8- Statistics and hypothesis testing in ABA Flashcards
You work Top : Large to small-
Theory
Hypothesis
Test hypothesis
Specific answer
Requires statistics to interpret large amounts of data (Quantitative/hard number)
majority of Social science researchers have a ____ orientation
Deductive Research Paradigm
AKA deductive approach
Work from Bottom Up, small to large:
Generalize Analysis - (Results: come to conclusions that you can generalize to other people about. ) Data
Fluid, qualitative approach
Examples of qualitative research:
interviews
observation of cultures
Focus groups
.
Inductive approach – research
Research in ABA is typically ……..in that we do not test hypotheses
but we are also quantitative
Reversal designs are : -flexible (ABA vs. ABAC) -quantitative, - without a pre-determined outcome Why the differences? Not withstanding the differences can we use the tools?
inductive
•Goal:
- To “Describe” Properties of the sample(s) you’re working with
- can talk about the central tendency of the sample or population in terms of what the most typical score in your sample or population look like.
- can talk about the variability Around the measure of typicalness be it mean median or mode. What is the variability around that measure of central tendency
- and talk about Effect size
”Descriptive” statistics
-Complements visual analysis
Already use them to describe:
•level change
• IOA
Can use in Program evaluation By aggregating data across clients
May open doors for Funding.
Ex. Effect size (Can be compared to other effect sizes)
Descriptive Statistics in ABA- Reasons for using
May hide Trends in behavior
Descriptive statistics in ABA: reasons for not using
Goal:
• To Use a sample data as a basis for Answering questions about the Population. (Can’t access whole populations. Instead we collect samples.)
• Since we rely on samples, we must to better understand how they relate to populations.
••Then we use HYPOTHESIS testing to make those inferences : T-tests, ANOVA etc
(The inferences about the samples are about the population from which the sample was drawn.)
(And the inferences are about relationships or features Of the population.)
Inferential statistics- Goal
Appropriate for certain types of research-
ex. When ABA does not use single case design such as contingency management – group
May open doors to funding
• hypothesis testing
Perceived weakness of reliance on Visual analysis in ABA.
Inconsistent?
Reasons for using Inferential statistics - ABA
• Do not tell us how likely the results are to be replicated.
- in ABA We use an ABA design or Multiple BASELINE design.
- INFERENTIAL statistics, we’re not Operating under circumstances that allow us to REPLICATE effect.
Do not tell us the probability that the results were due to Chance
Tells us The Probability is a CONDITIONAL probability event under true null hypothesis
- Very few situations in which there is only randomness in data.
- Best way to increase your chances of significance is increasing number of participants.
- A large number of variables that will have very small effects become important.
- Limits the reasons for doing experiments.
- Reduce scientific responsibility.
- Emphasizes population parameters at the expense of behavior.
“Behavior is something an individual does not what a group average does.”
•We should be attending to:
- value/social significance,
- durability of changes
- Number and characteristics of participants that improve in a socially significant manner.
Inferential - Some reasons for not using it in ABA
Looked at behavioral treatment and normal educational and intellectual functioning and young autistic children (Journal of consulting and clinical psychology, 1987)
Hypothesis: the construction of a special, Intense, and comprehensive learning environment for very young children with autism would allow them to catch up with their normal peer is by first grade.
Subjects were young children diagnosed with autism.
- Group one : 19 subjects – 40 hours a week of ABA
- Group twi: 19 subjects- 10 hours a week of ABA
- Group 3:21 subjects – other treatments
Groups of one and two received two or more years of therapy
Lovaas
Statistical analysis (MANOVA) used to compare the DV (IQ) To show that the intensive group demonstrated a large increase relative to the other conditions
He was a behavior analyst. Why hypothesis testing, statistics, and IQ as a dependent variable?-
- Intensive, long-term study that used measures and analysis that others NOT in our field would pay attention to.
- Control groups allowed for strong conclusions
Inferential Statistics
Lovaas Study
- Nominal (name) refers to categories
Ex. School districts and colors - Ordinal (order), Quantities that have an order
Ex. Physical fitness and pain scale
(Not a lot you can do with these two types of data) - Interval - difference between each value is Even
Ex. Degrees Fahrenheit - Ratio: when the difference between each value is even, has a true Zero
Ex. Time, weight, temperature in kelvin
Practically, interval and ratio are types of data we are interested in
data used in statistics 4x
- Mean
- Median
- Mode
More than one because many different types of Distributions are possible.
Three measures of central tendency
Descriptive statistics
The sum of the score is divided by the number of scores
Advantage: every number in the distribution is used in its calculation
However changing a single score or adding a new score will change it, except when the new score equals it
Most preferred measure
- Every score used it it’s calculation
- used to calculate other statistics
However Some situations in which mean cannot be calculated or is not most Representative measure.
Remember, the goal is to find a single value that best represents the entire distribution (median and mode)
Mean
The score that divides the Distribution exactly in half
A ____ Splits gives researchers two groups of equal sizes..
- Low Scores - High Scores
Median
- Collect all Odd number of scores
- List from Lowest to Highest
- It’s the Middle score
Ex., (10, 11, 12, 13, 14. )____. = 12
Even number of scores:
- List from lowest to highest
- Add the middle 2 scores and divide by two
Example, 2, 3, 5, 8, 10, 12, = 5+8/2 = 6.5
Calculate Median
Use when:
there are Extreme scores/skewed distribution’s
Undetermined Values
Open ended distribution’s
Median: When to use
Is the score or category that has the greatest flexibility ( Peak)
A distribution can have more than one mode,
• bimodal
•multimodal
Easy to find in basic frequency distribution tables
NOT A frequency. It’s a score or category
Mode
Two modes/peaks;
Can be equal or major/minor
BiModal
More than two modes
Multimodal
Use when It can be used in place of or in conjunction with other measures of central tendency. That is, when there are:
1. NOMINAL Scales; (only measure of central tendency for nominal Scales),
Ex. Are you male or female. 40 are male, 60 female. Can’t calculate the mean or median but can say the most TYPICAL participant is a female because thats 60% of the sample.
- Use when there are: Discrete Variable: “What is most typical” score; remember the goal of measures of central tendency
Ex. to know the number of golf clubs – calculate the mean.. Most typical score - Describing shape: easy to figure out
Mode
Describes the distribution in terms of Distance;
How far is that person from the central tendency whether mean, median, or mode
Distance between one score and another or,
Distance between one score and the mean
Describes how well each score or a group of scores describes the entire distribution.
Provides A quantitative measure of the degree to which scores in a distribution are spread out or clustered together.
Variability
- Range
2 interquartile
- standard deviation - Most important
Three measures of variability
The distance between the Largest score and the “Smallest” score plus 1
A crude, unreliable measure of variability because:
-Does not consider ALL the scores in the distribution
Calculate:
Ex. 1
1, 4, 5, 8, 9, 10
10 - 1 + 1 = 10
Ex. 2:
10, 15, 20, 25, 30, 35, 40
40- 10+ 1 = 31
Take Highest and lowest, ignore the others in the range. Not detailed variability.
Range – variability Measure
Most important measure of variability
Measures the “Typical” DISTANCE from the MEAN and uses ALL Of the scores in the distribution
How far is Score from the mean.
Using an ABA:
- can be used to identify variability in behavioral data (Autocorrelation can be used for this too).
- Can be described to identify important variability in IOA Data.
Mean and range tell us nothing about which set of circumstances we have which is why we should always report standard deviation over IOA scores along with mean.
Standard deviation – variability measure
The relationship between samples of populations
Cannot talk about the Exact Relationship between samples of populations…
But we can talk about Potential outcomes (I.e. Probability)
Probability - inferential statistics
To make ”inferences” about Populations based on sample data
We are Sampling the population with a certain Probability
Two kinds:
- Subjective
- Objective
Inferential statistics – Role
Based on experience or intuition
-Chance of rain, likelihood of recession, chance of getting married in the next year, likelihood of Miami Heat winning another championship
Subjective probability
Based on mathematical concepts and theory
Objective probability – inferential statistics
P(event) =. # of outcomes classified as the event divided by/ total number of Possible outcomes
The probability of event A, p(A), Is the ratio of the number of outcomes that include event A to the total number of possible outcomes
Example What is the probability that a selected Person has a birthday in October, assume 365 days in a year?
Step 1: how many chances are there to have a birthday in a year?
Step 2: how many chances are there to have a birthday in October?
Step 3: the probability that a randomly selected person has a birthday in October is:
P (October birthday) = 31/365 = 0.0849
Probability formula
Contained in a limited range 0-1.
If P = 0, the event will not occur
If P = 1, the event will always occur
Can be expressed as fractions, decimals, or percentages.
These values are always positive.
Ex, P = 3/4, P = 0.75, P = 75%
(All these values are equal)
In order To apply these rules to samples and populations, we must satisfy two requirements:
- Each individual in the population must have an equal Chance of being selected
- If more than one individual is to be selected for sample, there must be Constant probability for each and every selection (Sampling with replacement)
Example: you draw a number out of a hat and record it, you put the number back and it can be chosen again.
Remember, probability and proportion or equivalent. Thus, whenever a population is presented in a frequency distribution grass, it will be possible to represent probabilities of proportions of the graph.
Ex., if a population is presented in a graph, it is possible to represent probabilities as proportions. What is the probability of drawing an exam of B or better out of the pile of 31? Many students getting B or better = 24. 24/31 = 77 proportion or 77%. Can convert from a frequency distribution to probability
Probability values
Normal shape distributions are the most common occurring shape for population distribution’s.
Identify sections of a normal distribution using Z scores (Eg, 1 or 2 SD above mean)
The normal shape can also be described by the proportions of area contained in each section of the distribution.
Ex., 1). Left and right sides of distribution have the same proportions
2) Proportions apply to any normal distribution
Why is this important? We can now describe X values ( Raw scores) In terms of probability.
Ex., What is the probability of randomly selecting a person who is taller than 80 inches? 2.28% (See slide)
Ex., Raw score of 118 on IQ test converts to Z = 1.02. Look for corresponding proportion in table
Where Do These Percentages Come From?
Example: Raw score of 118 on IQ test converts to z = 1.02
Look for corresponding proportion in table
Probability And frequency distribution
A tool that allows you to see how you’ve done in a
normal distribution.
Identify sections of a normal distribution using Z scores (Eg, 1 or 2 SD above mean)
Collecting enough data tends to yield a normal distribution
If I get a particular score, I can convert it to a Z-score (if I know the SD and mean).
Z-score of 1.0 means I did better than 84% of the population
Needing the population standard deviation and mean is a large limitation.
Why use z-score? Because data are normally distributed along the axis. if I get a score and it translates into a 1, I know exactly how I did compared to everyone else. You can find Z score on a table
Application of Z-Scores Test 1 908 958 962 977 1000 1000 1045 1046 1047 1060 Mean 1000 SD 50 25 Test 2 109 121 125 145 152 158 165 170 178 180 What if I took both tests? Test 1 Score: 1100 Test 2 Score: 200
Application of Z-Scores 98% 2% Test 1 score: 1100 Z-Score: 2 Test 2 score: 200 Z-Score: 2 What if I get a Z-score that is not a pretty number?
Z – score review
Normally distributed population:
(Mean) = 24 years old
(SD) = 2 years
Normally distributed population: = 24, = 2
1. Draw a sample of 25 from population: = 22
2. Draw a second sample: = 22
3. Draw a third sample: = 20
4. Draw a fourth sample: = 18 5. Draw a fifth sample: = 26
6. Draw a sixth sample: = 22
7. Draw a seventh sample: = 24
8. Draw an eighth sample: = 24
9. Draw a ninth sample: = 26
10.Draw a tenth sample: = 24
Normally distributed population: =24, = 2 We now have 10 means from samples of 25:
22, 22, 20, 18, 26, 22, 24, 24, 26, 24
We take those 10 means and create a frequency
distribution of the means:
Closer inspection of the distribution of sampling means reveals a mean = 22.8 and SD (called standard error of the mean) = 2.52 ( Average distance between data points)
Distribution of Sample Means
What did we just do?
• Used a sample to provide information about a population
• What do we already know about this process?Samples provide incomplete pictures of the population called; Sampling Error
Sampling distribution of the means:
Inferential statistics
(The difference between the mean of a sample and the mean of the population)
Or..
The discrepancy or amount of error between a Sample statistic and its corresponding population parameter
From Illustration:
-Population mean = 24, SD = 2
- Sample mean = 22.8, ST = 2.52 (average distance between data points)
Samples will be different from the population because there are different individuals, different scores and therefore different sample means.
Sampling error
Sampling Error
How can you tell which sample best describes the population?
Can you predict how well a sample will describe its population?
What is the probability of selecting a sample that has a certain sample mean?
We answer this question by establishing a set of Rules that…
…Relate samples to populations
The collection of sample means for all possible random samples of a particular size ,(n), that pcan be obtained from a population.
Eg, 10 samples yielded a collection of sample means and each sample size was 25, (random samples of a particular size (n). )
Different samples taken from the same population will yield different statistics
In most cases, it is possible to obtain thousands of different samples from one population
The sample means tend to pile up around the population mean
The distribution of sample means is approximately NORMAL in shape
We can use the distribution of sample means to answer PROBABILITY questions about the sample means
How can we predict characteristics of the sample?
It’s not always possible to collect and compute ALL the possible sample means…
..So we need some general characteristics that describe a distribution of sample means. Leads to the Central Limit. Theorem
Distribution of sample means
Summary: The larger your number of samples, the more normal your distribution will be.
For any population, the distribution of sample means will approach a normal distribution as “n”. approaches infinity
The shape of the distribution of sample means will be almost perfectly NORMAL if either one of the following conditions is satisfied:
• Population from which sample selected is normal, and the number of scores (n) and each sample is relatively LARGE (n > 30)
• A sample mean is Expected to be near its population mean
Central Limit Theorem
The larger the sample size, the more probable it is that the sample mean will be CLOSE To the population mean.
Primary use of a distribution sample means is to find the probability associated with any specific Sample
The law of large numbers
A statistical method that uses sample data, statistics, to Evaluate a hypothesis, question, about a population parameter.
A basic,common inferential procedure that uses Z – score is, probability, and the distribution of sample means
Purpose: to help researchers differentiate between REAL patterns in data and RANDOM Patterns in data:
- .
Hypothesis testing
