Statistical Methods I & I PSYC 2020 6.0G (F/W 2012)

Statistical Methods I & IPSYC 2020 6.0G (F/W 2012)

Contact Information

Course InstructorLisa FiksenbaumOffice: 403 BSBTelephone: (416) 736-5125E-Mail: [email protected]

Office Hour: By Appointment

Teaching AssistantPearl GuttermanOffice: 3023 LassondeTelephone: (416)736-2100 (ext.

33113 )Email:

[email protected] Office Hour: Tuesday 4:30-5:30

Correspondence by email or phone

• Make sure that you identify yourself clearly (first and last name)

• Please send emails from a York email account and use PSYC2020 in the subject line; otherwise, emails will be will be deleted unread

• Consult the syllabus for administrative information

Book Information

Gravetter, F.J. & Wallnau, L.B. (2013) Statistics for the Behavioral Sciences, (9th ed). St. Paul: West Publishing Company.

Rounding

• Do not round numbers you are computing until the final answer.

• Rounding at each step results in answers that may be significantly different than the keyed answers for both exams and homework.

• Round only your final answer (to two decimal places) only after all calculations have been performed.

Course Evaluation

• 4 exams (definitions, multiple choice, true/false, matching, basic calculations, interpretation of data sets, and/or short essay questions ): – Exam 1 (20%) – Exam 2 (20%)– Exam 3 (20%) – Exam 4 (20%)

Course Evaluation• 4 assignments:

– Assignment 1 (5%) – Assignment 2 (5%) – Assignment 3 (5%) – Assignment 4 (5%)

• Due at the START of class (you will receive 0 if handed in late)

• NO electronic submissions will be accepted• Do NOT simply report the final answer for a

problem. Show the computations that produced that answer.

Exams• For the first exam:

– you will be allowed to use one side of a 3 inch x 5 inch index card on which you may put anything you consider useful (e.g., formulas, definitions, etc.).

• For all other exams:– you will be allowed to use both sides of

the card

Missed Exams• Make-up exams will be granted ONLY

under EXCEPTIONAL circumstances, such as serious illness, or death in the immediate family

• Must contact the instructor or TA in person, by telephone, or by email, within 48 hours of the missed exam

• PROPER DOCUMENTATION REQUIRED

Review of Preliminary Concepts

• Variables• Measures of central tendency• Measures of variability• Hypothesis testing

Types of Variables

• Variable: characteristics of objects, events, or people that can have different values

• Constant: is a characteristic of objects, events, or people that does not vary

• Continuous Variable: can take on an infinite number of values (e.g., reaction time)

• Discrete Variable: can take on a finite number of values (e.g., gender)

Types of Variables, cont'd• Dependent Variable (DV): the variable being

measured in an experiment, that is expected to be “dependent” on the independent variable

• Independent Variable (IV): : The variable that is expected to influence the DV– Manipulated IV: an IV controlled by the

experimenter (e.g., random assignment to groups)– Subject/Organismic IV: an IV that is an underlying

characteristic of the population (e.g., sex, age)

Population/Sample

• Population: the entire set of events (e.g., study habits of university students) to which are you are interested

• Sample: a subset of a given population that is used to make inferences regarding the population (e.g., an intro psych class)

Parameters/Statistics

• Parameter: a measure that refers to the entire population (Greek characters, e.g., µ, , ρ)

• Statistic: a measure that refers to a sample (English characters, e.g., X s, r)

Branches of Statistical Methods

• Descriptive Statistics: describing the data through frequency distributions, measures of central tendency and variability, etc.

• Inferential Statistics: Making inferences about populations by utilizing samples (e.g., are there IQ differences between the sexes)

Measures of Central Tendency (Ch. 3 G & W)

• Mean– in the population, this is symbolized by – in the sample, this is symbolized by X– it is calculated by the following formula:

X=X N

Mean

• Suppose a psychotherapist noted how many sessions her last 10 patients had taken to complete brief therapy with her. The sessions were as follows:

7, 8, 8, 7, 3, 1,6, 9,3, 8

X=X = 60 = 6 N 10

Advantages:– Familiar and intuitively clear to most people– Useful for performing statistical procedures

Disadvantages:– May be affected by extreme values– Tedious to compute

Mean

• Median– the score that divides a distribution of

scores into the upper and lower halves– aka the 50th percentile– median is better than the mean when

there are a few extreme scores


Median– Odd number of scores: line up all scores from lowest to highest,

middle score is median3 ,4 ,5, 7, 8Median = 5

– Even number of scores: list scores in order (lowest-highest), locate median by finding the point halfway between the middle 2 scores3, 3 ,4 ,5, 7, 8Median=4+5 = 4.5

2

• Mode– most frequently occurring score– may be more than one mode– not affected by extreme values


Mode - Examples

•No ModeRaw Data: 10.3 4.9 8.9 11.7 6.3 7.7

•One ModeRaw Data: 6.3 4.9 8.9 6.3 4.9 4.9

•More Than 1 ModeRaw Data: 21 28 28 41 43 43

When Do You Use Which Measure?

• Categorical or nominal data (e.g., eye colour) - use the mode

• Quantitative data (e.g., height, age, test scores) – use the mean and median

• Extreme scores - use the median

• No extreme scores - use the mean

Central Tendency & Shape of Distribution

• Normal Distribution– a purely theoretical

distribution– perfectly symmetrical

about its mean– Mean=Median=Mode


• Skewed Distributions– Greater proportion of observations fall

in one tail of distribution than the other.

• Positively Skewed – tail to right – mode<median<mean


• Negatively Skewed – tail to left– mean<median<mode


Measures of Variability (Ch. 4 G & W)

• Range– difference between the largest and

smallest scores in a distribution of scores– isn’t really a good description of the

variability for an entire distribution

“degree to which scores in a distribution are spread out or clustered” (G& W, p. 104)


• Interquartile Range– difference between the 75th and 25th

percentiles in a distribution of scores– the 75th percentile is the score where 75%

of scores fall below and the 25th percentile is the score where 25% of the scores fall below


• Standard Deviation (SD) & Variance– most widely used – determines whether scores are generally near

or far from the mean– in the population, the SD is symbolized by and

the variance is symbolized by 2

– in the sample, the SD is symbolized by s and the variance is symbolized by s2

Calculating the Variance and/or Standard Deviation

Variance: Standard Deviation:

1)( 2

2

N

XXs

1)( 2

N

XXs

Example:

1

4

9

4

9

1

1

2

-3

-2

3

-1

Data: X = {6, 10, 5, 4, 9, 8}; N = 6

Total: 42 Total: 28

Standard Deviation:

7642

NX

X

Mean:

Variance:

6.5528

1)( 2

2

N

XXs

37.26.52 ss

XX 2)( XX X

8

9

4

5

10

6

Hypothesis Testing• A hypothesis is a statement about a

relationship between variables. The cornerstone of hypothesis testing is the concept of the null hypothesis.

• The Null Hypothesis states there is no true difference between scores in the population.

Hypothesis Testing

The alternative hypothesis Ha, is that the difference in our sample is truly reflecting a real difference in the population, that the difference is not due to sampling error.

One –Tailed vs Two-Tailed Hypothesis Tests

One Tailed• Directional

hypothesis• Eg: “Those receiving

$1,000,000 will be happier than the general public”

Two-tailed • Direction not

specified• Eg: “Social skills

program changes the level of productivity”

Uncertainty & Errors in Hypothesis Testing

• Type I error– Null hypothesis is rejected, but it is true– Under control of researcher– α is the probability of making a Type I

error

Uncertainty & Errors in Hypothesis Testing

• Type II error– Fail to reject null hypothesis when it is false– β is the probability of making a Type II

error

Do not reject Ho Reject Ho

Reality

Ho is True

Ho is False

Correct Decision

Type II Error

Type I Error

Correct Decision

Possible Outcomes of Statistical Decision

Hypothesis Tests in Research Articles

(Wang et al, 1997, p. 148)

Statistical Methods I & I PSYC 2020 6.0G (F/W 2012)

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