Statistical analyses

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)

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.

Basics of computer-based

analysis

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 scaleThe data are replaced by numbers. E.g. Gender? 1. Male 2. Female The data do not signal order The data cannot be added

Statistical procedures

Descriptive statistics If we analyze actual persons,

that is population = samples Statistical indicators

Frequencies Central tendency Dispersion Correlation

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

Mathematical statistics

Analysis of differences The aims: to show the criteria in

which elements differ from each other

Types of data

Number of samples

Scale Ordinal Nominal

One One-sample t-samples test

Wilcoxon-test Crosstabs analysis,Chi-square test

Two Independent t-sampleF-test

Mann-Whitney-test

Cross database analysis,Chi-square test

Three or more

ANOVA analysis Kruskall-Wallis-test

Cross database analysis,Chi-square test

Mathematical statistics

Analyzing correlations

Types of data

Number of samples

Scale Ordinal Nominal

Two Correlate Spearmancorrelate

Crosstabs analysis,Chi-square test

Two or more Regression

More than two

Partial correlateFactor analysisCluster analysis

Descriptive statistics

Central Tendency

Mean

Modus : (most frequent data)

Median

Frequency1. 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 groupsBelow 2020-3030-40…

E.g.: God examples:Age groupsBelow 2020-2930-39…

Absolute frequency

Def: The number of items belonging to particular category is absolute frequency value.

the subgroup frequencies together create theabsolute frequency distribution of the sample.

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.

Dispersion indicators

Range: the range of the samples means the difference between the highest and lowest items.R = Xmax - Xmin

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.

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.

Standard deviation

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

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.

Relative standard deviation

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

standard deviationRelative deviation = mean

Quartiles

The quartiles are the quartering points of the sample.

Interquartiles half-extension: is the difference between the third and the first quartile: Q3-Q1

Interrelations

Interrelations between frequency and mean indicator

Left tendency: Modus > Median > Mean

Right tendency : Modus < Median < Mean

Normal distribution (bell curve) : All the three indicators coincideModus = Median = Mean

Interrelations between frequency and mean indicatior

Mathematical statistics

Relations examinations

Correlation

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

Correlation

There is correlation between the two samplestáblázatxy rr

táblázatxy rr There is no correlation between the two samples

Correlation coefficientThe interpretation of the correlation coefficient

0,9 – 1 extremely strong correlation between the two data lists

0,75 – 0,9 strong0,5 – 0,75 detectable0,25 – 0,5 weak0,0 – 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

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Relationship between/among variables – Crosstabs 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.

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

Hypothesis analyses

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

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)

ns

zt '

Where:

- mean

s - Standard deviationz

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

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

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.

F-test

The F-test is the quotient of the variance squares.

If Fnumber < Fchart there is no significant differenceIf Fnumber > Fchart there is a great difference between the variances

the T-test cannot be done. you can try the Welch-test.

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Independent t-test

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The degree of freedom = n+m-2.

Illustration of result

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Mean = 12,9Std. Dev. = 5,515N = 20

Histogram

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Mean = 12,9Std. Dev. = 5,515N = 20

REL

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Missing

Egyéni eredmény

Aim: to make the result look conceivable and visual

Frequency polygon

Illustrating frequency data with a line diagram.

Histogram

Illustrating frequency data with a bar diagram.

The title of the X axis is intervals.

Histogram shapes

Symmetrical, peaked

Symmetrical, normal

Histogram shapes

bimodal

Histogram shapes

Right side tendency

Histogram shapes

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