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The statistical tools that were used in the work include: Relative frequency distribution, mean score, percentages, relative importance index. The researcher also made use of inferential statistics such as one-factor analysis of variance, Z-test and one-sample t-Z-test to validate the research hypothesis. In addition, the study made use of regression techniques to model the relationship between performance and motivation of workmen in construction companies, while correlation analysis techniques were employed in ascertaining the level of agreement in opinions of the different categories of craftsmen selected for the study. All tests were judged at 5% level of significance.

3.8.1 Relative Frequency Distribution

This was used to answer questions raised in general information of section A of the questionnaire. This is the frequency of the respondents on each factor divided by the total frequency of all the respondents. It is generally expressed as percentage or average. It can be represented mathematically as:

% = 100 ………... (3.5)

Where

x = number of respondents agreeing with a particular variable.

n = total number of items or respondents sampled.

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3.8.2 Mean Score Index

In order to rank the severity of factors covered by the questionnaire, mean score index was used. Mean score index is mathematically represented as

MSI = …..……….. (3.6)

Where;

F = Frequency of respondents to each.

Xi = The score given to each factor by the respondents N = The total number of respondents concerning each factor

3.8.3. Relative Importance Index (RII) This tool was used to determine the relative importance to the respondents on the factors that motivate them to work harder, as well as the factors inhibiting management to effectively utilize motivation to increase project success. RII can be computed using the formula below:

RII= ……….... (.7)

Where

Wi = the weighting given to each variable by the respondents, ranging from 1- 5 Xi = the percentage of respondents scoring

i = the order number of respondents

3.8.4 Analysis of Variance (ANOVA)

ANOVA is used to determine whether a significant difference exists between means of three or more groups. This tool was used in this research to draw conclusion on the group means of the respondents (Masons, Carpenters, Steel Fitters), to ascertain if an observed difference between groups means will depend on the variance of observation within groups. The concept underlying ANOVA is that the total variation of scores is computed through the summation of between group variance and within group variance. This can be represented mathematically as;

SST = SSB + SSW ……….. (3.8)

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Where;

SST = Total Sum of Squares

SSB = Sum of Squares between group SSW = Sum of Squares within group

SST = ……… (3.9)

Where;

k = number of groups/population

ni = the sample size taken from group i

= the jth response sampled from the with group/population = the mean of all responses irrespective of the group

SSB = ) ………. (3.10)

Where;

= sample mean of responses from ith group = the mean of all responses

SSW = ………. (3.11)

Where;

ni = sample size taken from group i

si = the sample standard deviation from the ith group

The F statistic is calculated by dividing the mean of square between group by the mean of square within group and it is represented mathematically as:

F statistic = ……… (3.12)

Where;

MSB = mean of squares between group MSW = mean of squares within group

MSB = ……..………….. (3.13)

Where;

SSB = sum of squares between group k = number of groups/population

MSB = ……… (3.14) Where;

n = total sample size

k = number of groups/population

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3.8.5 Regression Model

Regression Model deals with the analysis of the relationship between a dependent variable (often called an „outcome‟ variable) and one or more independent variables (often called the „predictors‟, „covariates‟ or „features‟). It is the relationship between X and Y or the regression of X scores on Y scores.

The regression model was used to test hypothesis two and for building the model. The Regression equation is given as:

Y = + X + e ……….. (3.15)

Where;

=

=

= ……… (3.16)

Where;

Y = dependent variable (Productivity)

X = independent variable (Financial Motivation) α = intercept on Y – axis

β = slope or gradient of the regression line n = number of groups

e = error term

3.8.6 Correlation Coefficient

Correlation coefficient usually denoted by r, measures the degree of linear relationship between two variables. If the two variables X and Y are assumed to have a linear relationship, the value of r measures the extent to which sample observations on X are correlated with sample observations on Y.

Mathematically, the correlation coefficient (r) is represented as:

r = ……….. 3.18

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Where;

= mean of sample X = mean of sample Y

3.9 Validity and Reliability of Measuring Instrument Validity of an instrument refers to the extent an instrument of measurement actually measures what it is intended to measure (Ogunoh, 2008). An instrument is valid to the extent, that it is tailored to achieve the research objectives. The researcher ensured the validity of the questionnaire by undertaking a pilot survey within the research area using convenience sampling technique. The researcher achieved this by administering the questionnaire to some selected staff in the study area. The questionnaire was submitted to the research supervisor for vetting, correction and suggestions to ensure that the questionnaire was capable of soliciting responses that proffer answer to the research questions.

In order to achieve reliability of data from questionnaire distribution, the researcher exercised care and caution, to ensure that questionnaires was administered to the right respondents, only necessary questions was asked, which was neither offensive nor misleading and options of answers was provided to questions, except where opinion of respondents are needed to confirm the answers. Information contained in the questionnaire was also clear and unambiguous and the researcher collected the completed questionnaire.

The questionnaire was also subjected to internal consistency test using Cronbach‟s alpha in order to test the factors affecting employee motivation.

Sushil and Verma (2010) asserted that if a test has a strong internal consistency, it should only show moderate correlation among values (0.70 to 0.90). Too low values means unreliability and too high values revealing some items are redundant and should be removed from the test. For this study, α value of 0.7 was used as cut off value.

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CHAPTER FOUR

DATA PRESENTATION, ANALYSIS AND INTERPRETATION

4.1 Introduction

This chapter presents, analyses, and interprets the various data obtained from the field survey. The discussions are based on the different statistical analyses carried out on the collated data generated. Relevant instruments were employed and inferences drawn at a benchmark of 5% level of significance.