Morbidity Rate also known as?
**Prevalence** or **Prevalence Rate**
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Incidence
The number of **new cases** that have occurred during a given interval of time **divided by** the total population at risk
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What are **Adjusting Rates** used for?
To make a **fair** comparison between different populations and to **avoid _Confounding_**
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Examples of Confounding Factors
Age composition, Gender composition, Race/ethnic composition of a population
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Absolute Risk Reduction (ARR)
The **reduction in risk** (by the experiment) compared with the **baseline risk**
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Number Needed to Treat (NNT)
The number needed to treat in order to **prevent _one_ event**
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What is the reciprocoal of the absolute value of NNT?
Absolute Risk Increase or the **Number Needed to Harm**
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Relative Risk Reduction (RRR)
The amount of risk reductuion relative to the baseline risk
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Relative Risk
What types of studies is it mainly used in?
The ratio of the **incidence of a disease** **in people who are exposed** to a risk to the incidence of **people without exposure to risk**
Mainly used in **cohort studies**
(Prospective)
96
Odds Ratio
What type of study is this used in?
The odds that a person with the disease is exposed to a potential cause for the disease relative to the odds of a person without the disease is expose to the potential cause
Mainly used in a **case/control study**
(Retrospective)
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What does a RR or OR \<1, \>1, or =1 mean?
\< 1 = **Protective** exposure
\> 1 = **Risky** exposure
= 1 = **No effect**
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Inference (on RR and OR)
Inference is possible using the **normal distribution**
RR and OR distributions do not follow the theoretical probability distribution
The distribution of the **natural log** of RR and OR **do** follow **normal distribution**
\*\*\*Need to **transform** to generate inferential statistics\*\*\*
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When can you **reject** the **null hypothesis**?
When the p value involves **less error** than you were willing to commit (the **significance level, a**)
p-value of **0.03**
significance level of **0.05**
**\*\*\*\*Can reject** the null hypothesis in this case
