Unit 2 (F): Statistics in Psychological Research: Measures of Central Tendency Mr. Debes A.P....
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Transcript of Unit 2 (F): Statistics in Psychological Research: Measures of Central Tendency Mr. Debes A.P....
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?