BHS 204-01 Methods in Behavioral Sciences I

BHS 204-01Methods in Behavioral Sciences I April 18, 2003 Chapter 4 (Ray) – Descriptive Statistics

Scales of Measurement • Nominal (categorical) – all-or-nothing categorization or classification of responses. • Example: religions, political parties, occupations • Ordinal – ordered by an underlying continuum, degree of quantitative difference. • Example: small, medium, large; child, teen, adult • Rank orderings: best, second best, worst

Scales of Measurement (Cont.) • Interval – ordered by a single underlying quantitative dimension with equal intervals between consecutive values. • Example: thermometer, rating scales • Ratio – an interval scale with an absolute zero point. • Example: height, weight, yearly salary in dollars, heart rate, reaction time to press a button.

Appropriate Statistics • Numbers do not know or care where they came from (how you got them). • It is possible to apply any statistical test to almost any set of numbers, but that doesn’t make it right to do so. • Taking the average of football jersey numbers. • It is up to the experimenter to think about the nature of the data when selecting statistics.

Frequency Distributions • Data tells a story. • Techniques for analyzing data help you to figure out what story your data is telling. • Frequency distribution – how frequently does each score appear in your data set. • Bar graph • Frequency polygon (line graph)

Table 4.2. (p. 87)

Figure 4.1. (p. 88)Bar graph of dream data.

Figure 4.2. (p. 88)Frequency polygon of dream data.

Measures of Central Tendency • What single number best describes the data set? • Mean – arithmetical average of a set of scores. • Median – the middle score, so that half the numbers are higher and half lower. • Mode – the most frequently occurring score.

Figure 4.4. (p. 91)Mean, median, and mode of (a) a normal distribution and (b) a skewed distribution.

Types of Frequency Distributions • Normal – most scores are close to the mean. • Bimodal – the data set has two modes. • Positively skewed – extreme scores in the positive direction • Negatively skewed – extreme scores in the negative direction • In a skewed distribution, the mean is closest to the direction of skew.

Figure 4.3. (p. 89)Four types of frequency distributions: (a) normal, (b) bimodal, (c) positively skewed, and (d) negatively skewed.

Measures of Variability • Variability – how spread out are the scores. • Range – the distance between the highest and lowest scores (largest score minus the smallest scores). • Variance – the average of the squared distances from the mean. • Sum of the squares divided by the number of scores.

Figure 4.5. (p. 93)Two different distributions with the same range and mean but different dispersions of scores.

Standard Deviation • Average distance of scores from the mean. • Calculated by taking the square root of the variance. • The variance scores were squared so that the average of positive and negative distances from the mean could be combined. • Taking the square root reverses this squaring and gives us a number expressed in our original units of measurement (instead of squared units).

Graphing Data • Line graph – used for ordinal, interval, ratio data. • Independent variable on the x-axis • Dependent variable on the y-axis • Bar graph – used for categorical data.

Figure 4.6. (p. 97)Effects of room temperature on response rates in rats.

Figure 4.7. (p. 97)Effects of different forms of therapy.

Transforming Data • Sometimes it is useful to change the form of the data in some way: • Converting F to C temperatures. • Converting inches to centimeters. • Transformation lets you compare results across studies. • Transformation must preserve the meaning of the data set and the relationships within it.

Standard Scores • One way to transform data in order to compare two data sets is to express all scores in terms of the distance from the mean. • This is called a z-score. • z = (score – mean) / standard deviation • z-scores can be transformed so that all scores are positive: • This is called a T-score • T = 10 x z + 50

Measures of Association • Scatter plot – used to show how two dependent variables vary in relation to each other. • One variable on x-axis, the other on y-axis. • Correlation – a statistics that describes the relationship between two variables – how they vary together. • Correlations range from -1 to 1.

Figure 4.9. (p. 102)Scatter diagram showing negative relationship between two measures.

Figure 4.10. (p. 103)Scatter diagrams showing various relationships that differ in degree and direction.

BHS 204-01 Methods in Behavioral Sciences I