Unit 2 (F):Unit 2 (F):Statistics inStatistics in

Psychological Psychological Research:Research:

Measures of Central Measures of Central TendencyTendencyMr. DebesMr. Debes

A.P. PsychologyA.P. Psychology

Statistics in PsychologyStatistics in Psychology

Statistics:Statistics: The collection, The collection,

classification, analysis, and classification, analysis, and interpretation of numerical interpretation of numerical psychological datapsychological data

Descriptive Statistics:Descriptive Statistics: Describes collected dataDescribes collected data Frequency Distribution:Frequency Distribution:

Bar GraphBar Graph HistogramHistogram

Statistics in PsychologyStatistics in Psychology Types of Psychological Data:Types of Psychological Data:

Nominal:Nominal: CategoricalCategorical Non-numericalNon-numerical Bar graphBar graph E.g. Favorite ice cream flavorE.g. Favorite ice cream flavor

Ordinal:Ordinal: OrderedOrdered Non-numericalNon-numerical Bar graphBar graph E.g. 1E.g. 1stst place, 2 place, 2ndnd place, 3 place, 3rdrd place place

Statistics in PsychologyStatistics in Psychology Types of Psychological Data:Types of Psychological Data:

Interval:Interval: Equal interval between points; no true zero pointEqual interval between points; no true zero point Numerical; can compute meanNumerical; can compute mean HistogramHistogram E.g. Degrees in FahrenheitE.g. Degrees in Fahrenheit

Ratio:Ratio: Equal interval between points; trueEqual interval between points; true

zerozero pointpoint Numerical; can compute meanNumerical; can compute mean HistogramHistogram E.g. Height/weight E.g. Height/weight

Statistics in PsychologyStatistics in Psychology

Statistics in PsychologyStatistics in Psychology Inferential StatisticsInferential Statistics Allow us to determine if results can be Allow us to determine if results can be

generalized to a larger population.generalized to a larger population. Well reasoned Well reasoned inferencesinferences about the population in about the population in

questionquestion Representative sample is very importantRepresentative sample is very important

Random sample-everyone in the target Random sample-everyone in the target population has an equal chance of being population has an equal chance of being selected for the sampleselected for the sample

Sample size-the larger the sample size, the Sample size-the larger the sample size, the better, but there are trade-offs in time & money better, but there are trade-offs in time & money when it comes to sample sizewhen it comes to sample size

Statistics in PsychologyStatistics in Psychology Statistical SignificanceStatistical Significance How likely it is than an obtained result How likely it is than an obtained result

occurred by chanceoccurred by chance A level of significance is selected prior to A level of significance is selected prior to

conducting statistical analysis. Traditionally, conducting statistical analysis. Traditionally, either the 0.05 level (sometimes called the 5% either the 0.05 level (sometimes called the 5% level) or the 0.01 level (1% level) is used. If the level) or the 0.01 level (1% level) is used. If the probability is less than or equal to the probability is less than or equal to the significance level, then the outcome is said to significance level, then the outcome is said to be statistically significant. The 0.01 level is be statistically significant. The 0.01 level is more conservative than the 0.05 level. more conservative than the 0.05 level.

Measures of Central Measures of Central TendencyTendency

Mean:Mean: The arithmetic average of a distributionThe arithmetic average of a distribution Obtained by adding all scores together, and dividing Obtained by adding all scores together, and dividing

by the number of scoresby the number of scores

Median:Median: The middle score of a distributionThe middle score of a distribution Half of the scores are above it and half are below itHalf of the scores are above it and half are below it

Mode:Mode: The most frequently occurring score(s) in a The most frequently occurring score(s) in a

distributiondistribution

DistributionsDistributions Distribution: the way scores are Distribution: the way scores are

distributed (spread out) around the distributed (spread out) around the mean scoremean score Normal Distribution (normal curve/bell Normal Distribution (normal curve/bell

curve):curve): Symmetrical, Bell-shaped distributionSymmetrical, Bell-shaped distribution Mean, Median, Mode all are the sameMean, Median, Mode all are the same

DistributionsDistributions Skewed Distribution:Skewed Distribution:

PositivelyPositively skewed; “Skewed to the skewed; “Skewed to the RightRight”-”-scores pull the mean toward the higher end scores pull the mean toward the higher end of the scoresof the scores

NegativelyNegatively skewed; “Skewed to the skewed; “Skewed to the LeftLeft”-”-scores pull the mean toward the lower end scores pull the mean toward the lower end of the scoresof the scores

DistributionsDistributions

Positively Skewed DistributionPositively Skewed Distribution

Measures of VariationMeasures of Variation

Range:Range: The difference between the highest and The difference between the highest and

lowest scores in a distributionlowest scores in a distribution Standard Deviation:Standard Deviation:

A computed measure of how much scores A computed measure of how much scores vary around the meanvary around the mean

Measures of VariationMeasures of Variation Calculating standard deviation:Calculating standard deviation:

For your set of data, calculate the mean. Subtract the mean from each item of data (half

of your outcomes will be negative).  This is the DEVIATION of each value from the mean.

Square each deviation. Add all of the squares from step 3, and divide

by the number of items in the data set.  This is the VARIANCE. 

Take the square root of the variance.  This is the STANDARD DEVIATION. 

Measures of VariationMeasures of VariationData Set 1:44, 45, 47, 48, 49, 51, 52, 53, 55, 56

Data Set 2:2, 3 , 5, 7, 9, 17, 48, 49, 137, 223

1) Calculate mean: 500/10=502) Subtract mean from each

data point:-6, -5, -3, -2, -1, 1, 2, 3, 5, 6 (these are the individual

deviations)3) Square each individual

deviation:36, 25, 9, 4, 1, 1, 4, 9, 25, 364) Add all squares, then divide

by items in the data set: 150/10=15 (VARIANCE)5) Find the square root of the

variance:3.87 (STANDARD

DEVIATION)

1) Calculate mean: 500/10=502) Subtract mean from each

data point:-48, -47, -45, -43, -41, -33, -2, -

1, 87, 173 (these are the individual

deviations)3) Square each individual

deviation:2304, 2209, 2025, 1849, 1681,

1089, 4, 1, 7569, 299294) Add all squares, then divide

by items in the data set:48660/10=4866(VARIANCE)5) Find the square root of the

variance:69.76 (STANDARD

DEVIATION)

Measures of VariationMeasures of Variation Usefulness of Standard deviation:Usefulness of Standard deviation:

Standard deviation gives a better gauge of whether a set of scores are packed closely together, or more widely dispersed.

The higher the standard deviation, the less similar the scores are.

In nature, large numbers of data often form a bell-shaped distribution, called a “normal curve.”

In a normal curve, most cases fall near the mean, and fewer cases fall near the extremes

Normal DistributionNormal Distribution

Z-scoresZ-scores A z-score is the number of standard A z-score is the number of standard

deviations a score is from the meandeviations a score is from the mean If a Z-Score: Has a value of 0, it is equal to the group mean. Is equal to +1, it is 1 Standard Deviation above the mean. Is equal to -2, it is 2 Standard Deviations below the mean.

Z-Scores can help us understand: How typical a particular score is within bunch of scores. How typical a particular score is within bunch of scores. If data are normally distributed, approximately 95% of the If data are normally distributed, approximately 95% of the

data should have Z-score between -2 and +2. data should have Z-score between -2 and +2. Z-scores that do not fall within this range may be less Z-scores that do not fall within this range may be less

typical of the data in a bunch of scorestypical of the data in a bunch of scores . .

Measures of VariationMeasures of Variation

HomeworkHomework Explain the difference between the Explain the difference between the

following types of following types of datadata: : Nominal, Nominal, Ordinal, Interval, RatioOrdinal, Interval, Ratio

What is a What is a normal distributionnormal distribution?? What is theWhat is the differencedifference between a between a

positivelypositively and and negatively-skewednegatively-skewed distribution?distribution?

Explain the difference between the Explain the difference between the measures of variationmeasures of variation: : Range & Range & Standard DeviationStandard Deviation

What is a What is a Z-scoreZ-score? How is it computed?? How is it computed?