Lecture 8: Single Sample t test

Transcription

1 Lecture 8: Single Sample t test Review: single sample z-test Compares the sample (after treatment) to the population (before treatment) You HAVE to know the populational mean & standard deviation to use this test Single sample t-test Same research design as the single sample z-test BUT, you don t know the populational information Might know populational μ or σ, but won t know both 2 new concepts: VARIANCE (s 2 ): estimates the populational standard deviation (σ) Remember, s = standard deviation of sample Therefore, the variance is the sample standard deviation (s), squared (s 2 ) DEGREES OF FREEDOM (df): an analysis correction that makes populational estimates more accurate df = n 1 The smaller the sample size, the smaller the df, the larger the correction that is made The larger the sample size, the larger the df, the smaller the correction that is made Note: sometimes you will be given the sample mean, s, s 2, SS, the raw data, etc. You will have to decide how to solve the problem based on the information that you re given. But, you will ALWAYS start by diagraming your research Keep the midterm formula sheet handy

2 Classroom Practice Problem Study/original hypothesis: ginko biloba (cause), increases physical strength and stamina (effect) Population μ = 55 Sample M = 58.5 n = 36 SS = 5040 Variables: DV: strength and stamina IV: supplement 2 treatments being compared: Took ginko biloba sample data Did NOT take ginko biloba population data Before/after: we re comparing data collected before treatment (population) to data collected after treatment (sample) Population data: mean (μ) = 55 Sample data: mean (M) = 58.5 Looks like the treatment (ginko biloba) worked! But what about CHANCE? a. b. * non-directional * directional (increased) * two-tailed * one-tailed * α =.05 * α =.05 Step ONE: identify key information from the problem Is the research question directional or non-directional? a. is non-directional (two-tail): the IV had an effect on the DV b. is directional (one-tail, increase): the IV increased the DV

3 Step TWO: diagram your research (Hypothesis Testing) Population μ = 55 Sample M = 58.5 n = 36 SS = 5040 H1 ALTERNATIVE H0 NULL 2 explanations Prob. Calc. 2 outcomes HIGH Probability α =.05 LOW probability 2 decisions Accept NULL Reject NULL, accept ALTERNATIVE 2 Explanations/Hypotheses a. hypotheses are stated as non-directional H1: ginko biloba had an effect on stamina and strength H0: ginko biloba did NOT have an effect on stamina and strength b. hypotheses are stated as directional (increase) H1: ginko biloba increased stamina and strength H0: ginko biloba decreased or had no effect on stamina and strength

4 Step THREE: determine CRITICAL REGION(S) Draw a normal curve with tail(s) Calculate df = n 1 df = 36 1 = 35 Find the critical t-score by looking for the df (or closest value to it) with the corresponding alpha level and one-tail/two-tail columns in statistical t-table handout a. two-tail, α =.05, df = 35 critical t-score = +/ b. one-tail, α =.05, df = 35 critical t-score = Plot critical t-scores on graph a. b.

5 If your df is not listed, but falls between two listed dfs, choose whichever one is closest If your df is right in the middle between two listed dfs, choose whichever one you want Step FOUR: Calculate PROBABILITY (t-test) 1. Calculate variance (s 2 ) s 2 = Σx2 (Σx)2 n n 1 2. Calculate standard error (sm) 3. Calculate t-test = SS df = = 144 sm = s2 n = = 4 = 2 t = M μ = = 1.75 sm 2 Graph the calculated t-score onto graph(s) with critical t-score a. Calculated t-score falls into HIGH probability region b. Calculated t-score falls into LOW probability region

6 Step FIVE (consider 2 outcomes): based on where your calculated t-score falls on the curve, determine probability outcome Step SIX (consider 2 decisions): based on your probability outcome, refer back to your diagram to make a decision a. HIGH probability Accept NULL (H0) b. LOW probability Reject NULL (H0) and Accept ALTERNATIVE (H1) Step SEVEN: based on your decision, report results professionally a. Ginko biloba had a non-significant effect on strength and stamina (M= 58.5, SD = 12); t(35)= +1.75, p >.05, two-tailed. b. Ginko biloba had a significant effect on strength and stamina (M= 58.5, SD = 12); t(35)= +1.75, p <.05, one-tailed. Note on calculating SD/ standard deviation of sample (s): SD(s) = s 2 = 144 = 12 Remember, s 2 is the variance we calculated earlier Refer to midterm formula sheet Note on determining the direction of the arrow for p-level: For significant effect [i.e. when you re rejecting the null & accepting the alternative] the arrow should point in the less-than direction (p < ) For non-significant effect [i.e. when you re accepting/failing to reject null] the arrow should point in the greater than direction (p > ).