1. Lies, damned lies & statistics
Communication Research
week 10

2. Basics of descriptive statistics
Statisticians use mathematical methods to analyse, summarise and interpret data that have been collected
Descriptive statistics describe the basic features of the study and allows the researcher to get a feel for the data
The choice of statistical method of analysis depends on the data that have to be analysed
Communication Research Spring 2005

3. Descriptive vs inferential statistics
Descriptive statistics refer to methods used to obtain, from raw data, information that characterises or summarises the whole set of data
Inferential statistics allow us to generalise from the data collected to the general population they were taken from
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4. Communication Research Spring 2005

5. Different statistical measures
Raw data is unorganised but can be tabulated to make it easier to understand and to interpret
It is usually presented as a frequency table or graph
A frequency chart will allow a researcher to see trends or groupings of data and how they are distributed
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6. Some Basic Concepts Related to Statistics
Data: The raw material of statistics. Numbers that result from measurements or counting.
Statistics: The field of study concerned with the collection, organization, summarization and analysis of data and the drawing of inferences about a body of data when only a part of the data is observed.
Sources of Data
Routinely kept records
Surveys
Experiments
External Sources
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7. Communication Research Spring 2005
Some Basic Concepts Related to Statistics
Random Variable: A variable whose values arise as a result of chance factors and cannot be exactly predicted in advance.
Population: A population of entities is defined as the largest collection of entities for which we have an interest at a particular time.
Sample: A part of a population.
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8. Communication Research Spring 2005
The Simple Random Sample
Statistical Inference
The procedure by which we reach a conclusion about a population on the basis of the information contained in a sample that has been drawn from that population.
Simple random sample
If a sample of size n is drawn from a population of size N in such a way that every possible sample of size n has the same chance of being selected, the sample is called a simple random sample. 2 out of 4=2C4=6
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9. Characteristics of each distribution
Location – where on the axis is the distribution positioned?
Dispersion – how broad is the distribution?
Shape – what is the form (appearance, pattern) of the distribution?
The type of data you have to analyse will determine the statistical measure chosen
Statistics describing the location of the distribution are called measures of central tendency
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10. Measures of central tendency – the mean
The mean is the sum of all observed data values divided by the sample size (the arithmetic average)
Describing data that are interval or ratio in nature (eg speed of response, age in years) calls for the mean
One of the main disadvantages is that it is most profoundly affected by extreme scores
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11. Communication Research Spring 2005
Calculating a Mean Score
Scores: 79 81 82 86 88 91 93 95 97
total = 878
Divide by n = 10 scores
Mean = 87.8
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12. Measures of central tendency – the median
The median is the score or the point of distribution above which one half of the scores lie eg in a simple set of scores such as 1, 3, & 5 the median is 3
The median is best suited to data that are ordinal or ranked ( eg birth order, rank in class)
To compute the median
Order the scores from lowest to highest
Count the number of scores
Select the middle score
When the number of scores is even, find the mean of the two middle scores eg
N = 14 (no of scores); Median = ( ) ÷ 2 = 42.5
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13. Two distributions of scores Distribution 1 Distribution 216 19 22 25 28 30 35
Mean = 25
Range = 20 24 25 26
Mean = 25
Range = 3
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14. Measures of central tendency – the mode
The mode is the most frequently observed value in the frequency distribution ie it is the score that occurs most frequently
The mode is best used for nominal data and for data that are qualitative in nature such as gender, eye colour, ethnicity, school or group membership
In the following list of numbers:
The mode is 41 because it occurs 3 times
A common mistake is to identify the mode as how frequently the value occurs (3) not the value itself (41)
Communication Research Spring 2005

15. Which measure of central tendency?
Which measure when?
Which measure of central tendency?
Measure
Level of measurement
Examples
Mode
Nominal or categorical – ie qualitative
Gender, hair or eye colour, group membership, ethnicity, school etc
Median
Ordinal or ranked
Rank in class, birth order
Mean
Interval and ratio
Speed of response, age in years
Communication Research Spring 2005

16. Three Measures of Variability
Range: the difference between the highest and lowest scores in a distribution of scores.
Variance: a measure of dispersion indicating the degree to which scores cluster around the mean score.
Standard deviation: index of the amount of variation in a distribution of scores.
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17. Communication Research Spring 2005
Standard deviation
SD is a measure of the variability indicating the degree to which all observed values deviate from the mean
SD can only be used for interval and ratio data
It is the most frequently used statistic as a measure of dispersion or variability
The larger the SD, the more variable the set of scores is
Communication Research Spring 2005

18. COMPUTING DEVIATION SCORES
Raw Mean DEV. SQUARED
score score deviation score = = = = = = = = =
90/9 = = MEAN
70/9 = 7.77 = Variance
STANDARD DEVIATION: (Square Root of Variance) = 2.79
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19. Communication Research Spring 2005
Types of Variables
Variable
Element that is identified in the hypothesis or research question
Property or characteristic of people or things that varies in quality or magnitude
Must have two or more levels
Must be identified as independent or dependent
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20. Independent Variables
Manipulation or variation of this variable is the cause of change in other variables
Technically, independent variable is the term reserved for experimental studies
Also called antecedent variable, experimental variable, treatment variable, causal variable, predictor variable
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21. Communication Research Spring 2005
Dependent Variables
The variable of primary interest
Research question/hypothesis describes, explains, or predicts changes in it
The variable that is influenced or changed by the independent variable
In non-experimental research, also called criterion variable, outcome variable
Communication Research Spring 2005

22. Relationship Between Independent and Dependent Variables
Cannot specify independent variables without specifying dependent variables
Number of independent and dependent variables depends on the nature and complexity of the study
The number and type of variables dictates which statistical test will be used
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23. Issues of Reliability and Validity
Reliability = consistency in procedures and in reactions of participants
Validity = truth - Does it measure what it intended to measure?
When reliability and validity are achieved, data are free from systematic errors
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24. Threats to Reliability and Validity
If measuring device cannot make fine distinctions
If measuring device cannot capture people/things that differ
When attempting to measure something irrelevant or unknown to respondent
Can measuring device really capture the phenomenon?
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25. Other Sources of Variation
Variation must represent true differences
Other sources of variation
Factors not measured
Personal factors
Differences in situational factors
Differences in research administration
Number of items measured
Unclear measuring device
Mechanical or procedural issues
Statistical processing of data
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26. Communication Research Spring 2005
Types of variables
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27. Communication Research Spring 2005
Definitions
Variable: a characteristic that changes or varies over time and/or different subjects under consideration.
Changing over time
Blood pressure, height, weight
Changing across a population
gender, race/ethnicity
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28. Communication Research Spring 2005
Definitions (con’t)
Quantitative variables (numeric): measure a numerical quantity of amount on each experimental unit
Qualitative variables (categorical): measure a non numeric quality or characteristic on each experimental unity by classifying each subject into a category
Communication Research Spring 2005

29. Categorical variables
Nominal: unordered categories
Race/ethnicity
Gender
Ordinal: ordered categories
likert scales( disagree, neutral, agree )
Income categories
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30. Univariate statistics (numerical variables)
Summary measures
Measures of location
Measures of spread
Overall pattern (distribution)
Unimodal (one major peak) vs. bimodal) (2 peaks)
Symmetric vs. skewed
Outliers-an individual value that falls outside the overall pattern
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31. Communication Research Spring 2005
Skewness
The skewness of a distribution is measured by comparing the relative positions of the mean, median and mode.
Distribution is symmetrical
Mean = Median = Mode
Distribution skewed right
Median lies between mode and mean, and mode is less than mean
Distribution skewed left
Median lies between mode and mean, and mode is greater than mean
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32. Communication Research Spring 2005
Relative positions of the mean and median for (a) right-skewed, (b) symmetric, and (c) left-skewed distributions
Note: The mean assumes that the data is normally distributed. If this is not the case it is better to report the median as the measure of location.
Communication Research Spring 2005

33. Summary statistics Measures of spread (scale)
Variance: The average of the squared deviations of each sample value from the sample mean, except that instead of dividing the sum of the squared deviations by the sample size N, the sum is divided by N-1.
Standard deviation: The square root of the sample variance
Range: the difference between the maximum and minimum values in the sample.
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34. Normal curves same mean but different standard deviation
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35. Graphical display of numerical variables (histogram)
Class Interval Frequency
20-under 30 6
30-under 40 18
40-under 50 11
50-under 60 11
60-under 70 3
70-under 80 1
Communication Research Spring 2005 18

36. Graphical display of numerical variables (stem and leaf plot)
Raw Data
Stem
Leaf 2 3 4 5 6 7 8 9 3 9
7 9
5 6 9 86 76 23 77 81 79 68 92 59 75 83 49 91 47 72 82 74 70 56 60 88 97 39 78 94 55 67 89
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37. Graphical display of numerical variables (box plot)
Negatively
Skewed
Positively
Symmetric
(Not Skewed)
S < 0
S = 0
S > 0
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38. Univariate statistics (categorical variables)
Summary measures
Count=frequency
Percent=frequency/total sample
The distribution of a categorical variable lists the categories and gives either a count or a percent of individuals who fall in each category
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39. Communication Research Spring 2005
Displaying categorical variables
Rank
Cause of Death
Frequency (%) 1
Heart Disease
710,760 (43%) 2
Cancer
553,091 (33%) 3
Stroke
167,661 (11%) 4
CLRD
122,009
( 7%) 5
Accidents
97,900
( 6%)
Total
All five causes
1,651,421
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40. Communication Research Spring 2005
Common Applications
T-Tests – the independent t-test is used to test for a difference between two independent groups (like males and females) on the means of a continuous variablecontinuous variable.
one sample – compare a group to a known value
For example, comparing the IQ of convicted felons to the known average of 100)
paired samples – compare one group at two points in time
For example, comparing pretest and posttest scores
independent samples – compare two groups to each other
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41. Communication Research Spring 2005
Common Applications
The Pearson's correlation is used to find a correlation between at least two continuous variables. The value for a Pearson's can fall between 0.00 (no correlation) and 1.00 (perfect correlation).
Other factors such as group size will determine if the correlation is significant. Generally, correlations above 0.80 are considered pretty high
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42.
Days Absent
Non-significant t-test 60 50 40 30 20 10
Common Applications
Male
Female
Number of people
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43. Communication Research Spring 2005
Days Absent
Significant t-test 60 50 40 30 20 10
Common Applications
Male
Female
Number of people
Communication Research Spring 2005