Using PHStat2 to Perform Multiple Comparisons between Population MeansoStep 1: Insert data into spreadsheet▪Population 1 in column 1, etc.oStep 2: Add-ins > Multiple-Sample Tests > One-Way ANOVAoStep 3: Input data into box▪Level of significance (∞)-Usually equal to 0.05▪Group data cell range (all data points0▪Can include label, just specify in data▪CHECK Tukey-Kramer Procedureo4. Outcome▪Sample mean and size for each sample population

▪For comparisons-Absolute difference-Standard error of difference-Critical range-RESULTS – whether or not means are different➢11.2 – RANDOMIZED BLOCK ANOVA: EXAMINING THE EFFECTS OF A SINGLE FACTOR BY BLOCKING A SECOND FACTORoRandomized Block ANOVA– incorporates a blocking factor to account for variation outside of the mean factor in the hopes of increasing the likelihood of detecting a variation due to the main factor▪Ex: average sales calls per day needs to be blocked into days, rather than taking the whole week of calls and averaging the samples out that way▪Blocking factor– a second factor-Purpose = remove some of the variability in the sales calls associated with the weekday, which may allow us to better detect any differences due to the main factor (sales reps)▪Blocks– the levels of the blocking factor●Step 1: Identify the null and alternative hypothesesoHypothesis Statements = same as for one-way ANOVA▪H0 : µ1 = µ2 = µ3▪H1: not all µs are equaloSet the level of significance (∞)▪Set ∞ = 0.05●Step 3: Calculate the factor means, the block means, and the grand meanoTerms▪Factor means– the means for each of the columns, or populations▪Block means– the means for each of the rows, or blocks▪Grand mean– (sum of all data values) ÷ (total number of data points)●Step 4: Calculate the total sum of squares (SST)

oEasiest Way to Find SST▪Column 1 = xij-Shows each data value in a vertical column▪Column 2 = xx-Shows the same grand mean in every column▪Column 3 = (xij – )xx-(Column 1 – Column 2)▪Column 4 = (xij – )²xx-Square the data points in column 3▪ANSWER = sum of data points in column 4oAnswer = 38.4oMST = (SST) ÷ (n – 1)▪MST = 38.4 / 15 – 1= 2.74●Step 4: Partition SST into SSB, SSBL, and SSEoSST for randomized block ANOVA = partitioned into:▪Sum of squares between (SSB)▪Sum of squares block (SSBL)▪Sum of squares error (SSE)▪SST = SSB + SSBL + SSEoSSB:▪(data points in sample) • (sample mean – grand mean)²▪FOR EACH of the levels▪Sum up the levels → SSB▪SSB = 11.2oMSB▪MSB = (SSB) / (k – 1)▪MSB = 11.2 / 3 – 1 = 5.6-b/c have 3 sales representativesoSum of squares block (SSBL)– measures the variation between the block means and the grand mean▪SSBL = k ∑(sample mean – grand mean)²

▪K • sum of the SSBL found for each sample population▪SSBL = 20.4oMean Square Block (MSBL)– represents the variance associated with the sum of squares block (SSBL)▪MSBL = SSBL / (b – 1)-b = number of blocks (in our example, 5 b/c 5 days of week)▪MSBL = 20.4 / (5 – 1) = 5.1oSum of Squares Error(SSE) – represents the random variation in the data not attributed to either the main factor or the blocking factor▪