Chapter 2 Descriptives

2.1 Descriptives

An example from Kerlinger (1969, pp. 93-95):

Table 2.1: Data for Descriptives

Data
1
2
3
4
5

2.1.1 Results Overview

Table 2.2: Result Overview Descriptives

	By Hand	JASP	SPSS	SAS	Minitab	R
Mean	3.0	3.000	3.000	3.000	3.000	3.000
Variance	2.5	2.500	2.500	2.500	2.500	2.500
Median	NA	3.000	3.000	3.000	3.000	3.000
Standard Deviation	NA	1.580	1.580	1.580	1.580	1.580
SE(Mean)	NA	0.707	0.707	0.707	0.707	0.707

2.1.2 By Hand

Calculations by hand can be found in Kerlinger (1969, pp. 93-95).

Result:

Mean = 3

Variance = 2.5

Note: Kerlinger calculated the population variance, however as all statistical software computes the sample variance, the formula was adapted accordingly to be divided by N-1.

2.1.3 JASP

Figure 2.1: JASP Output for Descriptives

2.1.4 SPSS

DATASET ACTIVATE DataSet1.
DESCRIPTIVES VARIABLES=Data
  /STATISTICS=MEAN STDDEV VARIANCE MIN MAX SEMEAN.

Figure 2.2: SPSS Output for Descriptives

2.1.5 SAS

PROC MEANS DATA=work.Desc Mean STDDEV Median STDERR Var;
  VAR Data;
RUN;

Figure 2.3: SAS Output for Descriptives

2.1.6 Minitab

Figure 2.4: Minitab Output for Descriptives

2.1.7 R

mean(desc.data2$Data)

## [1] 3

sd(desc.data2$Data)

## [1] 1.581139

var(desc.data2$Data)

## [1] 2.5

median(desc.data2$Data)

## [1] 3

se <- function(x) sqrt(var(x)/length(x))
se(desc.data2$Data)

## [1] 0.7071068

2.1.8 Remarks

All differences in results between the software and hand calculation are due to rounding.

2.1.9 References

Kerlinger, F. N. (1969). Foundations of behavioral research. New York, US: Holt, Rinehart and Winston, Inc.