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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)

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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.

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

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

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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
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 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

Mathematical statistics
Analysis of differences
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The aims: to show the criteria in which elements differ from each other
Ordinal Nominal Types of data Scale
Number of samples
One One-sample tsamples test
Two Independent tsample
F-test
Three or more ANOVA analysis
Wilcoxon-test Crosstabs analysis,
Chi-square test
Mann-Whitney-test Cross database analysis,
Chi-square test
Kruskall-Wallistest
Cross database analysis,
Chi-square test

Analyzing correlations
Types of data Scale
Number of samples
Two Correlate
Ordinal
Spearman correlate
Two or more Regression
More than two Partial correlate
Factor analysis
Cluster analysis
Nominal
Crosstabs analysis,
Chi-square test

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Mean
 Modus : (most frequent data)
 Median

1.
2.
Determining the number of categories
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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)
Determining the intervals
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1, 2, 3, 5, 10  depending on the number of categories
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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…

 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.

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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.

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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.

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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.

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

 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.

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

 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

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Left tendency: Modus > Median > Mean
Right tendency : Modus < Median < Mean

 Normal distribution (bell curve) :
All the three indicators coincide
Modus = Median = Mean

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

r xy
 r táblázat
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There is correlation between the two samples r
 xy r táblázat 
There is no correlation between the two samples

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
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 Crosstabs – illustrating the distribution of two nominal or ordinal variables on the same chart.

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.
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It cannot be used efficiently if the value is less then
5 in more than 20% of the cells.

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

The paired-samples T-test is used when the same people are asked or tested twice (e.g. one-sample experiment)
Where: z - mean s - Standard deviation t
'  z s
 n

 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

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

 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.

F
 s
1
2 s
2
2
The F-test is the quotient of the variance squares.
If F number difference
< F chart
 there is no significant
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.

t
  x
 y i n 

1
( x
 x i
)
2 n

 m m  i


1
2
( y
 y i
)
2
 n
 n
 m m
The degree of freedom = n+m-2 .

Histogram
6
5
4
3
2 REL
1
0
0 5 10 15
REL
20 25 30
6
Mean = 12,9
Std. Dev. = 5,515
N = 20
5
4
3
2
1
0
0 5 10 15
REL
20 25 30
Mean = 12,9
Std. Dev. = 5,515
N = 20
Aim: to make the result look conceivable and visual
Egyéni eredmény
9
12
15
18
24
Missing

Illustrating frequency data with a line diagram.

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

Symmetrical, normal
Symmetrical, peaked

bimodal

Right side tendency

Left side tendency

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

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

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

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

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