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Grand Alexandra 1 Analysis Thema 9 / Analysis Grand Alexandra.

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Präsentation zum Thema: "Grand Alexandra 1 Analysis Thema 9 / Analysis Grand Alexandra."—  Präsentation transkript:

1 Grand Alexandra 1 Analysis Thema 9 / Analysis Grand Alexandra

2 Grand Alexandra 2 Analysis 1. Data Preparation organizing the data 2. Descriptive Statistics describing the data 3. Inferential Statistics testing hypotheses and models

3 Grand Alexandra 3 Conclusion Validity Internal Validity Is there a relationship between two variables (between cause and effect)? Assuming that there is a relationship in this study, is the relationship a causal one? „third variable“? there is no relationship there is a relationship Is the conclusion about the relationship reasonable? conclusion „Je mehr Fernseher vorhanden sind, desto schlechter wird die PISA-Leistung.“ (Presse, PISA-Sieger: Weiblich und ohne TV)

4 Grand Alexandra 4 Threats to conclusion validity Incorrect conclusion about a relationship in the observation 1. conclude that there is no relationship when in fact there is „missing the needle in the haystack“ „noise“ – factors that make it hard to see the relationship „signal“ – relationship you are trying to see signal-to-noise ratio problem 2. conclude that there is a relationship when in fact there is not „seeing things that aren´t there“

5 Grand Alexandra 5 Threats to conclusion validity threats: low reliability of measures low reliability of treatment implementation random irrelevancies in the setting random heterogeneity of respondents -> low statistical power violation of assumptions of statistical tests conclusionreality no relationshiprelationship conclusionreality relationshipno relationship threats: fishing and the error rate problem violation of assumptions of statistical tests „Finding a relationship when there is not one“ „Finding no relationship when there is one“ „noise“ producing factors add variability

6 Grand Alexandra 6 Improving Conclusion Validity good statistical power (should be > 0.8) power = „the odds of saying that there is an relationship, when in fact there is one“ good reliability -> reduce „noise“ good implementation Factors that affect power: sample size: use lager sample size effect size: increase effect size (e.g. increase the dosage of the program) signal -> increase noise -> decrease α-level: raise the alpha-level

7 Grand Alexandra 7 Statistical Inference Decision Matrix decision right  1-α (e.g. 0.95) confidence level decision wrong β (e.g. 0.20) β-error (Type II Error) decision wrong α (e.g. 0.05) α-error (Type I Error) significance level decision right  1-β (e.g. 0.80) Power H 0 is true H A is true accept H 0 accept H A REALITY two mutually exclusive hypotheses (H 0, H A ) decision: which hypothesis to accept and which to reject CONCLUSION

8 Grand Alexandra 8 Statistical Inference Decision α α β H 0 right H A right 1-α 1-β POWER what we want: high power and low Type I Error problem:the higher the power the higher the Type I Error

9 Grand Alexandra 9 Practical Ein in „Wirklichkeit“ hochbegabtes Kind wird als nicht hochbegabt diagnostiziert. Das Ergebnis einer Studie: WU-StudentInnen mit HAK-Abschluss erreichen eine höhere Punkteanzahl bei der MC-Prüfung in Buchhaltung. In Wirklichkeit gibt es aber keinen Unterschied zwischen HAK- und nicht HAK-Absolventen hinsichtlich der erreichten Punkteanzahl. Um welchen Fehler handelt es sich in diesem Fall?  α-Fehler (Fehler 1. Art/ Type I Error)  β-Fehler (Fehler 2. Art/ Type II Error) Um welchen Fehler handelt es sich in diesem Fall?  α-Fehler (Fehler 1. Art/ Type I Error)  β-Fehler (Fehler 2. Art/ Type II Error)

10 Grand Alexandra 10 Practical Durch Erhöhung des α-Fehlers von 0.01 auf 0.05 …  sinkt die Power (Teststärke)  sinken die Chancen einen Fehler 1. Art zu machen  sinken die Chancen einen β-Fehler zu machen  ist der Test restriktiver Kreuzen Sie die richtige Antwort an und stellen Sie die falschen Antworten richtig. steigt steigen weniger restriktiv

11 Grand Alexandra 11 Analysis Beispieldatensatz „Arbeitszufriedenheit“ – AZ Datensatz: AZ.sav Hinweis: Die Daten wurden zu Illustrationszwecken aus einem Datensatz* willkürlich gewählt! Etwaige Ergebnisse sollten daher nicht allzu ernst genommen werden. Stichprobengröße:n = 15 Variablen: dichotom:SEX, Items zu den Konstrukten Arbeitszufriedenheit** (AZ_... ), Betriebsklima** (BK_...), Arbeitsbelastung** (AB_... ) ordinal:POSITION (Position im Betrieb) metrisch:MITARB (Anzahl der Mitarbeiter), NETTO (monatl. Nettoverdienst in €) neue Variable: AZ „Arbeitszufriedenheit“(Annahme: intervallskaliert!)  Summenscore der einzelnen Variablen AZ_... * Böhnisch, B., Grand, A., Rechberger, R., Wimmer, W. (2006). Berufliche Zufriedenheit. Seminararbeit aus Empirische Forschungsmethoden. ** Items wurden übernommen von: Giegler, H. (1985). Rasch-Skalen zur Messung von „Arbeits- und Berufszufriedenheit“, „Betriebsklima“ und „Arbeits- und Berufsbelastung“ auf Seiten der Betroffenen.

12 Grand Alexandra Data Preparation 1.Logging the data 2.(Checking the data for accuracy) 3.Developing a database structure – Codebook (Kodierungsschema)Codebook 4.Entering the data into the computer (once only entry or double entry); Checking the data for accuracy Checking the data for accuracy 5.Data Transformation missing values item reversals (example: transform reversal items e.g. BK_2: old value: 1 „agree“, 2 „disagree“ -> new value: 2 „agree“, 1 „disagree“) recode variables (example: transform items „AZ_...“, „AB_...“, “BK_...“: old value: 1 „agree“, 2 „disagree“ -> new value: 1 „agree“, 0 „disagree“) scale totals (example: generate new variable „AZ“ (Arbeitszufriedenheit))  to get a total score for AZ add across the individual items AZ_...,) categories

13 Grand Alexandra 13 1.Data Preparation - Codebook SEX MITARB NETTO POSITION ID AZ_1 BK_2 AB_3 AZ_4 BK_ The codebook should include: variable name variable description variable format instrument/method of collection date collected respondent or group variable location in database The codebook should include: variable name variable description variable format instrument/method of collection date collected respondent or group variable location in database -

14 Grand Alexandra Data Preparation - Checking data for accuarcy summarize (e.g. frequency table) and check the data are the listed values reasonable? („wild codes“, outlier/Ausreißer) are there missing values? („missing values“) „wild code“ outlier/Ausreißer it acutally is an outlier or error in data entry outlier/Ausreißer it acutally is an outlier or error in data entry „missing values“ there exist no data or data weren´t entered „missing values“ there exist no data or data weren´t entered „missing values“

15 Grand Alexandra Descriptive Statistics Univariate Analysis - Analysis of one variable at a time Description of a single variable: distribution central tendency (Lagemaß) dispersion (Streuungsmaß) Bivariate Analysis – Analysis of two variables at a time Multivariate Analysis – Analysis of multiple variables at a time Descriptive statistics „quantitative description in a manageable form“ describe basic features of the data, provide simple summaries simple graphics analysis

16 Grand Alexandra Descriptive Statistics - Distribution Frequency distribution t a b l e g r a p h Geschlecht absolute Häufigkeiten relative Häufigkeiten männlich853% weiblich747% pie chart bar chart boxplot histogram (stem and leaf diagram) … absolute frequencies relative frequencies absolute frequencies relative frequencies Frequency table: Geschlecht crosstab

17 Grand Alexandra Descriptive Statistics - Distribution g r a p h s Kreisdiagramm - Geschlecht Histogramm – monatl. Nettoverdienst Boxplot – Anzahl der Mitarbeiter Balkendiagramm - Position

18 Grand Alexandra Descriptive Statistics – Central Tendency Mean (Mittelwert) Median Modus ordinal data metric data nominal data ordinal data metric data Central Tendencies / LAGEMASSE „sum of values x i / number n of values“ „center of the sample“ „most frequently occuring value“ if distribution is approx. normal distributed not robust against single extreme values („outliers“) computation data adequacy robust against outliers

19 Grand Alexandra Descriptive Statistics – Central Tendency / Practical Berechnen Sie den Mittelwert, Median und Modus der Variablen SEX, MITARB (Anzahl der Mitarbeiter) und POSITION - Achten Sie dabei auf eine sinnvolle Anwendung! Hilfestellung: aufsteigende Sortierung der Variablen Mitarbeiter und Position

20 Grand Alexandra Descriptive Statistics – Distribution / Practical_Solution VariableMeanMedianModus Mitarbeiter Position-21 Geschlecht--1

21 Grand Alexandra Descriptive Statistics - Dispersion Dispersions/ STREUUNGSMASSE Variance s² Standard Deviation s Range / Spannweite computation „square root of the variance“ „average of the sum of the squared deviations “ „highest value minus lowest value“ metric data ordinal data metric data data =

22 Grand Alexandra Descriptive Statistics - Dispersion Dispersions/ STREUUNGSMASSE Interquartile range IQR computation „difference between third and first quartile“ 3. quartile (Q3): 75% of the cases fall below this value 1. quartile (Q1): 25% of the cases fall below this value median: 50% of the cases fall above and below this value metric data data adequacy robust against outliers Q1 Q2 = median Q3 25% IQR min max

23 Grand Alexandra Descriptive Statistics – Dispersion / Practical_Solution VariableVarianceStandard Deviation Range (Spannweite) MinMax Netto- verdienst Berechnung der Varianz, Standardabweichung und der Spannweite der Variable NETTO (Nettoverdienst): n = 15, mean = 1553,3 ; min = 200, max = 2800 Steps (Variance): 1. compute distance between each value and the mean 2. square each discrepancy 3. sum the squares to get the Sum of Squares (SS) value 4. divide the SS by n - 1

24 Grand Alexandra 24 Correlation „A correlation is a single number that describes the degree of relationship between two variables“  correlation coefficient between -1 < r < 1  the higher the absolute r-value, the stronger the relationship between the variables uncorrelated r = 0 positive correlation r > 0 positive relationship  the higher the x-values the higher the y-values on average negative correlation r < 0 negative relationship  the higher the x-values the lower the y-values on average and vice versa exact linear correlation r = 1 (positive), r= -1 (negative)

25 Grand Alexandra 25 Correlation - Example VariableMeanStDevVarianceSumMinMaxRange Netto- verdienst Arbeits- zufried Example: Is there a relationship between the variable „Nettoverdienst“ and the variable „Arbeitszufriedenheit“? Descriptive statistics for „Nettoverdienst“ and „Arbeitszufriedenheit“ If yes, … 1.Which type of relationship? 2.How strong is the relationship? 3.Is the correlation significant?

26 Grand Alexandra 26 Example - Descriptive Statistics Boxplot – Arbeitszufriedenheit (AZ)Boxplot – monatl. Nettoverdienst in €

27 Grand Alexandra 27 Example – 1. Which type of relationship?

28 Grand Alexandra 28 Example – 2. How strong is the relationship? Product-Moment-Correlation (Pearson) variables (x,y) are metric and normal distributednormal distributed Calculating the correlation SPSS-Output: Korrelation AZ/NETTO

29 Grand Alexandra 29 Example – Q-Q Plot Q-Q Plot: AZ (Arbeitszufriedenheit) Q-Q Plot: monatl. Nettoverdienst in €

30 Grand Alexandra 30 Example – 3. Is the correlation significant? Testing the Significance of a Correlation Null Hypothesis: r = 0 Alternative Hypothesis:r <> 0 Steps: 1.determine the significance level alpha-level 2.compute the degrees of freedom df 3.one-tailed or two-tailed test? 4.look at the critical value α = 0.05 df = N-2 -> = 13 two-tailed test

31 Grand Alexandra 31 Example – 3. Is the correlation significant? Auszug: t-Verteilungen für Produkt-Moment-Korrelationen correlation is significant: r (0.692) > r crit (0.514) SPSS-Output: Korrelation AZ/NETTO

32 Grand Alexandra 32 Correlation Matrix symmetric matrix relationships between all possible pairs of variables e.g. between C1,…,C10  45 unique correlations N*(N-1) / 2

33 Grand Alexandra 33 Other correlations Pearson Product Moment (bivariate normal distribution, variables on interval scale) Spearman rank Order Correlation (rho) (two ordinal variables) Kendall rank order Correlation (tau) (two ordinal variables) Point-Biserial Correlation (one variable is on a continuous interval level and the other is dichotomous)

34 Grand Alexandra 34 Literatur Basisliteratur: Trochim, W. & Donelly, J.: The Research methods Knowledge Base (3rd edition) Atomic Dog Internet WWW page, URL: (version current as of October 20, 2006). Bortz, J., Döring, N. (2006). Forschungsmethoden und Evaluation. Heidelberg: Springer Verlag. Hatzinger, R. (2006). Angewandte Statistik mit SPSS. Wien: Facultas. Hatzinger, R., Nagel, H. (2009). PASW Statistics. Statistische Methoden und Fallbeispiele. München: Pearson Studium. Nagel, H. (2003). Empirische Sozialforschung.


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