Psychology’s StatisticsPsychology’s Statistics

Statistical MethodsStatistical Methods

StatisticsStatistics

The overall purpose of statistics is to The overall purpose of statistics is to make to organize and make data make to organize and make data more meaningful.more meaningful.

Ex. If a friend tells you that they Ex. If a friend tells you that they earned a 27 out of 30 on a history earned a 27 out of 30 on a history test – great…if they tell you that they test – great…if they tell you that they earned a 27 out of 100…well that is a earned a 27 out of 100…well that is a different story.different story.

Two central ways of using numbersTwo central ways of using numbers

Inferential Statistics: Are used to Inferential Statistics: Are used to determine if two or more groups are determine if two or more groups are essentially the same or different.essentially the same or different.

Descriptive Statistics: simple Descriptive Statistics: simple quantitative description or summary.quantitative description or summary.– Batting average in baseballBatting average in baseball– Grade-point averageGrade-point average

Describing dataDescribing data

We characterize the general trend or We characterize the general trend or character of data using two key character of data using two key statistics:statistics:

1. Central tendency or general “drift” of the 1. Central tendency or general “drift” of the scores.scores.– Mode Mode most common scoremost common score– Median Median middle of the distributionmiddle of the distribution– Mean Mean average scoreaverage score

Describing data continuesDescribing data continues

2. 2. Variance: how diverse the scores are Variance: how diverse the scores are (how much they vary from each other).(how much they vary from each other).

Measures of VariationMeasures of Variation Range: Range: describes the describes the

spread between the spread between the high score and the low high score and the low score.score.

Range provides a Range provides a limited amount of limited amount of information. Uses the information. Uses the two most extreme two most extreme scoresscores

Standard Deviation Standard Deviation (SD): (SD): is a statistical is a statistical measure that tells us measure that tells us how much scores vary how much scores vary around a mean score. around a mean score.

If scores are packed If scores are packed tightly around the tightly around the mean, the standard mean, the standard deviation will be deviation will be smallsmall. . If scores are spread If scores are spread out widely on either out widely on either side of the mean, the side of the mean, the SD will be SD will be largerlarger..

What are the important What are the important characteristics of a normal characteristics of a normal

distribution?distribution?

Scores fall near the mean and very few Scores fall near the mean and very few scores fall at the extremes.scores fall at the extremes.

Normal distributions are not skewedNormal distributions are not skewed The mean, median, and mode all fall at the The mean, median, and mode all fall at the

high point of the graph.high point of the graph.

What are the important What are the important characteristics of a normal characteristics of a normal

distribution? Continue..distribution? Continue..

In a normal distribution, 68% of the In a normal distribution, 68% of the population fall within one SD of the population fall within one SD of the average, and 95% fall within two SDs average, and 95% fall within two SDs of the mean.of the mean.

More than 99.7% fall within three SDMore than 99.7% fall within three SD

Frequency distributionFrequency distribution

A list of scores placed in order from A list of scores placed in order from highest to lowest (or vise versa).highest to lowest (or vise versa).

Info can be presented as a bar graph, Info can be presented as a bar graph, bell curve, etc.bell curve, etc.

Put the scores/numerical data in Put the scores/numerical data in order this creates a frequency order this creates a frequency distribution and that makes the raw distribution and that makes the raw data much more meaningful.data much more meaningful.

Benefits of using a Frequency Benefits of using a Frequency DistributionDistribution

Shows how often each possible score Shows how often each possible score actually occurred.actually occurred.

You can compare different groupsYou can compare different groups

Graphing the DataGraphing the Data

Graph:Graph:

A drawing that depicts numerical A drawing that depicts numerical relationships.relationships.

Routinely used by psychologists.Routinely used by psychologists.

Different types of graphsDifferent types of graphs

Histogram/bar graphHistogram/bar graph

Draw rectangles (bars) Draw rectangles (bars) above each score, above each score, indicating the # of indicating the # of times it occurred by times it occurred by the rectangle’s height.the rectangle’s height.

Frequency Frequency Polygon/line graphPolygon/line graph

Frequency of each score Frequency of each score is indicated by a dot is indicated by a dot placed directly over placed directly over the score on the the score on the horizontal axishorizontal axis

Measures of Central TendencyMeasures of Central Tendency

Three primary methods of finding the Three primary methods of finding the center of a distribution of scores:center of a distribution of scores:

1.1. modemode

2.2. meanmean

3.3. medianmedian Each one has its own strengths and Each one has its own strengths and

weaknesses.weaknesses.

Determining Which “average” to Determining Which “average” to use/siteuse/site

I want to limit the # of hours students I want to limit the # of hours students work per week.work per week.

Mean= 9 hours per weekMean= 9 hours per week Mode= 6 hours per weekMode= 6 hours per week Median= 5 hours per week.Median= 5 hours per week. Official report I would say that the average Official report I would say that the average

number of hours worked to be 9 since this number of hours worked to be 9 since this was the highest number and it would was the highest number and it would support my case.support my case.

Steps for calculating the SDSteps for calculating the SD

1.1. calculate the meancalculate the mean 2.2. determine how far each score determine how far each score

deviates from the average.deviates from the average. 3.3. square the deviation scores and square the deviation scores and

add them together.add them together. 4.Take the square root of the 4.Take the square root of the

average of the squared deviation average of the squared deviation scores.scores.

Steps for calculating the SD Steps for calculating the SD continuescontinues

Remember SD tells us how clustered Remember SD tells us how clustered or spread out the individual scores or spread out the individual scores are around the mean; the more are around the mean; the more spread out the less “typical” the spread out the less “typical” the mean is.mean is.

The difference b/w percentage and The difference b/w percentage and percentile rank? Comparative percentile rank? Comparative

StatisticsStatistics Percentage: Percentage:

compares a score to compares a score to an imaginary set of an imaginary set of one hundred.one hundred.

Ex. Student scores Ex. Student scores 83% on a test---that 83% on a test---that student would have student would have had 83 right on a test had 83 right on a test with 100 questions.with 100 questions.

Percentile rank: Percentile rank: compares one score compares one score with other scores in an with other scores in an imaginary group of imaginary group of 100 individuals. 100 individuals.

Tells you where a Tells you where a particular score stands particular score stands in that group and how in that group and how many people had many people had equal or lower scores.equal or lower scores.

Example of percentile rankExample of percentile rank

Student scores at the 83Student scores at the 83rdrd percentile, percentile, it means that score would have it means that score would have equaled or exceeded 83 of every 100 equaled or exceeded 83 of every 100 people who took the test.people who took the test.

CorrelationsCorrelations

A relationship b/w 2 variables, in A relationship b/w 2 variables, in which changes in one variable are which changes in one variable are reflected in changes in the other reflected in changes in the other variable.variable.

Correlation Coefficient: a number Correlation Coefficient: a number between -1.0 and +1.0 expressing between -1.0 and +1.0 expressing the degree of relationship b/w two the degree of relationship b/w two variables.variables.

Correlations continueCorrelations continue

Positive correlation: both variables Positive correlation: both variables increase or decrease together. Ex. increase or decrease together. Ex. The more a person trains, the The more a person trains, the stronger he/she will become.stronger he/she will become.

CorrelationsCorrelations

Negative correlation: involves two Negative correlation: involves two variables that change in opposite variables that change in opposite directions. Ex. Floss more, have directions. Ex. Floss more, have fewer cavities.fewer cavities.

Correlation coefficientCorrelation coefficient

Let Let rr stand for “correlation coefficient” stand for “correlation coefficient” r = -1, we have a r = -1, we have a perfect negative perfect negative

correlationcorrelation. Every time one variable . Every time one variable increases by a certain amount, the other increases by a certain amount, the other variable would decrease by an equally variable would decrease by an equally certain amount.certain amount.

r = +1, we have a r = +1, we have a perfect positive perfect positive correlationcorrelation. Every time one variable . Every time one variable increases by a certain amount, the other increases by a certain amount, the other variable will also increase by an equally variable will also increase by an equally certain amount. Similarly—decrease.certain amount. Similarly—decrease.

THERE IS NO CORRELATION THERE IS NO CORRELATION WHATSOEVER BETWEEN TWO WHATSOEVER BETWEEN TWO

VARIABLES IF VARIABLES IF r r =0.=0.

Statements: +, -, noStatements: +, -, no 1.1. Increased milk drinking occurs with Increased milk drinking occurs with

increased cancer rate.increased cancer rate. 2.2. increased smoking produces increased smoking produces

increased lung cancerincreased lung cancer 3. Increased absences occur with 3. Increased absences occur with

decreased grades in school.decreased grades in school. 4. increased studying occurs with 4. increased studying occurs with

increased gradesincreased grades

ExamplesExamples 5.5. increased listening to loud music increased listening to loud music

sometimes increases and sometimes decreases sometimes increases and sometimes decreases hearing abilityhearing ability

6.6. city dwellers have greater cancer rates.city dwellers have greater cancer rates. 7. increasing education occurs with decreasing 7. increasing education occurs with decreasing

unemployment.unemployment. 8. eyesight decreases as age increases.8. eyesight decreases as age increases.

Making Inferences with inferential Making Inferences with inferential statisticsstatistics

Inferential statistics Inferential statistics are used to are used to assess whether the results of a study assess whether the results of a study are reliable or whether they might be are reliable or whether they might be simply the result of chancesimply the result of chance

Inferential statisticsInferential statistics

Are used to determine if two or more Are used to determine if two or more groups are essentially the same or groups are essentially the same or different.different.

Gives us guidelines for deciding Gives us guidelines for deciding whether, for example, data supports whether, for example, data supports our hypotheses.our hypotheses.

Statistical significanceStatistical significance

Example of an Inferential statisticsExample of an Inferential statistics; A ; A statistical statement of how likely it statistical statement of how likely it is that a result occurred by is that a result occurred by chance chance alone. alone.

most most psychologistspsychologists are willing to are willing to accept up to a accept up to a 5% a.k.a=5% a.k.a=P<0.05 P<0.05 likelihood that experiment’s results likelihood that experiment’s results are due to chance, “luck of the draw”are due to chance, “luck of the draw”

95% is a result of the manipulation of 95% is a result of the manipulation of the independent variable.the independent variable.

Three most important factors Three most important factors involved in inferential statistics.involved in inferential statistics.

1.1. the difference between the two the difference between the two groups’ means. If the means are far apart, groups’ means. If the means are far apart, the result is more likely to be significant.the result is more likely to be significant.

2.2. the # of participants. If each group the # of participants. If each group has only a few people, the results are not has only a few people, the results are not as likely to be significant as they would be as likely to be significant as they would be if each group has a large # of randomly if each group has a large # of randomly selected people in it.selected people in it.

3.3. the standard deviation of the two the standard deviation of the two groups. groups.

Review questionsReview questions

Which of the following coefficients Which of the following coefficients of correlation indicates the of correlation indicates the strongest relationship?strongest relationship?

a.a. +.50+.50

b.b. +.10+.10

c.c. -.25-.25

d.d. -.75-.75

Review questionReview question

The mean and standard deviation The mean and standard deviation are ________ statistics.are ________ statistics.

a.a. Inferential Inferential

b.b. DescriptiveDescriptive

c.c. CorrelationalCorrelational

d.d. Case studyCase study

Review questionReview question

Significance tests tell the researcher how Significance tests tell the researcher how likely it is that the results of the study likely it is that the results of the study are due to________, and the results are are due to________, and the results are said to be significant if this likelihood is said to be significant if this likelihood is very________.very________.

a.a. chance; lowchance; low

b.b. The independent variable; lowThe independent variable; low

c.c. Change; highChange; high

d.d. The independent variable; highThe independent variable; high

ReviewReview

hypothesis:hypothesis:

An investigator’s An investigator’s testable testable predictionprediction about the outcome about the outcome of research.of research.

Theory: Theory:

A testable A testable explanationexplanation for a for a set of facts or set of facts or observations. A observations. A theory is not just theory is not just speculation or a speculation or a guess.guess.

ReviewReview Operational Definition:Operational Definition:A statement of the A statement of the

procedures (operations) procedures (operations) used to define research used to define research variables.variables.

A specification of the exact A specification of the exact procedures used to make a procedures used to make a variable specific and variable specific and measurable for research measurable for research purposes.purposes.

Describes the actions or Describes the actions or operations that will be operations that will be used to measure or control used to measure or control a variable.a variable.

++allows anyone to replicate ++allows anyone to replicate their observations.their observations.

If researchers re-create a If researchers re-create a study with different study with different participants and materials participants and materials and get similar results, and get similar results, then our confidence in the then our confidence in the finding’s reliability grows.finding’s reliability grows.