Chapter 3 Normal Curve, Probability, and Population Versus Sample Part 2

Using the Table: From % back to Z or raw scores Steps for figuring Z scores and raw scores from percentages: 1. Draw normal curve, shade in approximate area for the % (using the 50%-34%-14% rule) 2. Make rough estimate of the Z score where the shaded area starts 3. Find the exact Z score using the normal curve table: –look up the % and find its z score (see example)

(cont.) 4. Check that your Z score is similar to the rough estimate from Step 2 5. If you want to find a raw score, change it from the Z score, using formula: x = Z(SDx) + Mx

Probability –Expected relative frequency of a particular outcome Outcome –The result of an experiment

Probability Range of probabilities –Proportion: from 0 to 1 –Percentages: from 0% to 100% Probabilities as symbols –p–p –p <.05 (probability is less than.05) Probability and the normal distribution –Normal distribution as a probability distribution –Probability of scoring betw M and +1 SD =.34 (In ND, 34% of scores fall here)

Sample and Population Review difference betw sample & pop Methods of sampling –Random selection – everyone in the pop has equal chance of being selected in sample –Haphazard selection (e.g., convenience sample) – take whomever is available, efficient  may differ from pop.

Sample and Population Population parameters and sample statistics– note the different notation depending on whether we refer to pop or sample –M for sample is  for population –SD for sample is  for population

Ch 4 – Intro to Hypothesis Testing Part 1

Hypothesis Testing Procedure for deciding whether the outcome of a study (results for a sample) support a particular theory (thought to apply to a population) Logic: –Considers the probability that the result of a study could have come about if the experimental procedure had no effect –If this probability is low, scenario of no effect is rejected and the theory is supported

The Hypothesis Testing Process 1.Restate the question as a research hypothesis & a null hypothesis Research hypothesis –supports your theory.  Job satisfaction of Dr. Johnson is higher than national average (M = 3.5 on 1-5 scale)  Null hypothesis – opposite of research hyp; no effect (no group differences). This is tested.  Job satisfaction of Dr. J does not differ from national average

The Hypothesis Testing Process 2.Determine the characteristics of the comparison distribution  Comparison distribution – what the distribution will look like if the null hyp is true.  If null is true, Dr. J’s score = National M (which was 3.5). Note – given sampling errors, we know that the Dr. J is likely to differ from 3.5 at least a little…so…

The Hypothesis Testing Process 3.Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected  Cutoff sample score (critical value) – how extreme a difference do we need (betw Dr. J & nat’l M) to reject the null hyp?  Conventional levels of significance: p <.05, p <.01  We reject the null if probability of getting a result that extreme is.05 (or.01…)

Step 3 (cont.)  How do we find this critical value?  Use conventional levels of significance: p <.05, p <.01  Find the z score from Appendix Table 1 if 5% in tail of distribution (or 1%) For 5%  z = 1.64  We reject the null if probability of getting a result that extreme is.05 (or.01…)  Reject the null hyp if my sample z > 1.64  Means there is only a 5% (or 1%) chance of getting results that extreme if Null is true, so we’d reject the null if we’re in the rejection region (z > 1.64)

The Hypothesis Testing Process 4.Determine your person’s score on the comparison distribution  Collect data, calculate the z score for your person of interest  Use comparison distribution – how extreme is that score? 5.Decide whether to reject the null hypothesis  If your z score of interest falls within critical/rejection region  Reject Null. (If not, fail to reject the null)  Rejecting null hypothesis means there is support for research hypothesis.  Example?