# Quantitative Basics Descriptive Statistics Class 2a

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Quantitative BasicsDescriptive StatisticsClass 2a

For TomorrowRead, then write two abstracts for articles (not lit reviews) related to your study. Taken from list for today. Read entire articlewrite summarycompare w/ abstract if there is oneEmail to me as soon as you finishRead: Hash, P. M. (2010). Preservice Classroom Teachers Attitudes toward Music in the Elementary Curriculum. Journal of Music Teacher Education, 19(2), 6-24.All current abstracts from the JRME and Update.

Writing an AbstractInclude an APA citationAccurate & dense w/ informationNonevaluative (not a review)Coherent, concise, readable. Use active voiceHighlight most important aspects150-200 words. (Use word count tool)Purpose of the studyParticipants (subjects) & their important characteristicsMethodology (what the researcher[s] did)Basic findingsConclusions & Implications

Sample 1This study examined performance anxiety (PA) among middle school vocal soloists. Participants included male (n = 63) and female (n = 221) middle school students (N = 284) participating in an all-district solo and ensemble festival. Students completed the Smith Performance Anxiety Inventory (SPAI) immediately following their performance. This survey consisted of 15-closed response questions measuring various physical and emotional phenomena on a seven-step Likert scale. Total SPAI scores indicate that 72% (n = 204) of participants reported moderate to high levels of anxiety and that these students experienced trembling, sweaty palms, and difficulty concentrating at significantly higher levels (p < .01) than other responses measured by the SPAI. Data also indicated that among students that experienced moderate to high levels of PA (n = 204), 86% (n = 175) were female. Recommendations for managing PA include 1) openly discussing PA among students, 2) videotaping performance for self-assessment, and 2) simulating the performance environment many times before the event.

Hash, P. M. (2011). Effect of pullout lessons on the academic achievement of eighth grade band students (2011). Update: Applications of Research in Music Education, 30(1), 16-22.This study examined the effect of pullout instrumental lessons on the academic achievement of eighth-grade band students. Participants (N = 353) included 292 nonband students and 61 band students pulled once per week for music lessons in a single suburban K8 school district in Midwestern United States. Data indicated that eighth-grade band students achieved significantly higher mean scores on the ACT Explore test than students who dropped band prior to eighth grade (n = 58) or never enrolled in the program (n = 234). In addition, no significant differences existed between all band students and the highest achieving nonband students, or between students who discontinued band after at least 1 year and those who never enrolled. Although band students in this study tended to be more academically successful than nonband students at the outset, these results support the assertion that pullout lessons had no negative effect on academic achievement, regardless of the number of years students participated in the program.

Quantitative BasicsExperimental & Surveys

Samples of individuals/entitiesSample vs. populationSome vs. AllExamples where entire population could be sampled?Relationship between sample specificity and generalizabilityRepresentative sampleCaptures relevant and essential characteristics of the populationWhat about a sample of teachers? What should the sample look like?

Sampling MethodsSystematicRandom start and sampling intervali.e., Randomly select pages from IHSA directory choose every ? Name (random number b/w 1-X)Conveniencenot as valuable but frequent in ed. research why?i.e., intact classes, pre-service teachers from one institution, conference session attendeesPurposiveParticipants fit a particular profile (female band directors in small towns)Exclude those who do not fit profileOften consists of volunteers (problematic)

Types of SamplesSimple RandomEveryone has equal chance of selectionReduce systematic bias error created by sampling methodPhone book, MENC membership list (But??)Stratified RandomSimilar proportions between sample and populationGender, race, age, instrument, etc.Cluster RandomGroups rather than individualsi.e., classes or ensembles in CPSThen groups can be assigned randomlyTwo-stage random - groups then individualsi.e., choose classes then assign individual students or groups to control or treatment group

Sample SizeAs large as possible given reasonable expenditure of time and energyMost likely to get significant resultsMore statistically powerful (more likely to find a significant difference b/w groups)Sample size relative to: the size of population (50 Cook Co. band directors vs. 50 band students throughout US)variability within population (years of teaching, gender, etc.)sampling method (need a large enough pool from which to draw)study design (qualitative vs. quantitative)

Types of Data AnalysisDescriptiveDescribes dataRelational (correlation)Relationships b/w variables within dataDifferences (inferential statistics)b/w groups

Measurement ScalesLevels of Measurement[NOIR]NominalCategorical, frequency counts (gender, color, yes/no, etc.)OrdinalRank-order (Contest Ratings, Likert data??)IntervalContinuous scale with consistent distances between points. No meaningful absolute zero (test scores, singing range, temperature, knowledge).RatioContinuous scale with consistent distances between points and an absolute zero (decibels, money) N-choir robes; O div. 1 at contest; I 96/100 score; R festival score twice as high as last year.

Other TermsReliability = ConsistencyTest/retest (regardless of yr., location, etc.)Interrater (every judge the same)Validity = the extent to which an assessment or survey measures what they purport to measureIndependent Variable factors manipulated by researcher Dependent Variable the test to determine outcomeSignificant Results did not occur by chance. Based on statistical calculation not opinion.

Descriptive Statistics

BasicsDescriptive stats describe populationCentral Tendency Mean (M)Mode (Mo)Median (Mdn)VariabilityRangeVarianceStandard Deviation (SD)

Visual Summaries of Data Frequencies

HistogramVersus a bar graph?Bar graph = categorical data, Histogram = quantitative/continuous data

Rank

Degree of agreement

Number

1

Strongly agree

20

2

Agree somewhat

30

3

Not sure

20

4

Disagree somewhat

15

5

Strongly disagree

15

Central TendencyMeanSum of all scores divided by number of scores (average)X --- single score (your test grade) --- sum (add it all up!)X --- mean (class average on test)N or n --- number of individuals/entities (number of people in class) X = X/nModeMost frequently occurringMedianPoint at which half fall below, half fall above

Variability (spread)RangeDistance between lowest and highest score (H-L=R)VarianceA measure of the dispersion (spread) of a set of scores. For the population = The sum of the squared deviations from the mean/N (number of scores)For a sample = The sum of the squared deviations from the mean/n-1 (number of scores minus 1).Previous formula underestimates the variance in a sample. Think of -1 as a correctionAbstract but good for comparing groups on similar characteristicsNeeded to find SD5681011

Variance Problem Population http://www.calculatorsoup.com/calculators/statistics/descriptivestatistics.php Data set: 5, 6, 8, 10, 11.Calculate the MeanSubtract the mean from each score.Square all the numbers that you obtained from subtracting each set number by the mean (2 neg. make a pos.):Add the resultsDivide the sum of the numbers by the number of numbers in the set minus 1.The variance for the example set of numbers is ?.

Solution

Standard DeviationA single number which describes the entire distribution of scores in terms of a relationship to the mean. SD=Average distance from the mean expressed in actual units (points in a test, 1-7 scale on a survey)SD = Square Root of [(X-X)2/n] or [n-1] (variance)SD score vs. SD unit (coming up)

ApplicationUSE: http://www.calculatorsoup.com/calculators/statistics/descriptivestatistics.php MS Band and string students are pulled from class for lessons once per week. The MS classroom teachers are concerned that instrumental students might fall behind and score lower on standardized tests, which will affect the classroom teachers student growth data used in their annual performance evaluations.Divide into pairs (and a trio) to determine the M, Mo, Var., & SD of 8th gr. instrumental and non-instrumental students ACT Explore scores inReadingMathScienceSocial StudiesDraw conclusions based on the data. How do inst. & non-inst scores compare? How would you respond to the MS teachers concerns?

Normal Curve/Distribution

Altogether.. describes the shape of a distributionMore on distributions..Normal Curve (bell curve)Most scores clustered at the middle with fewer scores falling at the extreme highs and lowsSkewness - When the scores tend to bunch upon the HIGH END = Negative Skew = less than -1on the LOW END = Positive Skew = greater than +1Kurtosis - When the distribution isPEAKED = positive kurtosis = leptokurtic = greater than +1 or +2 depending on who you askSMALLER PEAK (flatter) THAN A NORMAL CURVE = negative kurtosis = platykurtic = less than -1Bi-ModalWhen there are two humps in the curve, more than one mode

Kurtosis shapeplatykurtic leptokurtic

-1 to +1 = a near normal curve

Skew

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