Descriptive Statistics

FrequencyFrequency tells you the number of participants in a group or category. SPSS will also calculate the percentage. Central Tendency & VariabilityCentral Tendency represents the most typical score in a distribution, variability tells you how much the scores varied from the central tendency. The Mean (average) is the best measure of central tendency for interval and ratio scales (provided the data are normally distributed). When you report the mean, you should also report the Standard Deviation, which is a measure of variability. Use the Mean and SD for interval & ratio data that are normally distributed.

The Median (middle score, or score that splits the distribution in half) is the best measure of central tendency for ordinal scales or interval/ratio scales that are skewed. When you report the mean, you should also report the minimum and maximum scores (commonly called the range of scores, although the “real” definition of range is a single number that is the max score minus the min score). Use the Median for interval & ratio data that are skewed and for ordinal data.

The Mode (most common score) is the best measure of central tendency for nominal scales. However, simple frequencies may be more appropriate to report for certain scales (knowing that the modal gender is female is less useful than knowing what percentage of the sample are female vs. male). Use the Mode as the measure of central tendency for nominal data (although you should also report the frequency).

Normal Distribution & SkewnessThe analyses we will conduct in this class assume that your interval and ratio data are normally distributed – meaning that the mean is the average score, and 95% of the scores fall within 2 standard deviations of the mean.

A data distribution may be skewed:

You can calculate a Skewness Statistic in SPSS that tells you how skewed your distribution is. A zero (0) skewness statistic indicates a perfectly normal distribution; a positive skewness statistic indicates a positive skew; and a negative skewness statistic indicates a negative skew.

A skewness statistic between –1 and 1 meets the criteria for normality. A skewness statistic between –2 and 2 suggests some skewness, but it

is still within the acceptable range.

Calculating FrequenciesCalculate the frequency to describe nominal data such as gender, year in school, religious affiliation, etc.

The Normal Curve:

Negative Skew: Positive Skew:

On SPSS Menu Bar,Click Analyze Descriptive Statistics Frequencies

The Frequencies Box will open:

1. Click on the variable(s) you want to analyze in the variable list

2. Send to the “variable box” by clicking

3. Click “OK”

This output tells us: How many total participants there are (10)

How many of these participants were male (5) and female (5)

The percentage of the sample in each group or category (50% of the sample was male and 50% female)

Calculating the central tendency, variability, and skewness (option 1):

Analyze Descriptive Statistics Frequencies

The Statistics Box will open:

1. Send the variable(s) you want to analyze to the “variable “box”

2. Click “Statistics”

Click on the Statistics you want to run. Here we select more options than we will use - we will make decisions based on the skewness statistic.

Click “Continue” when you are done

SPSS OUTPUT:

Statistics

age100

29.600028.5000

10.895462.224.687

19.0058.00

ValidMissing

N

MeanMedianStd. DeviationSkewnessStd. Error of SkewnessMinimumMaximum

A skewness statistic of 2.22 = a significant positive skew.

When you have skewed data, you should report the min-max and median: “ages ranged from 19-58, with a median score of 28.5.”

The frequency table outlines the exact ages of your participants. Looking at the cumulative percent can be useful with skewed data:“Ninety percent of the sample were between the ages of 19 and 32.”

You can also request a chart of the distribution

The Charts Box will open:

Click “Charts”

Click “Histograms”&Click “With normal curve”

Click “Continue”

After clicking “continue” you will return to the 1st frequency box,Click “OK” to run the analyses

Note that the Histogram can give you an idea of what the data look like, and might indicate if there is a positive or negative

skew.

However, base decisions about whether or not a distribution is skewed on the skewness statistic, not the graph.

The histogram illustrates the results of the skewness statistic. Here we have a positively skewed distribution.

Calculating the central tendency, variability, and skewness (option 2):

Analyze Descriptive Statistics Descriptives

The Descriptives Box will open:

The Options Box will open:

After clicking “continue” you will return to the 1st Descriptives box,

Click “OK” to run the analyses

SPSS OUTPUT

Descriptives

1. Send the variable(s) you want to analyze to the “variable” box

2. Click “Options”

Click on the Statistics you want to run & Click “Continue” when you are done

Descriptive Statistics

10 4.00 11.00 8.1000 2.23358 -.754 .68710

totalattitudesValid N (listwise)

Statistic Statistic Statistic Statistic Statistic Statistic Std. ErrorN Minimum Maximum Mean Std.

DeviationSkewness

Should I use the “frequencies” or “descriptives” command??

Use “frequencies” when you have nominal data. Don’t request any additional statistics (the mean of gender doesn’t make sense).

When you have interval or ratio data, you can get much of the same descriptive information from running either “frequencies” or “descriptives.” However, Frequencies allows for additional information (charts, median, mode) that is often useful, particularly if you have skewed data.

Writing Up Results

General Guidelines: The goal in a results section is to summarize the statistics that you

believe are most important and useful in understanding your study. You should be selective in the results you report and how you report them – don’t just provide a laundry list of data that overwhelms the reader!

The output tells us the observed minimum and maximum scores (4 to 11), the Mean (8.1), and the SD (2.23). It also can provide the skewness statistic (-.75), which in this case indicates a distribution within the normal range.

Good writing skills are just as important in a results section as any other writing assignment. For example, you should use correct grammar and sentence structure, vary your sentence length and structure, avoid passive voice, avoid awkward statements, be concise, etc.

In a results section, you will be using statistical notation that is likely new to you. This manual will provide guidelines for using correct statistical notation. Keep in mind that the examples provided in this manual are just examples! Think about your data and results mean and then consider the best way to describe your results to your reader.

When reporting numbers:

o Use words for numbers that start a sentence (e.g., Seventy participants took surveys.) or are less than 10 (e.g., There were three groups.).

o Use digits when the number doesn’t start the sentence, when stating the number of participants, when reporting numbers 10 and over or numbers in a series in which at least one number is 10 or above (e.g., There were 47 children who ranged in age from 7 to 15 (M = 10.6, SD = 2.56)).

If you find that the text is getting too wordy or complicated, consider creating a table in Word to help report your results. You can explain what the results mean in the text of your report, then refer to the table for the specific statistics. (Remember that you should never cut and paste SPSS output into a research report!)

Writing up Descriptive StatisticsReporting Frequency Results for Nominal DataHere are several options:

Option 1: A total of 10 (5 male, 5 female) participants completed surveys.

Option 2: A total of 10 participants completed surveys. Fifty percent were male and 50% were female.

Option 3: Five males and 5 females completed surveys.

Option 4: Our sample was evenly split between males (N = 5) and females (N = 5).

Reporting Descriptive Statistics for Skewed Data:Here’s an example (you don’t always need to report all this information, pick what is most relevant):

Ages ranged from 19-58, with a median of 28.5. Data

were significantly skewed due to one participant who was 58.

Ninety percent of the sample were between the ages of

19 and 32.

Reporting Descriptive Statistics for Normally Distributed Data:Here are a few examples:

The Research Methods Attitude Survey has a possible

range of scores of 3-12. The mean attitude score of students

in our sample was 8.1 (SD = 2.23).ORThe Research Methods Attitude Survey has a possible

range of scores of 3 – 12. Observed scores ranged from 4 –

11 and were normally distributed (M = 8.3, SD = 2.41).