1. Statistical analyses

2. SPSS  Statistical analysis program  It is an analytical software recognized by the scientific world (e.g.: the Microsoft Excel program is not recognized by the scientific world)

3. SPSS  Let’s start the SPSS software!  Paste the data onto the DATA VIEW window!  It has two windows, one of them contains the data (DATA VIEW), and the types of the variables must be given in the other one (VARIABLES).  Exact coding of variables is the basis of successful SPSS use.

4. Basics of computer-based analysis

5. Types of data  Measurable data  Differences between data are equal  E.g.  interval scale  How old are you?  How much is your weight?  Ordinal data  Data originating from gradation  Special type: reletad gradation positions  Nominal scale The data are replaced by numbers.  E.g. Gender? 1. Male 2. Female  The data do not signal order  The data cannot be added

6. Statistical procedures  Descriptive statistics  If we analyze actual persons, that is population = samples  Statistical indicators  Frequencies  Central tendency  Dispersion  Correlation

7. Statistical procedures  Mathematical statistics It provides the information whether we may draw conclusion based on the representative sample referring to the population.  Definition  Population: the group which the conclusions refer to  E.g.: university student; German people; teachers  Sample: the ones actually involved in the surveys  Representative sample: when the composition of the sample mirrors the composition of the population.  E.g.: Gallup’s deal with the Public Opinion Office around the time of the presidential elections in 1936

8. Mathematical statistics Analysis of differences  The aims: to show the criteria in which elements differ from each other Types of data Number of samples ScaleOrdinalNominal OneOne-sample t- samples test Wilcoxon-testCrosstabs analysis, Chi-square test TwoIndependent t- sample F-test Mann-Whitney-testCross database analysis, Chi-square test Three or moreANOVA analysisKruskall-Wallis- test Cross database analysis, Chi-square test

9. Mathematical statistics Analyzing correlations Types of data Number of samples ScaleOrdinalNominal TwoCorrelateSpearman correlate Crosstabs analysis, Chi-square test Two or moreRegression More than twoPartial correlate Factor analysis Cluster analysis

10. Descriptive statistics

11. Central Tendency  Mean  Modus : (most frequent data)  Median

12. Frequency 1. Determining the number of categories  An odd number between 10 and 20  If the number of the samples is low (e.g.50 responders) there can be fewer categories (7 categories) 2. Determining the intervals  1, 2, 3, 5, 10  depending on the number of categories  Disjunction: It should be noted that the each item in the sample must be categorized into one particular category, so the groups may not overlap. E.g.: Bad samples: Age groups Below 20 20-30 30-40… E.g.: God examples: Age groups Below 20 20-29 30-39…

13. Absolute frequency  Def: The number of items belonging to particular category is absolute frequency value.  the subgroup frequencies together create the absolute frequency distribution of the sample.

14. Further frequency indicators  Relative frequency means the quotient of the absolute frequency values and the number of the samples. The relative frequency gives the percent of the responders in one particular category compared to the total number of samples.  Cumulative frequency means how many items of the sample can be found all together below the upper limit of the category.  Cumulative percent means the quotient of the cumulative frequency and the number of the sample. IT shows what percent of the sample can be found below the upper limit of the category.

15. Dispersion indicators  Range: the range of the samples means the difference between the highest and lowest items. R = X max - X min  Average difference: the average distance (absolute deviation) of the items from the average.  Square sum: Sum of the quadrant of the deviation from the average.

16. Variance  Variance the square sum divided by the degree of freedom of the sample  Degree of freedom is the number of the independent elements (the number of the responders) of the sample.

17. Standard deviation  Standard deviation is the square root with a positive sign of the variance.

18. Theorem  More than 2/3 of the data belong to a 1 standard deviation extending to the positive and negative directions from the mean.  More than 90% of the data belong to a 2 standard deviation taken from the mean.  More than 90% of the data belong to a 3 standard deviation taken from the mean.

19. Relative standard deviation  The Relative deviation is an indicator related which provides what percent of the mean is the standard deviation. standard deviation Relative deviation = mean

20. Quartiles  The quartiles are the quartering points of the sample.  Interquartiles half-extension: is the difference between the third and the first quartile: Q 3 -Q 1

21. Interrelations

22. Interrelations between frequency and mean indicator  Left tendency: Modus > Median > Mean  Right tendency : Modus < Median < Mean

23.  Normal distribution (bell curve) : All the three indicators coincide Modus = Median = Mean Interrelations between frequency and mean indicatior

24. Mathematical statistics

25. Relations examinations

26. Correlation  Correlation coefficient is the indicator which shows the direction and strength between two data list.

27. Correlation  There is correlation between the two samples  There is no correlation between the two samples

28. Correlation coefficient The interpretation of the correlation coefficient 0,9 – 1 extremely strong correlation between the two data lists 0,75 – 0,9 strong 0,5 – 0,75 detectable 0,25 – 0,5 weak 0,0 – 0,25 no relationship Direction  If the correlation coefficient is negative  contrasting relationship  E.g. The numbers of hours doing sports – your weight  If the correlation coefficient is positive  data changing simultaneously  E.g. The size of your home library – the rate of loving to read 28

29. Relationship between/among variables – Crosstabs  Crosstabs – illustrating the distribution of two nominal or ordinal variables on the same chart.

30. Crosstabs- Chi-square  It is an indicator which shows whether the correlations in the cross tabs are valid only for the samples or for the population as well.  It cannot be used efficiently if the value is less then 5 in more than 20% of the cells.

31. Hypothesis analyses  It is a method to decide whether the differences in data are significant or random.

32. Paired-samples T-test The paired-samples T-test is used when the same people are asked or tested twice (e.g. one-sample experiment) Where: - mean s - Standard deviation

33.  Match the t-number with the value of the „Critical values of the t-distribution” chart  If t’ > t chart the different is significant  If t’ < t chart the different is random Paired-samples T-test

34. T-test with computer It is not necessary use the „Critical values of the t-distribution” chart, because most software provides the „p” value (Signif of t, Sig.Level). The „p” shows what percent is the failure rate. If „p”<0.05 (5%) then the difference is significant

35. Independent t-test  H0: two independent samples taken from the same population.  (H0 definition: the zero hypothesis is that the difference is random )  This type of test can only can be conductived if the variances of the two groups not too different.  The F-test can give the answer.

36. F-test The F-test is the quotient of the variance squares. If F number < F chart  there is no significant difference If F number > F chart  there is a great difference between the variances  the T-test cannot be done.  you can try the Welch-test.

37. Independent t-test The degree of freedom = n+m-2.

39. Illustration of result Aim: to make the result look conceivable and visual

40. Frequency polygon Illustrating frequency data with a line diagram.

41. Histogram Illustrating frequency data with a bar diagram. The title of the X axis is intervals.

42. Histogram shapes Symmetrical, peaked Symmetrical, normal

43. Histogram shapes bimodal

44. Histogram shapes Right side tendency

45. Histogram shapes Left side tendency

46. Interrelations between frequency and mean indicator Normal distribution: Mean = Median = Modus Skewness = 0

47. Interrelations between frequency and mean indicator Symmetric with two modes Bimodul Skewness = 0

48. Interrelations between frequency and mean indicator Right side tendency Mode<Median<Mean Skewness = (-)

49. Interrelations between frequency and mean indicator Right side tendency Mean < Median < Mode Skewness = (+)

50. Normal distribution with different standard deviation Kurtosis = 1  normal If the Kurtosis value is bigger the polygon is flatter