Quick Answer: Skewness Result

The main SPSS result for G3 final grade showed Skewness = -0.913, Standard Error of Skewness = 0.096, Mean = 11.91, Median = 12.00, Mode = 11, SD = 3.231, and N = 649. Since the skewness value is negative, the skewness of the distribution is left skewness. This means the left tail is longer or more extreme than the right tail, and some low G3 values pull the distribution toward the lower end.

The test of skew can be summarized with a z-style check: Skewness / Standard Error of Skewness = -0.913 / 0.096 ≈ -9.51. This is far beyond the common ±1.96 reference rule, so the G3 distribution is not perfectly symmetric. The practical conclusion is that G3 has meaningful negative skewness, while absences has strong positive skewness.

What Is Skewness?

Skewness is a descriptive statistic that measures the asymmetry of a distribution. A perfectly symmetric distribution has skewness close to zero. If the tail extends to the right, the distribution has positive skewness. If the tail extends to the left, the distribution has negative skewness or left skewness.

In practical reporting, Skewness helps answer questions such as: Is the distribution balanced around the center? Are there extreme low values or high values? Is the mean pulled away from the median? Does the shape suggest that normality checks are needed before using parametric tests?

For example, the G3 final grade distribution has Skewness = -0.913. This means the shape has left skewness. In contrast, absences has Skewness = 2.021, which means it has strong positive skewness or right skewness. The two variables show different types of asymmetry, so they should not be interpreted with the same shape description.

Skewness is often used with normality guides such as the Q-Q plot normality check, P-P plot normality check, Kolmogorov-Smirnov test, Lilliefors test, D’Agostino-Pearson test, and Cramer-von Mises test.

Skewness Formula and Interpretation

The sample Skewness formula compares each observation with the mean, raises the standardized difference to the third power, and averages the result. A simplified expression is:

The third power is important because it preserves direction. Values above the mean contribute positive cubic values. Values below the mean contribute negative cubic values. If the right tail is stronger, skewness becomes positive. If the left tail is stronger, skewness becomes negative.

Skewness z Statistic

SPSS reports Skewness and the Standard Error of Skewness. A common quick check divides skewness by its standard error:

For G3, the result is:

z_skewness = -0.913 / 0.096
z_skewness ≈ -9.51

This indicates clear asymmetry. However, with large samples, even small deviations from symmetry can become statistically noticeable. Therefore, always combine the test of skew with histograms, boxplots, mean-median comparison and practical judgment.

Positive Skewness, Negative Skewness, Right and Left Skewness

The phrases positive or negative skewness, right and left skewness, and skewness positive negative all describe the direction of the long tail. These terms are often confusing because “right skewness” and “positive skewness” mean the same thing, while “left skewness” and “negative skewness” mean the same thing.

Test of Skew and Hypothesis Context

Skewness is primarily descriptive, but the test of skew can be explained with a hypothesis-style decision. This is helpful when reporting normality screening and distribution shape.

For formal normality decisions, do not rely on skewness alone. Use distribution charts and normality tools such as the Q-Q plot normality check 2, Kolmogorov-Smirnov test, Lilliefors test, and D’Agostino-Pearson test.

Dataset and Variables Used

The worked example uses the student performance dataset. The main variable is G3 final grade. Other numeric variables such as G1, G2, age and absences are included to compare Skewness across variables. This makes the guide stronger because it shows that not all variables have the same direction or degree of asymmetry.

Before interpreting skewness, review distribution basics using descriptive statistics, frequency distribution, histogram interpretation, box plot interpretation, and five-number summary.

Verified SPSS Output Interpretation

The SPSS output verifies the Skewness values, standard errors, descriptive statistics, and related kurtosis values. The key result is that G3 has negative skewness, while absences has strong positive skewness. This comparison is important because it shows how different variables can have different distribution shapes in the same dataset.

Main SPSS Descriptive Table

Detailed G3 Interpretation

For G3, SPSS reported Skewness = -0.913. Because the sign is negative, the distribution has left skewness. The mean is 11.91, while the median is 12.00. The mean is slightly lower than the median, which is consistent with the negative skewness result. The G3 distribution is affected by unusually low scores, including zero values, which extend the left tail.

The G3 Standard Error of Skewness is 0.096. Dividing -0.913 by 0.096 gives a z-style value of about -9.51. This indicates that the skewness is not trivial. However, the practical interpretation should still be based on charts and context, not only the z-style statistic.

SPSS Decision Summary

Skewness and Kurtosis Together

Skewness and kurtosis are often reported together because they describe different parts of distribution shape. Skewness describes asymmetry and tail direction. Kurtosis describes tail heaviness or peakedness relative to a normal distribution. In the SPSS output, G3 has Skewness = -0.913 and Kurtosis = 2.712. This means G3 is left-skewed and also has a heavier or sharper tail pattern than a normal distribution under the SPSS excess-kurtosis style.

The phrase kurtosis and skewness is common in normality reporting. If both values are close to zero, the distribution may be closer to normal shape. If either value is large, charts and normality tests should be reviewed. For more detailed kurtosis interpretation, connect this post with your kurtosis guide and normality guides such as Q-Q plot normality check and P-P plot normality check.

Python Chart-by-Chart Interpretation

The Python charts show the main Skewness interpretation visually. The charts include the G3 distribution with mean and median, skewness comparison across variables, boxplots with long tails, and mean-minus-median comparison. These charts are essential because skewness should be interpreted visually, not only numerically.

Python Chart 1: Distribution with Mean and Median

This chart shows the skewness of the distribution for G3. The histogram displays the grade pattern, while the mean and median lines help explain the direction of skewness. In a left-skewed distribution, low-end values pull the mean downward. In the G3 result, the mean is slightly below the median, which supports the SPSS result of negative skewness.

The distribution does not look perfectly symmetric because some low scores stretch the left side of the distribution. This is why the G3 skewness value is negative. The chart is useful for readers because it shows why the number -0.913 has a real shape meaning rather than being just a table value.

Python Chart 2: Skewness Comparison Across Variables

This chart compares Skewness across variables. G1 is almost symmetric, G2 is mildly negative, G3 is clearly negative, age is mildly positive, and absences is strongly positive. This comparison is important because it shows that skewness is variable-specific. One dataset can contain both left-skewed and right-skewed variables.

Absences stands out because it has strong positive skewness. Most students have few absences, while a smaller number have many absences, creating a long right tail. G3 shows the opposite direction because very low grades create left-tail influence. This chart directly supports the keywords positive skewness, left skewness, right and left skewness, and positive or negative skewness.

Python Chart 3: Boxplots and Long Tails

This chart explains skewness of box and whisker plots. A boxplot can show skewness through uneven whiskers, off-center median lines, and outliers concentrated on one side. For G3, the boxplot supports left-tail concern because unusually low values stretch the lower side. For absences, the boxplot supports right-tail concern because high absence values stretch the upper side.

This is why skewness box and whisker interpretation should not be skipped. A table may report a skewness number, but the boxplot shows the shape and outlier structure behind that number. When the whisker or outliers extend more strongly on one side, it visually supports positive or negative skewness.

Python Chart 4: Mean Minus Median

This chart uses mean minus median as a supporting shape indicator. When the mean is greater than the median, the distribution often has positive skewness. When the mean is less than the median, the distribution often has negative skewness. The chart does not replace the formal skewness value, but it helps readers understand why the mean and median positions matter.

For G3, the mean is slightly below the median, which is consistent with left skewness. For absences, the mean is above the median, which is consistent with positive skewness. This chart is useful for teaching because it links descriptive statistics with distribution shape.

R Chart-by-Chart Validation

The R charts validate the Python and SPSS Skewness interpretation using a separate workflow. The same pattern appears again: G3 is left-skewed, absences is right-skewed, and mean-median differences support the direction of asymmetry.

R Chart 1: Distribution with Mean and Median

The R distribution chart confirms the Python chart. The G3 distribution is not perfectly symmetric, and the mean-median position supports a negative skewness interpretation. This validation is useful because it shows that the conclusion is not dependent on one software package.

The same reporting conclusion applies: G3 has left skewness. The distribution should be described as negatively skewed because low values extend the left side of the distribution.

R Chart 2: Skewness Comparison Across Variables

The R comparison chart confirms the variable-by-variable skewness pattern. G1 is almost symmetric, G2 has mild negative skewness, G3 has stronger negative skewness, age has mild positive skewness, and absences has strong positive skewness.

This chart supports the main statistical message: the researcher should not describe the whole dataset as skewed in one direction. Instead, each variable should be interpreted separately.

R Chart 3: Boxplots and Long Tails

The R boxplot chart validates the skewness of box and whisker plots interpretation. It shows that tail direction and outliers are visible in boxplot form. Variables with long upper tails show positive skewness; variables with long lower tails show negative skewness.

This chart is useful for readers who prefer visual diagnostics. It also supports normality-check decisions because boxplot asymmetry can suggest the need for transformation, robust analysis or nonparametric methods.

R Chart 4: Mean Minus Median

The R mean-minus-median chart confirms the Python result. The sign of mean minus median supports the direction of asymmetry. G3 has a mean slightly below the median, which supports negative skewness. Absences has a mean above the median, which supports positive skewness.

The correct conclusion is that mean-minus-median is a supporting diagnostic. It should be interpreted with the formal skewness value, histogram and boxplot.

SPSS, R, Python and Excel Workflows for Skewness

Skewness can be calculated in SPSS, R, Python and Excel. The workflow is similar in each tool: select numeric variables, calculate skewness, compare mean and median, inspect histograms and boxplots, and report whether the distribution shows positive skewness, negative skewness or approximate symmetry.

SPSS Workflow

R Workflow

Python Workflow

Excel Workflow

Code Blocks for Skewness

SPSS Syntax for Skewness

* Skewness analysis in SPSS.
* Main variable: G3 final grade.

TITLE "Skewness Descriptive Statistics".

FREQUENCIES VARIABLES=G1 G2 G3 age absences
  /STATISTICS=MEAN MEDIAN MODE STDDEV VARIANCE SKEWNESS SESKEW KURTOSIS SEKURT RANGE MINIMUM MAXIMUM
  /HISTOGRAM NORMAL
  /ORDER=ANALYSIS.

EXAMINE VARIABLES=G1 G2 G3 age absences
  /PLOT BOXPLOT HISTOGRAM NPPLOT
  /COMPARE GROUPS
  /STATISTICS DESCRIPTIVES
  /CINTERVAL 95
  /MISSING LISTWISE
  /NOTOTAL.

OUTPUT EXPORT
  /CONTENTS EXPORT=VISIBLE
  /PDF DOCUMENTFILE="Skewness-SPSS-Output.pdf".

Python Code for Skewness

import pandas as pd
import numpy as np
from scipy import stats

df = pd.read_csv("dataset.csv")

numeric_vars = ["G1", "G2", "G3", "age", "absences"]

rows = []
for col in numeric_vars:
    x = pd.to_numeric(df[col], errors="coerce").dropna()
    n = len(x)
    skew_value = stats.skew(x, bias=False)
    se_skew = np.sqrt(6 / n)
    z_skew = skew_value / se_skew

    rows.append({
        "variable": col,
        "n": n,
        "mean": x.mean(),
        "median": x.median(),
        "standard_deviation": x.std(ddof=1),
        "skewness": skew_value,
        "se_skewness": se_skew,
        "z_skewness": z_skew,
        "shape": "positive skewness" if skew_value > 0 else "negative skewness" if skew_value < 0 else "symmetric"
    })

skewness_table = pd.DataFrame(rows)
print(skewness_table)

# Main interpretation for G3
g3 = skewness_table[skewness_table["variable"] == "G3"].iloc[0]
print("G3 skewness:", g3["skewness"])
print("G3 z-style skewness:", g3["z_skewness"])

R Code for Skewness

# Skewness analysis in R

df <- read.csv("dataset.csv")

# install.packages("e1071")
library(e1071)

numeric_vars <- c("G1", "G2", "G3", "age", "absences")

rows <- lapply(numeric_vars, function(v) {
  x <- na.omit(as.numeric(df[[v]]))
  n <- length(x)
  skew_value <- skewness(x, type = 2)
  se_skew <- sqrt(6 / n)
  z_skew <- skew_value / se_skew

  data.frame(
    variable = v,
    n = n,
    mean = mean(x),
    median = median(x),
    standard_deviation = sd(x),
    skewness = skew_value,
    se_skewness = se_skew,
    z_skewness = z_skew,
    shape = ifelse(skew_value > 0, "positive skewness",
                   ifelse(skew_value < 0, "negative skewness", "symmetric"))
  )
})

skewness_table <- do.call(rbind, rows)
print(skewness_table)

Excel Formula Block for Skewness

Assume G3 values are in cells A2:A650.

Mean:
=AVERAGE(A2:A650)

Median:
=MEDIAN(A2:A650)

Standard deviation:
=STDEV.S(A2:A650)

Sample size:
=COUNT(A2:A650)

Skewness:
=SKEW(A2:A650)

Approximate standard error of skewness:
=SQRT(6/COUNT(A2:A650))

Skewness z statistic:
=SKEW(A2:A650)/SQRT(6/COUNT(A2:A650))

Interpretation:
If skewness > 0, positive skewness / right skewness.
If skewness < 0, negative skewness / left skewness.
If skewness is close to 0, approximate symmetry.

APA Reporting Wording for Skewness

When reporting Skewness, include the variable, sample size, skewness value, standard error of skewness if relevant, and shape interpretation. If skewness is used as part of a normality check, also mention the visual evidence from histogram, boxplot, Q-Q plot or P-P plot.

APA-Style Skewness Report

Short Reporting Version

Skewness and Kurtosis Reporting Version

Common Mistakes in Skewness Interpretation

When to Use Skewness

Use Skewness when you need to describe distribution shape, check normality assumptions, compare variables, identify tail direction, understand mean-median differences, or decide whether transformations or nonparametric methods may be needed.

For transformations and assumption decisions, review related guides such as reciprocal transformation, central limit theorem, Levene’s test, Brown-Forsythe test, and effect size.

Downloads and Resources for Skewness

The SPSS output PDF below verifies the Skewness values, standard error of skewness, kurtosis, descriptive statistics, confidence intervals and supporting output used in this guide.

Related Statistical Guides

Use these related guides to connect Skewness with normality checks, descriptive statistics, shape diagnostics, transformations, assumption tests and reporting.