Think of a topic to study Review the previous literature and research Develop research questions and hypotheses Specify how to measure the variables in your hypotheses (operationalize) Write your questionnaire Generate a sample Distribute your questionnaires Prepare code book and SPSS data file Enter survey results in data file Analyze data statistically Write up results and conclusions The Research Process

Presenting Univariate Data – Describing the Variables  frequency distributions or tables  graphs or charts  statistical measures

Pie Chart

Bar Graph

Are younger children in a class over-represented in referral to the educational psychology service? This was one of the most marked results of the study. From the 695 referrals collated from the psychological service it was evident that children born towards the end of the school year were significantly more likely to be referred to the psychology service. The results of the referral information indicated that as the cut-off birth date (end of June) for school entry approaches the number of referrals to the board psychological service appears to increase (see Figure 1).

Histogram

Histogram with Normal Curve

Line Graphs

Frequency curves

STATISTICS Measures of Central Tendency There are three measures that summarize where the responses in a distribution for a variable tend to be clustered: the Mean, Median, and Mode. Mean The mean provides information about the mathematical center of a distribution. It is the sum of all the values in a distribution divided by the number of values. Median The median – like the median that runs down the middle of the highway – is the halfway point in a distribution. It is the value above which half the values fall and below which the other half are. It has virtually nothing to do with the actual values, just the number of values. Mode The mode is obtained by finding the most frequently selected value in a distribution of a variable. Do not confuse the mode with the "majority" answer which is a response that is more than 50%; the most frequently occurring value could have been selected by fewer than 50 percent of the respondents and still qualify as the modal response. But a majority response is always the mode.

Standard Deviation Knowing the central measure does not tell us how spread out the values in a distribution are. The standard deviation provides a mathematical measure of dispersion or variability. It is somewhat like the average variation of all the values in a distribution from the mean. Percentiles A percentile tells you the percentage of responses that fall above and below a particular point. For example, the median is the 50th percentile.

Common Core of Data (CCD), a program of the U.S. Department of Education's National Center for Education Statistics, focusing on “Characteristics of the 100 Largest Public Elementary and Secondary School Districts in the United States: ” Median pupil/teacher ratios in public elementary and secondary schools in the 100 largest school districts in the United States and jurisdictions: School year

Students’ Ages Deviations Mean = 30/5 = 6 Median6 Standard Deviation (s) = 10-6 = = = = = -4 Sum of the deviations = 0  X – mean) Deviations Squared 4 2 = 4 * 4 = 16 2 * 2 = 4 0 * 0 = 0 -2 * -2 = 4 -4 * - 4 = 16 Sum of the deviations squared (sum of squares) = 40  (X – mean) 2 Variance =  (X – mean) = = 10 N -1 4 square root of variance  10 = 3.16 How to Calculate a Standard Deviation

Purposes of the Standard Deviation 2, To compare the distribution of values of a variable in a sample with the distribution of the same values in another sample, For example: (a) to compare the scores on a reading test in one class with the scores on the same reading test for another class; (b) to compare the dispersion of weights in a sample of men with a sample of women; (c) to compare the distribution of values on a measure of self-esteem before a new therapy program with scores after the program 1.To describe the dispersion of values of a variable (interval/ratio) around its mean. For example: If the mean of a variable (such as age) is 32 with a standard deviation of 0, then we know that everyone is exactly 32 years of age in the sample. If it were 3.5 then we know that there is some dispersion of ages around 32. But if s= 10.7 then we would know that the dispersion is even larger. People are more spread out in terms of age around the average of 32.

Purposes of the Standard Deviation 3.To compare the distribution of values of a variable in a sample with the distribution of the values of a different variable in the same or another sample. For example: Let’s say you wanted to compare the scores on the SAT with scores on a Reading test but they are measured differently (SAT scores go from 200 to 800 and the Reading Test ranges from 0 to 100). The means and standard deviations would be different, so you must first standardize the scores in order to compare values originally measured with two different units. To do this, we standardize the measuring units by converting them to z-scores. Z-scores are “standard deviation units” that locate a score on a normal distribution – they tell you exactly how far away a particular score is from the mean.

Verbal Reading The percentages under the normal curve are the proportion of respondents who have scores in that particular range. They also represent percentiles, and probabilities. So one could say that respondents who have a z-score of 0 are at the 50 th percentile, or there are 50% of the respondents below a z-score of 0, or the probability of finding someone by chance with z-scores above 2 is 2.27%. Using the logic of probability theory, the odds of finding someone either above 2 or below -2 are 2.27% % = 4.54% or approximately p=5% (in proportion terms: =.0454 (p=.05)

Try this one: A normal distribution of values for the variable “Weight” has a mean of 120 pounds, and a standard deviation of What is the median weight and the modal weight? 2. What proportion or percentage of a sample would be between 100 and 140 pounds? 3. What are the chances of finding someone randomly who is above 120 pounds? Above 140 pounds? Below 80 pounds? 4. What is the probability of finding someone either significantly heavier than the average or significantly lighter than the average? Use p<.05

Example: Interpret these findings