Descriptive statistics 922. Hypothesis (Linguistic) Participants Task (stimuli = questions,...

Descriptive statistics

Hypothesis (Linguistic) Participants Task (stimuli = questions, responses = answers) Results Conclusions

Key terms: stimulus design, response measure

What do we need to run an experiment?

Example

Show me the cat that bit the dog

Show me the cat that the dog bit

Picture from:

Friedmann &Novogrodsky (2001)

Design

Number of conditions Within subject / between subject How many items to each participant Order of items

Measure Response

Variables Scales Analysis

Descriptive Inferential

Variables Any experimental category that has a

value that can vary. Anything that is not constant and can

change over time, or be different in different people is a variable

Variables can take many forms Variables can be manipulated and

observed

Properties of Variables Continuous variable – along a continuum

with equal intervals (e.g., age, height, weight, grade in a test)

Ordinal variables – rating along a continuum with estimated intervals (e.g., evaluation)

Discrete variables (categorical, nominal) – divide to categories (e.g., language, yes/no, correct/incorrect)

Types of Variables Independent variables –

Characteristics of the subject (Participant variable)Conditions chosen by the experimenter

Dependent variables – what the experiment measures (e.g., degree of success)

Intervening variables – variables which are not measured or manipulated, but could influence the results (e.g., concentration, intelligence)

Field, A. & G. Hole. 2003. How to design and Report Experiments. London: A Sage Publications Company

Scales

Nominal Ordinal Interval Ratio

Scales

Two things with the same number are similar (same name)

Scales

Four is more than three (but not the same as three from two)

Scales

Four is more than two (but not twice)

Scales

Nominal Ordinal Interval Ratio Four is more than

three, same as three from two, and is twice two

Which scale are the following variables rated on? Height Celsius degrees TV channel number Grades in an exam (1-100) Psychological rating (anxiety on a scale of 1-

10) Time (13:00, 14:00) Time (one hour, two hours, three hours) Phone number Rating places in a race

Variables and Scales: summary

Choose an appropriate task Measure responses Be aware of the variables and their

properties Choose the mathematical operations

appropriate for the scale

Factorial design

Tests all possible combinations, e.g., a 2x2 design – one participant variable and one independent variable with two conditions.

Subject relatives

Object Relatives

Practical questions for offline tasks How many subjects? At least 25 How many categories? 2x2 How many items? More subjects >> fewer

items. For 25 – 6 items per category For 50 – 3 is enough For case studies and within subject analysis

at least 10.

SIMPLE NUMERICAL COMPUTATIONS

The relation between two nominal variables

V/N ratio: 60/80=3/4

N/V ratio: 80/60=4/3

Nouns80

Verbs60

Other words

Total190

Example

Goofy said that the Troll had to put two hoops on the pole to win.

Does the Troll win?

Musolino (2004)

Yes/no ratio: 8/12=2/3

Proportion

Relation between a group and its part (Verb/Word, Pronouns/Subject position). Ratio out of the total

Verb/Word proportion: 60/190=1/3=0.31

Percentage(%)

Relative proportion out of a hundred Verb percentage (out of all words):

100*(60/190) =31%

The relative frequency (for population out of a 1000)7% of children have SLI >> 0.07 * 1000 = 70 70 children out of a 1000 have SLI

Frequency

Count the number of times a score occurs.

How many times a value of a variable occurs?

Example

Show 10 pictures, and check for number of “correct” response

Is every bunny eating a carrot?

Roeper, Strauss and Zurer

Pearson (2004)

Picturecorrect

Total6

Frequency

Count the number of times a score occurs

ChildScore

Frequency

Raw scoreChildScore

FrequencyScoreFrequency

Frequency=how many children got this score

Frequency graph

Score on the test is the horizontal axis (X-axis)

Frequency is on the vertical axis (Y-axis)

Percentile

The cumulative frequency - how many scores are below a particular point in the distribution

Percentile = 100(Cumulative Frequency/Total N)

Grade Frequency cumulative frequency

percentile

100 2 30 100% 90 5 28 93% 80 10 23 77% 70 8 13 43% 60 4 5 17% 50 1 1 3% Total N 30

Frequency polygon (the curve)Frequency distribution

50 60 70 80 90 100

The frequency polygon (the curve) is a picture of the data

Types of distributions (Fig. 4.3 &4.4, pp. 113-116)

A bell shaped curve - a symmetric distribution, a unimodal distribution (one midpoint, one peak),

normal distribution

Pointy distribution (Leptokutic) Flat distribution (Platykutic)

In skewed distribution the tail is skewed in one direction:Positively skewed distribution - most scores are low, the tail is directed towards the high (positive) scores which skewed the distributionNegatively skewed distribution - most scores are high, the tail is directed towards the low (negative) scores which skewed the distribution

Bimodal distribution - a double peaked curve

Min (the lowest score) and Max (the highest score)

Range – the range of observed values. Range = Max-Min

But the range changes with the extreme scores (unstable but useful informal measure).

Descriptive Statistics - Some definitions

Mode - most frequently obtained score Mean (average) – average of a set of

numbers Median – the middle score of a group

(when odd) or the average of the two middle scores (when even)

In a bell curve (normal) distribution mode, mean and median will be the same

GradeFrequency

total30

Which grade is most frequent?

Highest in “frequency” column

Mean (average)

GradeFrequency

total30

Compute a sum of all grades

Divide by number of grades

Mean (average)

Grade x times

50x150

60x4240

70x8560

80x10800

90x5450

100x2200

total2300

mean2300/30

Median

GradeFrequency

total30

Order all grades in a row according to value

The grade in “the middle” of the row is the median

Median

GradeFrequency

total30

We have a row of 30 grades:

50,60,60,60,60,70… Half of 30 is 15 The grade in the 15th

position is the median

Median

GradeFrequency

total30

Slight complication: we have 15 grades on both sides of the median

Compute mean of the grades in the 15th and 16th positions

Variability

Questions: Are both curves the same? How? Are they different? How?

We need to measure the accuracy of the mean.

Coming attractions

How to draw valid statistical inferences?We have to look at the relation between our

sample and the population Today we looked at where the ‘center’ of

the data is – what is the big picture Look at variance, how the data is distributed

DeviationThe distance between a score and the Mean (see Table 4.2, p. 125), how much a score deviates from the average

Sum of squared errors (SS)

Variance Average error in the sample, average error

in the population Variance in the sample = SS/N

33.7143/7=4.8163 Variance in the population = SS/(N-1)

33.7143/6=5.6191 Why N-1? Degree of freedom (read box

4.5, page 129)

Standard deviation (SD)

The average distance between a score and the Mean (square root of the Variance)

SD= √5.6191 = 2.37

What can SD tell us about the distribution (pointy distribution vs. flat distribution)?

Standard Error (SE)

How well does the sample represent the population?

Different samples of the population might yield different means. The SE is the average of the SDs of the means of several samples. Large value - big difference, small value- small difference.

SE = SD/√ N

Confidence Interval

The limits within which 95% or 99% of the samples fall

Lower boundary = Mean-2SE Upper boundary = Mean+2SE

Inferential statistics

z-score and T-score

How can we use the standard deviation (SD) to compare two samples? two exams? two tests?

We translate the raw scores into distance in SD from the mean, by subtracting the mean from the raw score and dividing by the SD.

So for Table 4.2:

1-3.57 8-3.57--------- = -1.08 --------- = 1.86 2.37 2.37

These scores are z-scores. Some z-scores are negative and some are positive. Why?

So for Table 4.2:

1-3.57 8-3.57--------- = -1.08 --------- = 1.86 2.37 2.37

These scores are z-scores. Some z-scores are negative and some are positive. Why?

If you prefer a scale with only positive numbers, you can use the T-score

T score = 10 * z-score +50

10 * -1.08 +50 = 39.2

10*1.86+50 = 68.6

A few words on Covariance and Pearson correlation

Covariance - how much two variables co-vary?

Cov = (X - X) (Y- Y)

But we are interested in sets of scores so we need to sum up all the individual covariance and divide, as always by N-1.

Σ (X-X)(Y-Y)COVxy= ----------------------

What do we need covariance for? To measure correlations (Pearson correlation coefficient is considered the best way to estimate correlation between X & Y).

Since the two samples do not have the same

SD, we must adjust the covariance to the amount of variation

COVx y

r= --------------

SDx * SDy

What does r mean ?

Positive r - positive correlation Negative r - negative correlation Small r - small correlation Big r - big correlation

inferential statistics.xls

Effect size We can use correlations to measure

experimental effect size r2 - the coefficient of determination - is the

fraction of the variance that is accounted for by a linear correlation.

r=0.1 (small effect) - only 1% of the variance is accounted for by our task (1%=.01=r2)

r=0.3 (medium effect) - 9% of variance is accounted for by our task (9%=.09=r2)

r=0.5 (large effect) - 25% of variance is accounted for by our task (25%=0.25=r2)

r = 1 A perfect effect

Probability How probable it is to get a certain correlation? How probable is it to get a certain score? How probable is it to get a certain mean? How probable is it that two samples are the

same/different?

Playing "Head or tails?" Throwing a dice.

Probability can be calculated by dividing the number of desired events by the number of possible outcomes.

What is the probability of getting a score above the mean?

What is the probability of getting a score which is up to 1SD above the mean? up to 1SD from the mean? (For every z-score there is a probability)

Or by relaying on SD

Confidence Interval

The limits within which 95% of the samples fall

Lower boundary = Mean-2SE Upper boundary = Mean+2SE

Hypothesis testing

How likely is it (how probable is it) that our hypothesis is right?

The probability that some results could happen by chance is less than 5% (or 1%)

p<0.05 (or p<0.01) - the level of significance

Null hypothesis - there is no difference between our sample and the population

Positive hypothesis - the sample does better than the population.

Negative hypothesis - the sample worse better than the population

Alternative hypothesis - the sample is different but there is no direction.

p>0.05

p<0.05

If the data falls in the shaded area of 8.5 - the null hypothesis is confirmed

If the data falls in the shaded area of 8.6 - the null hypothesis is rejected

If the data falls in the shaded higher tail of 8.6 - the scores are higher than the population and the null hypothesis is rejected

If the data falls in the shaded negative tail of 8.6 - the scores are lower than the population and the null hypothesis is rejected

Since there is no direction specified by the null hypothesis, we must consider both tails - thus we use a two tailed test (with .025 in each tail).

If we test a directional hypothesis, the level of significance applies to one tail only.

A score in the shaded area in 8.7 confirms the _____________ hypothesisA score in the shaded area in 8.8 confirms the _____________ hypothesis

Descriptive statistics 922. Hypothesis (Linguistic) Participants Task (stimuli = questions,...

Documents

RESPONSE TO STIMULI - StudyWise · RESPONSE TO STIMULI STIMULUS – a detectable change in the internal or external environment of an organism that produces a response RESPONSE –

Mathematics Stimulus Considerations Stimulus Materials Module Overview Define the purpose of stimuli Identify types of stimuli Apply general guidelines

Classical Conditioning. Associative Learning Nonassociative HabituationSensitization A single type of stimulus The relationship between two stimuli Classical

LivingNon-livingDead Organisms must respond to stimuli appropriately in order to stay alive Stimulus = anything in an organism’s external

The Nervous System Chapter 44. Nervous System Organization All animals must be able to respond to environmental stimuli Sensory receptors – detect stimulus

BCBA.exam... Exam A QUESTION 1 Gradually transferring stimulus control from prompts to other discriminative stimuli is a process called _____

Introduction Muscle & nerve are called excitable tissues because they respond to chemical, mechanical, or electrical stimuli A stimulus produces change

15 10 Stimuli - Hampshirebork.hampshire.edu/~alan/pub/2002_n170_faces/n170psychon_post… · beginning 200 ms before stimulus onset and ending 1000ms after stimulus presentation

Multiple Auditory Steady-State Responses to Bone ...€¦ · dB HL bone-conduction stimuli and to 30–60 dB HL air-conduction stimuli were compared.The effect of alternating stimulus

Outline DimensionalityofthePerceptualSpaceof Stimulus ... · Color perception Stimuli Fechnerian Scaling Analysis Color perception • We have a tendency to treat color as a property

Correct the errors - facweb.plattsburgh.edufacweb.plattsburgh.edu/wendy.braje/students/psy205/... · Correct the errors The stimuli was a large red star. The stimulus was a large

Matching Derived Functionally-Same Stimulus Relations ... · During the first test, referred to as the equivalence test, B stimuli served as samples and C stimuli as comparisons,

Stimulus & Response TEKS 7.13A investigate how organisms respond to external stimuli found in the environment such as phototropism and flight or fight

Stimulus Control Procedures to Facilitate Visual ... · 6 Stimulus-Prompt Procedures Stimulus Fading: – Adding stimuli to, or enhancing teaching stimuli Size Color Position Texture

Nervous System All animals must respond to environmental stimuli – Sensory receptors – detect stimulus – Motor effectors – respond to stimulus The nervous

Sensation The process by which our sensory receptors receive stimulus energies from our environment. Sensory receptors detect millions of stimuli

Topic E Stimulus and Response. Stimuli Stimulus- A distinguishable change in the internal or external environment Response- The reaction to a stimulus

Teaching Receptive Language Skills receptive language skills are not optimal, sev- ... of the antecedent stimuli and avoid the development of faulty stimulus control

7 TH SCIENCE RESPONSE TO STIMULI REVIEW. STIMULUS: Anything that causes a reaction

Psychology 2250 Last Class Characteristics of Habituation and Sensitization -time course -stimulus-specificity -effects of strong extraneous stimuli (dishabituation)